Description
Different types of bonds, difference between debt and equity, bonds with embedded options, yield to maturity, bond valuation, zero coupon bonds, how treasury auction is done, STRIPS, floating rate bonds, callable bonds, puttable bonds, convertible bonds, exchangeable bonds, different types of risks, YTM of zero coupon bond, significance of reinvestment risk, yield to call.
Part-06
1/30/2013
Part-02 An Introduction to Fixed Income Securities
1
Basics
?What is debt?
?It is a financial claim.
?Who issues it?
?The borrower of funds
?For whom it is a liability
?Who holds it?
?The lender of funds
?For whom it is an asset
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Basics (Cont…)
?What is the difference between debt and equity?
?Debt does not confer ownership rights on the holder. ?It is merely an IOU
?A promise to pay interest at periodic intervals ?And to repay the principal at a prespecified maturity date.
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Basics (Cont…)
?It usually has a finite life span ?The interest payments are contractual obligations
?Borrowers are required to make payments irrespective of their financial performance ?Interest payments have to be made before any dividends can be paid to equity holders. ?In the event of liquidation
• The claims of debt holders must be settled first • Only then can equity holders be paid.
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Fixed Income Securities
?Why are bonds and debentures termed as Fixed Income Securities
?Once the rate of interest is set at the onset of the period for which it is due
?It is not a function of the profitability of the firm
?Thus even floating rate bonds are fixed income securities
?Failure to pay the promised interest will tantamount to default
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Basics (Cont…)
?Bonds may be secured or unsecured
?Unsecured dent securities are termed as Debentures in the US ?Unsecured implies that no specific assets have been earmarked as collateral ?Secured debt issues require the firm to earmark specific assets as collateral
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Basics (Cont…)
?Debt securities may be negotiable or nonnegotiable
?Negotiable securities can be traded in the secondary market
?Can be endorsed by one party in favor of another
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Plain Vanilla & Bells and Whistles
? The most basic form of a bond is called the Plain Vanilla version.
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Plain Vanilla (Cont…)
? This is true for all securities, not just for bonds. ? More complicated versions are said to have `Bells and Whistles’ attached.
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Plain Vanilla (Cont…)
?Floating rate bonds are similar to conventional bonds
?The difference is that the interest rate does no remain fixed ?It varies from period to period based on the benchmark to which it is linked
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Bonds With Embedded Options
?Convertible bonds can be converted to shares of stock ?Callable bonds can be prematurely retired by the issuer ?Putable bonds can be prematurely surrendered by the holders
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Face Value
?It is the principal value underlying the bond.
?It is the amount payable by the borrower to the last holder at maturity. ?It is the amount on which the periodic interest payments are calculated. ?A.K.A as
?Par Value ?Redemption Value ?Maturity Value ?Principal Value
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Term to Maturity
?It is the time remaining in the life of the bond.
?It represents the length of time for which interest has to be paid as promised. ?It represents the length of time after which the face value will be repaid. ?A.K.A as
?Maturity ?Term
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Coupon
?The coupon payment is the periodic interest payment that has to be made by the borrower.
?The coupon rate when multiplied by the face value gives the dollar value of the coupon. ?Most bonds pays coupons on a semi-annual basis. ?In the earlier days bonds were accompanied by a booklet of post-dated coupons ?Each coupon could be detached and redeemed on the corresponding coupon payment date
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Example of Coupon Calculation
?Consider a bond with a face value of $1000. ?The coupon rate is 8% per annum paid semi-annually.
?So the bond holder will receive
1000 x 0.08 ___ = $40 every six months. 2
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Yield to Maturity (YTM)
? Yield to maturity is the rate of return for an investor if he buys the bond at the prevailing market price and holds it till maturity. ? In order to get the YTM, two conditions must be satisfied.
?The bond must be held till maturity. ?All coupon payments received before maturity must be reinvested at the YTM.
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YTM (Cont…)
?At any point in time the YTM may be
?Greater than ?Less than or ?Equal to the Coupon Rate
?YTM is the IRR of a bond
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17
Value of a Bond
? A bond holder gets a stream of contractually promised payments. ? The value of the bond is the value of this stream of cash flows. ? However you cannot simply add up cash flows arising at different points in time.
?Cash flows have to be discounted before being added.
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18
Price versus Yield
?Price versus yield is a chicken and egg story
?We cannot say which comes first.
?If we know the yield that is required we can quote a price accordingly. ?Similarly, once we acquire the asset at a certain price, we can work out the corresponding yield.
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Bond Valuation
?A bond is an instrument that will pay identical coupons every period, usually every six months, and will then repay the face value at maturity. ?The periodic cash flows obviously constitute an annuity. ?The terminal face value is a lump sum payment.
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Bond Valuation (Cont…)
? Consider a bond that pays a semi-annual coupon of $C/2, and which has a face value of $M. ? Assume that there are N coupons left, and that we are standing on a coupon payment date.
?That is, we are assuming that the next coupon is exactly six months away.
? The required annual yield is y, which implies that the semi-annual yield is y/2.
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Bond Valuation (Cont…)
?The present value of the coupon stream is:
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Bond Valuation (Cont…)
?The present value of the face value is:
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Bond Valuation (Cont…)
? So the price of the bond is:
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Illustration
?IBM has issued a bond with a face value of $1,000. ?The coupon is 8% per year to be paid on July 15 and January 15 every year. ?Assume that today is 15 July 2002 and that the bond matures on 15 January 2022. ?The required yield is 10% per annum.
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Illustration (Cont…)
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26
Par, Discount & Premium Bonds
? In the above example, the price of the bond is less than the face value of $1,000. ? Such a bond is called a Discount Bond, since it is trading at a discount from the face value. ? The reason why it is trading for less than the face value is because the required yield of 10% is greater than the rate of 8% that the bond is paying by way of interest.
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Par, Discount & Premium Bonds (Cont…)
? If the required yield were to equal the coupon rate, the bond would sell for $1,000. ? Such bonds are said to be trading at Par. ? If the required yield were to be less than the coupon rate the price will exceed the face value. ? Such bonds are called Premium Bonds, since they are trading at a premium over the face value.
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Par Discount and Premium (Cont…)
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Par Discount and Premium (Cont…)
?If c = y, P = M
?Thus if the coupon is equal to the YTM, the bond will always sell at Par
?It can be shown that the bond price is a monotonically increasing function of the coupon
?Obviously if the coupon is less than the YTM the price will be less than the face value ?If the coupon is greater than the YTM the price will be in excess of the face value
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Par Premium and Discount (Cont…)
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Par Premium and Discount (Cont…)
?Why would a bond trade at a premium or a discount?
?The price of a bond is the PV of all the cash flows emanating from it ?If YTM = coupon the return demanded by investors will be equal to the rate offered by the issuer
?Obviously the bond will sell at PAR
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Par Premium and Discount (Cont…)
?What if the YTM is less than the coupon
?Assume c = 10% while YTM = 8% ?An investor will be willing to pay more than the face value ?The price would be bid up to a level where the YTM is equal to 8%
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Par Premium and Discount (Cont…)
?On the other hand what if YTM is greater than the coupon
?Assume coupon = 8% while YTM = 10% ?Investors will only pay less than the face value ?The price will be driven down to a level where the yield is exactly 10%
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Evolution of The Price
?Consider the change in price of a bond from one coupon date to another assuming that the YTM is constant
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Evolution (Cont…)
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Evolution (Cont…)
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Evolution (Cont…)
?If y = c, then ?P = 0 ?Thus if the YTM remains constant, the price of a par bond will remain at par as we go from one coupon date to the next ?If the YTM > Coupon, ?P > 0
?Thus a discount bond will steadily increase in price as we go from one coupon date to another
?If YTM < Coupon ?P < 0
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?A premium bond will steadily decline in price as we go from one coupon date to another
38
Illustration
?Consider a bond with 10 years to maturity and a par value of 1,000
?YTM is 8% per annum ?Coupon = 6% per annum ?Price = 864.10
?If we move 6-M ahead the price will be 868.66 if the YTM were to remain constant
?Obviously since it is a discount bond the price has increased
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Illustration (Cont…)
?Now consider a bond with 10 years to maturity and a face value of 1,000
?YTM = 8% ?Coupon = 10% ?Price = 1135.90
?Six months later if the yield were to remain constant the price will be 1131.34
?Obviously the price has declined
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Zero Coupon Bonds
? A Plain Vanilla bond pays coupon interest every period, typically every six months, and repays the face value at maturity. ? A Zero Coupon Bond on the other hand does not pay any coupon interest. ? It is issued at a discount from the face value and repays the principal at maturity. ? The difference between the price and the face value constitutes the interest for the buyer.
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Illustration
?Microsoft is issuing zero coupon bonds with 5 years to maturity and a face value of $10,000. ?If you want a yield of 10% per annum, what price will you pay? ?The price of the bond is the present value of a single cash flow of $10,000, discounted at 10%.
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Illustration (Cont…)
?In practice, we usually discount the face value using a semi-annual rate of y/2, where y in this case is 10%. ?This is to facilitate comparisons with conventional bonds which pay coupon interest every six months.
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Zero Coupon Bonds (Cont…)
?Zero coupon bonds are called Zeroes by traders. ?They are also referred to as Deep Discount Bonds. ?They should not be confused with Discount Bonds, which are Plain Vanilla bonds which are trading at a discount from the face value.
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Zero Coupon Bonds (Cont…)
?A zero coupon bond can never sell at a premium
?It will always trade at a discount prior to maturity ?At maturity it will trade at par
?Can a zero coupon bond give rise to a capital gain or a loss?
?If it is bought and held to maturity there will obviously be a capital gain
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Zero Coupon Bonds (Cont…)
?If a zero coupon bond is sold prior to maturity there may be a capital gain or a capital loss ?Consider a bond with 10 years to maturity
?The YTM at the time of purchase was 10% ?The cost was $376.90 ?A year later it is sold at a prevailing YTM of 12% ?The corresponding price is $350.35 ?Obviously there is a capital loss
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Treasury Securities
?They are fully backed by the federal government of the issuing nation. ?Consequently they are devoid of credit risk or the risk of default. ?The interest rate on such securities is used as a benchmark for setting rates on other kinds of debt.
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U.S. Treasury Securities
?The Treasury issues three categories of marketable securities. ?T-bills are discount securities
?They are issued at a discount from their face values and do not pay interest.
?T-notes and T-bonds are sold at face value and pay interest periodically.
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U.S. Treasury Securities (Cont…)
?T-bills are issued with a original time to maturity of one year or less.
?Consequently they are Money market instruments. ?They have maturities of either 1, 3, 6, or 12 months at the time of issue.
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US. Treasury Securities (Cont…)
?T-notes and T-bonds have a time to maturity exceeding one year at the time of issue.
?They are therefore capital market instruments. ?T-bonds have an original maturity in excess of 10 years, extending up to 30 years.
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U.S. Treasury Securities (Cont…)
?T-notes are similar to T-bonds except that their terms to maturity range from one to ten years.
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U.S. Treasury Securities (Cont…)
?At times an issue may be followed later by a further issue with the same remaining time to maturity and the same coupon
?The issuance of further tranches is termed as a Re-opening.
?Six months ago a 10-year note was issued with a coupon of 8% per annum. ?Today if a note with 9 ½ years to maturity and a coupon of 8% issued it will add to the pool that is already trading in the market ?Thus it is a re-opening of an existing issue
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U.S. Treasury Securities (Cont…)
?The secondary market is liquid and transparent and trades take place through banks and primary dealers. ?Securities are also listed on the NYSE to accommodate overseas investors who may be permitted by regulations to trade only in listed securities.
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U.S. Treasury Securities (Cont…)
?Settlement is arranged through FEDWIRE, which is the Federal Reserve’s wire transfer system
?Foreign investors need to arrange for a local custodian with access to FEDWIRE.
?Three month and six month bills are issued on a weekly basis. ?One year bills are issued every month.
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U.S. Treasury Securities (Cont…) Issue of T-notes and Bonds
Issue 2 Year Frequency Monthly Auction Month Every month
3, 10 Year
5 Year 30 Year
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Quarterly
Monthly
Feb, May, Aug, Nov Every month
Semi-annually Feb and Aug
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U.S. Treasury Securities (Cont…)
?Interest from these instruments is exempt from state income taxes. ?Guidelines of Mutual Reciprocity.
?Federal bonds are exempt from state taxes ?Bonds issued by state governments are exempt from federal taxes ?The exemption applies only to interest income. ?Capital gains are taxable at normal rates.
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FEDWIRE
? It is an RTGS (Real Time Gross Settlement) Funds transfer system
?Operated by the Federal Reserve Banks ?Electronically transfers funds between more than 8900 participants ?It is the primary US network for large-value or timecritical domestic and international payments ?The average daily value of transfers = 2.3 trillion USD ?Daily average number of payments = 532,000
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Primary Dealers
? Who is a primary dealer?
?A PD is a bank or securities broker-dealer that directly deals in U.S. government securities with the Federal Reserve Bank of New York. ?As of November 2007 there are 20 primary dealers, down from a number of 44 in 1988.
? The most important reason is consolidation. ? That is many firms have merged or refocused their core lines of business.
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Primary Dealers (Cont…)
?The FED requires primary dealers to participate meaningfully in both open market operations as well as Treasury Auctions. ?The current list of primary dealers is as follows.
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List of Primary Dealers
? BNP Paribas Securities ? Banc of America Securities ? Barclays Capital Inc. ? Cantor Fitzgerald & Co. ? Citigroup Global Markets ? Credit Suisse Securities ? Daiwa Capital Markets America ? Deutsche Bank Securities ? Goldman, Sachs & Co. ? HSBC Securities (USA)
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? Jefferies & Company, Inc. ? J.P. Morgan Securities LLC ? Mizuho Securities USA Inc. ? Morgan Stanley & Co. Incorporated ? Nomura Securities International, Inc. ? RBC Capital Markets Corporation ? RBS Securities Inc. ? UBS Securities LLC.
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Primary Dealers (Cont…)
?These dealers purchase the vast majority of Treasury securities sold at Treasury auctions and resell them to the public ?They also account for over 70% of FOREX trading volume
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Primary Dealers in India
? Deutsche Securities ? ICICI Securities Primary Dealership ? IDBI Gilts ? Morgan Stanley India Primary Dealer ? Nomura Fixed Income Securities ? PNB Gilts ? SBI DFHI ? Kotak Mahindra Bank ? Standard Chartered Bank ? Axis Bank
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? ABN AMRO ? Bank of America ? Bank of Baroda ? Canara Bank ? Citibank ? Corporation Bank ? HDFC Bank ? STCI Primary Dealer ? HSBC ? JP Morgan Chase
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Treasury Auctions
?The U.S. Treasury sells bills, notes, and bonds by way of a competitive auction process. ?Most of the treasury securities are bought by primary dealers. ?Individual investors who submit noncompetitive bids participate on a much smaller scale.
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Treasury Auctions (Cont…)
?The auction process begins with a public announcement by the Treasury giving the following information.
?Offering amount ?Description of the offering ?Strips information
?Is the security eligible for stripping
?Procedures for submission of bids; minimum bid amount; and payment terms
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Treasury Auctions (Cont…)
?Description of the offering includes:
?Term and type of security ?CUSIP number ?Auction date ?Issue date ?Dated date ?Maturity date ?Interest payment dates
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Treasury Auctions (Cont…)
? Bids may be:
? Competitive ? Non-competitive
? Small investors and individuals generally submit noncompetitive bids
? The bidder merely indicates the quantity sought ? The price is determined by the auction process ? A non-competitive bidder may not bid for more than $5MM worth of securities in a bill or bond auction
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Treasury Auctions (Cont…)
? Primary dealers who bid for their accounts or on behalf of their clients usually submit large competitive bids
?These bids indicate not only the quantity that is sought ?But also the maximum price that the bidder is prepared to pay if it is a price based auction ?Or the minimum yield that the bidder is prepared to accept if it is a yield based auction
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Treasury Auctions (Cont…)
?Bidders are forbidden from bidding both competitively and non-competitively for the same account in the same auction. ?Competitive bidders can submit multiple bids
?But no bidder may receive more than 35% of the security being sold.
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Treasury Auctions (Cont…)
?Bids are submitted in terms of discount rates for bills
?Stated in 3 decimal places ?In 0.005 percent increments
?In note and bond auctions
?They are expressed as yields up to 3 decimal places ?In 0.001 percent increments
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Treasury Auctions (Cont…)
?Competitive bids are accepted till 1:00 p.m. EST on the day of the auction ?The deadline for non-competitive bids is 12:00 EST on the auction date
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Treasury Auctions (Cont…)
? Once the bids are received the Treasury will net out the total amount of non-competitive bids and will begin allocating the balance to competitive bidders. ? There are two ways in which securities can be allotted
?The multiple price/yield auction mechanism ?The uniform price/yield auction mechanism
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Illustration
?Assume that the Treasury is offering 15 billion dollars worth of T-bonds. ?2 billion dollars worth of non-competitive bids have been received. ?So 13 billion dollars worth of bonds are available to be offered to the competitive bidders.
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Illustration (Cont…)
?Assume that there are six competitive bidders who have submitted the following yields.
?The bids have been arranged in ascending order of yield. ?Had it been a price based auction the bids would have been arranged in descending order of price.
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Illustration (Cont…)
Bidder Alpha Beta Gamma Delta Charlie
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Bid Yield 5.370 5.372 5.373 5.375 5.375 5.380
Bid Amount 3.0 bn 3.0 bn 4.0 bn 3.0 bn 2.0 bn 2.0 bn
Aggregate Amount 3.0 bn 6.0 bn 10 bn 13 bn 15 bn 17 bn
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Tango
Illustration (Cont…)
?The aggregate demand equals the amount on offer at a yield of 5.375. ?A multiple yield auction will lead to the following allocation.
?Alpha will get 3 bn at a yield of 5.370 ?Beta will get 3 bn at 5.372 ?Gamma will get 4 bn at 5.373
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Illustration (Cont…)
?By the time we reach a yield of 5.375 we have only 3 bn left to allocate. ?There is a demand of 5 bn at this yield
?3 bn from Delta and 2 bn from Charlie.
?So there will be pro-rata allocation
?3/5 of 3 bn or 1.8 bn will go to Delta ?2/5 of 3 bn or 1.2 bn will go to Charlie
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Illustration (Cont…)
?The highest yield that is accepted at the auction is called the Stop Yield
?In this case it is 5.375
?The ratio of bids received to the amount awarded is known as the bid to cover ratio
?The higher the ratio the stronger is the auction
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Illustration (Cont…)
?The difference between the average yield of all accepted bids and the stop yield is called the tail of the auction. ?A multiple price/yield auction is also known as a discriminatory auction
?Since each successful bidder is allotted at the price/yield bid by him or her.
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Illustration (Cont…)
? The second type of auction is called a uniform price/yield auction. ? In our case aggregate demand is equal to the supply at a yield of 5.375%. ? Consequently everyone who bid less will be allotted the quantities sought by them at this yield. ? The two bidders at 5.375 will also be awarded at this yield but on a pro-rata basis.
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Illustration (Cont…)
?Those who bid more than 5.375 will get nothing and are said to be shutout of the auction. ?Since 1999 the U.S. Treasury has been conducting only uniform yield auctions.
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Treasury Auctions (Cont…)
? The auction results are released to the public within two hours of the auction. ? The following information is made public:
?The amount of bids received ?The total bids accepted ?The bid to cover ratio ?High, low and median bids ?The issue price
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Illustration-I: A Real Treasury Auction
? Announcement date: 2 August ? Offering amount: $ 10 billion ? Term and type of security:
?4 ¾ year note (reopening of a 5 year note) ?Series: E 2005 ?CUSIP No.: 912827 6D9 ?Auction date: 8 August 2000 ?Issue date: 15 August 2000 ?Dated date: 15 May 2000 ?Maturity date: 15 May 2005
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Illustration-I (Cont…)
?Interest rate: 6 3/4 % ?Amount currently outstanding: $15.426 billion ?Yield: To be determined at the auction ?Interest payment dates: 15 November and 15 May ?Minimum bid amounts and multiples: $ 1,000 ?Premium or discount: To be determined at the auction
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Analysis
? This auction is a re-opening of a 5 year note issued on 15 May 2000.
?Consequently the securities being issued have 4 ¾ years to maturity.
? Although the auction is announced on 2 August the actual auction date is 8 August. ? The securities will however be issued only on 15 August. ? The dated date is 15 May which is when the original 5 year security was issued.
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Analysis (Cont…)
? The dated date is different from the issue date because the issue is being reopened. ? The maturity date is 15 May 2005. ? The interest rate or the coupon is known since the security is already trading in the market. ? The yield will be determined at the auction.
?Consequently the issue price and the premium/discount with respect to the face value will also be determined at the auction.
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Illustration-II
? Auction announcement date: 2 August ? Offering amount: 10 billion ? Term and type of security: 10 year note ? Series: C 2010 ? CUSIP No.: 912827 6J6 ? Auction date: 9 August 2000 ? Issue date: 15 August 2000 ? Dated date: 15 August 2000 ? Maturity date: 15 August 2010
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Illustration-II (Cont…)
? Interest rate: Determined based on the highest accepted competitive bid ? Amount currently outstanding: Not applicable ? Yield: Determined at auction ? Interest payment dates: 15 Feb and 15 August ? Minimum bid amounts and multiples: $ 1,000 ? Premium/discount: To be determined at the auction
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Analysis
? This auction represents a fresh issue of a 10 year T-note ? The coupon rate is unknown at the outset since it will be fixed based on the bids received.
?Assume that the market clearing yield is 4.920% ?The coupon will be set after rounding down the winning bid to the nearest multiple of 1/8th which in this case is 4.875%.
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Zero Coupon Treasury Securities
? The Treasury per se does not issue zero coupon securities. ? But there exist two types of treasury based zero coupon securities. ? The principle behind both forms is the same.
?Take a large quantity of a T-note or bond and separate all the coupons from each other and from the principal. ?Sell the entitlement to each cash flow separately.
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Zero…(Cont…)
?Take the case of a two-year T-note. ?It can be separated into five zero coupon securities maturing after:
?6 months ?12 months ?18 months ?24 months
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Zero…(Cont…)
?Earlier investment banks used to buy regular coupon bonds from the Treasury and then separate the cash flows themselves. ?Each cash flow was then sold separately as a zero coupon bond. ?Such issues are called trademarks.
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Zero…(Cont…)
? The issue of trademarks has now ceased. ? This is because investment banks can now create such instruments in concert with the Treasury itself. ? These zero coupon bonds are known as STRIPS – Separate Trading of Registered Interest and Principal of Securities.
?These are not issued or sold by the Treasury ?The market is made by investment banks. ?But such issues are considered to be an obligation of the Treasury.
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Trademark Products
?Some of the older trademark products which have not yet matured continue to trade. ?The process of issuing trademarks was begun by Merrill Lynch and Salomon Brothers in 1982. ?These securities are synthetic zero coupon Treasury receipts.
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Trademarks (Cont…)
? The process of separating each coupon payment as well as the principal and selling securities backed by them is referred to as Coupon Stripping. ? The receipts issued in the process are not created by the Treasury. ?But the underlying asset in the bank custody account is an obligation of the Treasury. ?Thus the cash flows from the underlying asset are guaranteed.
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Trademarks (Cont…)
?Merrill Lynch marketed its Treasury receipts as Treasury Income Growth Receipts – TIGRS for short. ?Salomon Brothers called its receipts as Certificates of Accrual on Treasury Securities – CATS for short. ?Lehman Brothers offered Lehman Investment Opportunities Notes or LIONS for short.
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Trademarks (Cont…)
?These securities are called trademarks because each is associated with a particular investment banking firm. ?They are called Animal Products for obvious reasons. ?This segment of the financial market was also referred to as the Zoo.
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Trademarks (Cont…)
? Receipts created by one firm were rarely traded by others.
?So the secondary market was illiquid.
? What is the motivation for investment banks to create such products? ? In practice arbitrage is possible when a Treasury coupon security is purchased at a price that is lower than what could be obtained by selling each cash flow separately.
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Trademarks (Cont…)
?The initial reason for the popularity of these securities was tax related. ?Under the then US law, the discount on a bond purchase could be treated as a capital loss.
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Illustration
?Assume that an investor could buy a 30 year zero for $8. ?He could then deduct $92 from his taxable income per $100 of par value ?At the same time he was guaranteed a payoff of $100 after 30 years
?This loophole was plugged in 1982.
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STRIPS
?The Treasury launched this programme in 1985 to facilitate the stripping of designated Treasury securities.
?All new T-bonds and notes with a maturity of 10 years or more are eligible. ?The zeroes created in the process are direct obligations of the U.S. government. ?They are cleared through the Federal Reserve’s book-entry system.
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STRIPS (Cont…)
?On dealer quote sheets and vendor screens, STRIPS are identified as follows.
Cash Flow Source Coupon Symbol ci
Principal from T-bond bp Principal from T-note np
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STRIPS (Cont…)
?The mechanism of issue is as follows.
?A dealer who owns a bond or note can ask the FRB where it is held
?To replace it with an equivalent set of STRIPS representing each payment as a separate security. ?Each of these securities can be traded independently of others.
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STRIPS (Cont…)
?Most coupon and principal payments fall on the same set of dates ?These are
?15 February ?15 May ?15 August ?15 November
?So a lot of bonds would have coupons on the same date.
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STRIPS (Cont…)
?All these interest payments would be converted in to the same security
?Regardless of the bond they were stripped from ?Consequently coupon payments are said to be fungible ?Principal payments falling on the same date are not fungible
?They have different CUSIP numbers
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STRIPS (Cont…)
?In 1987 the Treasury started to allow dealers to reverse the process
?This is called STRIPS RECONSTUTUTION
?How does this work?
?If a dealer owns STRIPS representing all the coupon and principal payments of a bond
?The FED can on request convert these holdings into a single position in the corresponding bond
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Floating Rate Bonds
? In the case of a Plain Vanilla Bond, the coupon rate that is specified at the outset, is valid for the life of the bond. ? In the case of a Floating Rate bond, the coupon rate is reset at the beginning of every period, and is therefore valid for only the next six months. ? Thus when you buy such a bond, the coupon will be known only for the first six months. Subsequent coupons will be unknown.
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Floaters
? For instance the rate on a floating rate bond, also called a Floater, may be specified as LIBOR + 50b.p. in which case the spread is positive. ? Or it may be specified as LIBOR – 30b.p., in which case the spread is negative. ? The rate of interest on a floater will move directly with changes in the benchmark. ? Thus if LIBOR rises, the rate will increase, whereas if LIBOR falls, the rate will decrease.
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Inverse Floaters
? In the case of an inverse floater the coupon varies inversely with the benchmark. ? For instance the rate on an inverse floater may be specified as 10% - LIBOR. ? In this case as LIBOR rises, the coupon will decrease, whereas as LIBOR falls, the coupon will increase.
?In this case a floor has to be specified for the coupon.
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Inverse Floaters (Cont…)
?In the absence of a floor the coupon can become negative in principle.
?In the above case, if LIBOR were to exceed 10%, then we would be confronted with the spectre of a negative coupon.
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Callable Bonds
? In the case of such a bond, the issuer has the right to call back the bond prematurely.
?He can buy it back from the holder before maturity by paying him the face value.
? In this case the option is with the issuer, and so he has to pay a price for it.
?This compensation will manifest itself as a lower price for the bond as compared to a Plain Vanilla Bond.
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Callable Bond (Cont…)
?Since prices and yields are inversely related a lower price means a higher yield.
?Thus buyers of callable bonds demand a higher yield from them as compared to buyers of otherwise similar plain vanilla bonds. ?This is because a buyer of a callable bond is exposed to cash flow uncertainty.
?That is, he can never be sure as to when a bond will be recalled.
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Callable Bonds (Cont…)
?When will a callable bond be recalled?
?Obviously when interest rates or required yields are falling. ?Under such conditions, the issuer can call back the bonds and issue fresh bonds with a lower coupon. ?However this is precisely the scenario when a holder would like to hold on to his bonds, since they are yielding a higher rate of interest.
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Callable Bond (Cont…)
? Thus the call provision works in favour of the borrower and against the lender.
?Hence it is not surprising that callable bonds command a lower price.
? The way to look at it is as follows
?At the time of issue a callable bond has to carry a higher coupon than an equivalent Plain Vanilla Bond ?Subsequently a callable with a given coupon will have a lower price than a Plain Vanilla with the same coupon.
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Callable Bonds (Cont…)
?A bond may be discretely callable or continuously callable ?A discretely callable bond may be recalled only at certain pre-specified dates
?For instance the coupon dates over a period of the bond’s life
?A continuously callable bond may be called at any time after it becomes callable
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Callable Bond (Cont…)
?Freely callable bonds can be called at any time.
?Thus they offer the lender no protection.
?Deferred Callable Bonds on the other hand do offer some protection.
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Callable Bonds (Cont…)
?This is because they have a Call Protection Period during which they cannot be recalled.
?For instance if a bond with 20 years to maturity has a call protection period of 10 years, then it cannot be recalled for the first 10 years.
?After that, it will of course become freely callable.
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Callable Bond (Cont…)
?In practice when a bond is recalled, the issuer will pay the lender not just the face value, but usually also one year’s coupon.
?This additional amount is called the Call Premium. ?The call premium acts as a sweetener
?That is it makes such bonds more attractive to potential investors.
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Callable Bond (Cont…)
?One of the risks in a callable bond is therefore reinvestment risk
?That is, the bond will be called back when market rates are low and consequently the proceeds will have to be invested at a lower rate of interest.
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Callable Bond (Cont…)
?Second, the price appreciation potential for a callable bond in a declining interest rate environment is limited.
?This is because the market will increasingly expect the bond to be redeemed at the call price as rates fall.
?This is referred to as Price Compression.
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Callable Bond (Cont…)
?Given the reinvestment risk and price compression why would any investor want to hold such a bond.
?If he receives sufficient compensation in the form of a higher yield he may be willing to take the risk.
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Puttable Bonds
?Such bonds give the lender or the bondholder, the right to return the bond prematurely, and take back the face value.
?The option in such cases is with the bondholders or the lenders, and consequently they have to pay an option premium.
?This will manifest itself as a higher bond price, as compared to that of an otherwise similar plain vanilla bond.
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Puttable Bonds (Cont…)
?A higher bond price obviously means a lower yield. ?When will such a put option be exercised?
?Obviously when interest rates are rising. ?Under such conditions holders can return the bonds and buy fresh bonds with a higher coupon rate. ?This is precisely the scenario when the issuers would prefer that the holders hold on to the bonds.
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Puttable Bonds (Cont…)
?Since the put option works in favour of the holder and against the issuer, such bonds are characterized by higher prices or lower yields.
?At the time of issue a puttable will carry a lower coupon than an equivalent Plain Vanilla ?Subsequently a puttable will carry a higher price than a Plain Vanilla with the same coupon.
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Puttable Bonds (Cont…)
?The price at which a bond can be sold back by the holder acts as a floor price for the bond when interest rates rise. ?Since the holders can always return the bonds to the issuer at this price, they will never sell them to anyone else at a lower price.
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Convertible Bonds
?A conversion provision, if present in the bond, grants the bondholder the right to convert the bond into a predetermined number of shares of common stock of the issuer.
?It is therefore a Plain Vanilla corporate bond with a call option to buy the common stock of the issuer.
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Convertible Bonds (Cont…)
? The number of shares of common stock that a bondholder will receive if he converts the bond is called the Conversion Ratio.
?The conversion privilege may extend for all or only some portion of the bond’s life. ?The stated conversion ratio may also decline over time. ?The conversion ratio is always adjusted proportionately for stock splits and stock dividends.
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Convertible Bonds (Cont…) Illustration
? ABC Corporation has issued the following bond
?Maturity = 10 years ?Coupon rate = 8% ?Conversion ratio = 40 ?Face value = $1,000 ?Current market price = $900 ?Current share price = $20 ?Dividends per share = $1
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Convertible Bonds (Cont…)
?The conversion price = 1000 ------- = $25 40 ?The conversion value of a convertible bond is the value if it is converted immediately.
?Conversion value = Share price x Conversion Ratio
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Convertible Bond (Cont…)
?The minimum price of a convertible bond is the greater of:
?Its conversion value or ?Its value as a bond without the conversion option .
?This is also called the straight value of the bond.
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Convertible Bond (Cont…)
?To estimate the straight value we must determine the required yield on a nonconvertible bond with the same credit rating and similar investment characteristics.
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Convertible Bond (Cont…)
?In our case the conversion value is
?$20 x 40 = $800
?To determine the straight value we have to obtain the YTM of a comparable straight bond.
?Assume it is 10%.
? Straight value = 40PVIFA(5,20)+1000PVIF(5,20)
= $875.38
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Exchangeable Bonds
? These are a category of convertible bonds where the holder gets the shares of a different company when he converts the bonds.
? For instance if IBM were to issue convertible bonds, the holders would get shares of IBM if they were to convert. ? On the other hand, if IBM were to issue exchangeable bonds, the holders would get shares of another company, say Hewlett Packard.
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Exchangeable Bonds (Cont…)
?Exchangeable bonds may be issued by firms which own blocks of shares of another company and intend to sell them eventually.
?They may like to defer the sale and issue such bonds, because they may perceive a rise in the value of the shares. ?It may also be the case that they desire to defer their capital gains tax liability.
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Risks Inherent in Bonds
?What is risk? ?Risk is the possibility of loss arising due to the uncertainty regarding the outcome of a transaction. ?All bonds are exposed to one or more sources of risk.
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Credit Risk
? This risk refers to the possibility of default by the borrower. ? That is, it refers to the risk that coupon payments and/or principal payments may not be forthcoming as promised. ? Except for Treasury securities, which are backed by the full faith and credit of the Federal government, all debt securities are exposed to credit risk of varying magnitudes.
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Credit Evaluation
? At the time of issue, it is the issuer’s responsibility to provide accurate information about his financial soundness and creditworthiness. ? This is provided in the Offer Document or the Prospectus. ? But every potential investor cannot be expected to be able to properly evaluate the creditworthiness of a borrower. ? Thus in practice we have credit rating agencies.
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Credit Rating Agencies
? Such agencies specialize in evaluating the credit quality of a bond at the time of issue. ? They also monitor the issuing company, throughout the life of the bond, and modify their recommendations if required. ? The main rating agencies in the U.S. are
? Moody’s Investors Service ? Standard and Poor’s Corporation ?and Fitch Ratings.
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Rating Criteria
?Ratings are based on an in-depth analysis of the issuer’s financial condition and management ?And the specific source of revenue that has been specified as collateral for the bond.
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Investment Grade Ratings
Credit Risk
Highest Quality High Quality Upper Medium Medium
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Moody’s Ratings Aaa
Aa
S&P’s Ratings AAA
AA
Fitch’s Ratings AAA
AA
A
Baa
A
BBB
A
BBB
139
Non Investment Grade Ratings
Credit Risk
Somewhat Speculative
Moody’s
Ba
S&P
BB
Fitch
BB
Speculative
Highly Speculative Most Speculative Imminent Default Default
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B
Caa Ca C C
B
CCC CC C D
B
CCC CC C D
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Changes in Ratings
?Ratings can change over the course of time. ?If a rating change is being contemplated, the agency will signal its intentions.
?S&P will place the security on Credit Watch. ?Moody’s on Under Review. ?Fitch on Rating Watch.
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Bond Insurance
?A company can have its issue insured in order to enhance its credit quality.
?An insurance premium will have to be paid, but the coupon rate will come down. ?The insurance company will then guarantee the timely payment of the principal and interest.
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List of Specialist Insurance Companies
American Municipal Bond Assurance Corporation (AMBAC) ACA Financial Guaranty Asset Guaranty Insurance Company AXA Re Finance Capital Guaranty Insurance Company Capital Reinsurance Company Enhance Reinsurance Company Financial Guaranty Insurance Company Financial Security Assurance
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Insured Bonds
?Insured bonds receive the same rating as the insurance company, which is based on the insurer’s capital and claims-paying ability. ?In the U.S., the buyer of an uninsured bond can separately buy insurance for it on his own.
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Liquidity Risk
?This risk refers to the possibility that the market may be illiquid or thin at a time when the asset holder wants to buy or sell the security. ?A liquid market is characterized by the presence of a sizeable number of buyers and sellers at any point in time.
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Illiquid Markets
?In illiquid markets, potential buyers will have to offer a large premium over the fair value of an asset in order to acquire it, whereas potential sellers will have to accept large discounts at the time of sale. ?Illiquid markets are characterized by large bid-ask spreads, because trades will be few and far between.
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Interest Rate Risk
?The interest rate or yield is the key variable of interest in debt markets. ?The yield is the fundamental variable that drives the market. ?Interest rate risk refers to the fact that rates may move in an adverse fashion from the standpoint of the holder of the debt instrument.
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Interest Rate Risk
?Interest rate risk impacts fixed income securities in two ways.
?Firstly, all bonds with the exception of zeroes pay coupons
?These have to be reinvested.
?Reinvestment risk is the risk that market rates of interest may decline by the time a coupon is received.
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Interest Rate Risk (Cont…)
?If so, the coupon will have to be reinvested at a lower than anticipated rate of interest. ?Secondly a bond may not be held to maturity.
?If it is sold prior to maturity, it will have to be at the prevailing market price
?This will be inversely related to the prevailing yield.
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Interest Rate Risk (Cont…)
?Market Risk or Price Risk, is the risk that interest rates may be higher than anticipated at the time of sale, in which case the bond will have to be sold at a lower than anticipated price. ?The two risks work in opposite directions.
?Reinvestment risk arises because rates may fall subsequently ?Market risk arises because rates may rise subsequently.
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Inflation Risk
?Inflation refers to the erosion in the purchasing power of money. ?Most bonds promise fixed cash flows in dollar terms. ?Inflation risk is the risk that the purchasing power of money may have eroded by more than what was anticipated, by the time the cash flow from the bond is received.
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Inflation Risk (Cont…)
?High inflation will reduce the effective or Real rate of interest. ?The interest rate in monetary terms is called the Nominal Rate of interest. ?The Real Rate, on the other hand, is the nominal rate adjusted for changes in the purchasing power.
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Indexed Bonds
?These are bonds whose coupons are linked to a price index. ?Price indices are used as barometers of changes in the purchasing power of a currency. ?If inflation is high, so will be the index level and vice versa.
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Indexed Bonds (Cont…)
?Thus indexed bonds will offer higher cash flows during times of high inflation ?And relatively lower cash flows during periods of lower inflation
?This will ensure that the cash flow in real terms is kept at a virtually constant level.
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Timing Risk
? In the case of Plain Vanilla bonds, there is no uncertainty regarding the times to receipt of the cash flows. ? However, callable bonds can be recalled at any time. ? For a callable bond holder there is cash flow uncertainty, since he is unsure as to how many periods he is going to get coupons for, and also as to when the face value will be repaid.
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Timing Risk (Cont…)
?Thus holders of callable bonds will demand a premium for bearing this risk.
?That is why callable bonds trade at a lower price than otherwise comparable plain vanilla bonds.
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Foreign Exchange Risk
?This risk arises when the cash flows from a bond are denominated in a foreign currency. ?If the foreign currency depreciates in value with respect to the home currency, the returns will be lower than anticipated.
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Illustration
? A bond promises to pay a coupon of $10 every six months. ? Assume that the rate of exchange is Rs 50 per dollar.
?So an Indian bondholder will expect to receive Rs 500 every six months.
? However, what if the exchange rate at the time of the coupon payment is Rs 45.
?If so, he will receive only Rs 450.
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Valuation in between Coupon Dates
?While valuing a bond we assumed that we were standing on a coupon payment date.
?This is a significant assumption because it implies that the next coupon is exactly one period away.
?What should be the procedure if the valuation date is in between two coupon payment dates?
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The Procedure for Treasury Bonds
?Calculate the actual number of days between the date of valuation and the next coupon date.
?Include the next coupon date. ?But do not include the starting date.
?Let us call this interval N1.
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Treasury Bonds (Cont…)
?Calculate the actual number of days between the coupon date preceding the valuation date and the following coupon date.
?Once again include the ending date but exclude the starting date.
?Let us call this time interval as N2.
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Treasury Bonds (Cont…)
?The next coupon is then k periods away where
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Illustration
?There is a Treasury bond with a face value of $1,000. ?The coupon rate is 8% per annum, paid on a semi-annual basis. ?The coupon dates are 15 July and 15 January. ?The maturity date is 15 January 2022. ?Today is 15 September 2002.
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No. of Days Till the Next Coupon Date
Month No. of Days
September
October November December January TOTAL
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15
31 30 31 15 122
164
No. of Days between Coupon Dates
Month July August September October November December January TOTAL No. of Days 16 31 30 31 30 31 15 184
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Treasury Bonds (Cont…)
?K = 122/184 = .6630 ?This method is called the Actual/Actual method and is often pronounced as the Ack/Ack method. ?It is the method used for Treasury bonds in the U.S.
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The Valuation Equation
?Wall Street professionals will then price the bond using the following equation.
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Valuation
?In our example
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The Treasury Method
?There is a difference between the Wall Street approach and the approach used by the Treasury to value T-bonds.
?The difference is that the Treasury uses a simple interest approach for the fractional first period.
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The Treasury Method (Cont…)
? The Treasury will thus use the following equation.
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The Treasury Method (Cont…)
?The Treasury approach will always give a lower price because for a fractional period the simple interest approach will always give a larger discount factor than the compound interest approach.
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The 30/360 PSA Approach
? The Actual/Actual method is applicable for Treasury bonds in the U.S. ? For corporate bonds in the U.S. we use what is called the 30/360 PSA method.
?In this method the number of days between successive coupon dates is always taken to be 180. ?That is each month is considered to be of 30 days.
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The 30/360 Approach (Cont…)
?The number of days from the date of valuation till the next coupon date is calculated as follows. ?The start date is defined as ?D1 = (month1, day1,year1) ?The ending date is defined as ?D2 = (month2,day2,year2)
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The 30/360 Approach (Cont…)
?The number of days is then calculated as ?360(year2 – year1) + 30(month2 – month1) + (day2 – day1)
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Additional Rules
?If day1 = 31 then set day1 = 30 ?If day1 is the last day of February, then set day1 = 30 ?If day1 = 30 or has been set equal to 30, then if day2 = 31, set day2 = 30
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Examples of Calculations
Start Date
Jan-01-86 Jan-15-86 Feb-15-86 Jul-15-86 Nov-01-86 Dec-15-86 Dec-31-86 Feb-01-88 1/30/2013
End Date
Feb-01-86 Feb-01-86 Apr-01-86 Sep-15-86 Mar-01-87 Dec-31-86 Feb-01-87 Mar-01-88
Actual Days Days Based on 30/360 31 30 17 16 45 46 62 60 120 120 16 16 31 31 29 30 176
Pricing of A Corporate Bond
?Let us assume that the bond considered earlier was a corporate bond rather than a Treasury bond.
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Pricing (Cont…)
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30/360 ISDA
?The difference between 30/360 PSA and 30/360 ISDA is that the additional rule pertaining to the last day of February is not applicable.
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30/360 SIA
?The additional rules for this convention are the following.
?If day1 = 31, then set day1 = 30. ?If day1 is the last day of February and the bond pays a coupon on the last day of February then set day1 = 30. ?If day1 = 30 or has been set equal to 30, then if day2 = 31, set day2 = 30.
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30/360 European Convention
?In this convention, if day2 = 31, then it is always set equal to 30. ?So the additional rules are: ?If day1 = 31 then set day1 = 30 ?If day2 = 31 then set day2 = 30
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Examples of Calculations
Start Date End Date Actual Days Days Based on 30/360E
Mar-31-86
Dec-31-86
275
270
Dec-15-86
Dec-31-86
16
15
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Actual/365 Convention
?The difference between this and the Actual/Actual method is that the denominator in this convention will consist of 365 even in leap years.
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Actual/365 Japanese
?This is used for Japanese Government Bonds (JGBs) ?It is similar to the Actual/365 method. ?The only difference is that in this case, the extra day in February is ignored in leap years, while calculating both the numerator and the denominator.
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Actual/365 ISDA
? This day count convention is identical to the Actual/365 convention for a coupon period that does not include days falling within a leap year. ? However for a coupon period that includes days falling within a leap year, the day count is given by: #of days falling within the leap year ______________________________ + 366 #of days not falling within the leap year _________________________________ 365
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Actual/360 Convention
?This is a simple variant of Actual/365. ?This is the convention used for money market instruments in most countries.
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Global Conventions
Country Japan Japan Japan UK UK UK US Security T-bills JGBs Other Bonds Fixed rate gilts Index linked gilts Strips T-bills Convention Act/365 Japanese Act/365 Japanese Act/365 Japanese Act/Act Act/Act Act/Act Act/360
US
US India
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T-notes and T-bonds
Other bonds Government bonds Corporate bonds
Act/Act
30/360 PSA 30E/360
187
India
Act/365
Accrued Interest
? The price of a bond is the present value of all the cash flows that the buyer will receive when he buys the bond.
?Thus the seller is compensated for all the cash flows that he is parting with.
? This compensation includes the amount due for the fact that the seller is parting with the entire next coupon, although he has held it for a part of the current coupon period.
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Accrued Interest (Cont…)
?This compensation is called Accrued Interest. ?Let us denote the sale date by t; the previous coupon date by t1; and the following coupon date by t2 ?The accrued interest is given by
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Accrued Interest (Cont…)
?Both the numerator and the denominator are calculated according to the conventions discussed above.
?That is for U.S. Treasury bonds the Actual/Actual method is used, whereas for U.S. corporate bonds the 30/360 method is used.
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Why Accrued Interest?
?Why should we calculate the accrued interest if it is already included in the price calculation?
?The answer is that the quoted bond price does not include accrued interest. ?That is, quoted prices are net of accrued interest.
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Why Accrued Interest? (Cont…)
?The rationale is as follows. ?On July 15 the price of the Treasury bond using a YTM of 10% is $829.83. ?On September 15 the price using a yield of 10% is $843.5906.
?Since the required yield on both the days is the same, the increase in price is entirely due to the accrued interest.
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Why Accrued Interest (Cont…)
?On July 15 the accrued interest is zero. ?This is true because on a coupon payment date, the accrued interest has to be zero. ?On September 15 the accrued interest is
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Why Accrued Interest? (Cont…)
? The price net of accrued interest is ? $843.5906 - $13.4783 = $830.1123$, which is very close to the price of $829.83 that was observed on July 15. ? We know that as the required yield changes, so will the price. ? If the accrued interest is not subtracted from the price before being quoted, then we would be unsure as to whether the observed price change is due to a change in the market yield or is entirely due to accrued interest.
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Why Accrued Interest? (Cont…)
?However if prices are reported net of accrued interest, then in the short run, observed price changes will be entirely due to changes in the market yield.
?Consequently bond prices are always reported after subtracting the accrued interest.
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Clean versus Dirty Prices
?Quoted bond prices are called clean or add-interest prices. ?When a bond is purchased in addition to the quoted price, the accrued interest has also to be paid. ?The total price that is paid is called the dirty price or the full price.
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Negative Accrued Interest
? One logical question is
?Can the accrued interest be negative? ?That is, can there be cases where the seller of the bond has to pay accrued interest to the buyer.
? The answer is yes.
?In markets where bonds trade ex-dividend the dirty price will fall by the present value of the next coupon on the ex-dividend date and the dirty price will be less than the clean price.
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Example
?Take a T-bond that matures on 15 July 2021. ?It pays a 9% coupon semi-annually on 15 January and 15 July every year. ?The face value is 1000 and the YTM is 8%. ?Assume that we are on 5 January 2002 which is the ex-dividend date.
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Example (Cont…)
? Using the Actual/Actual convention we can calculate k to be 0.0543.
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Example (Cont…)
?The moment the bond goes ex-dividend the dirty price will fall by the present value of the forthcoming coupon, because the buyer will be no longer entitled to it.
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Example (Cont…)
? Thus the ex-dividend dirty price is
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Example (Cont…)
?This is the amount payable by the person who buys the bond an instant after it goes ex-dividend. ?The accrued interest an instant before the bond goes ex-dividend is: 0.09x1000 174 ________ x ____ = $ 42.5543 2 184
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Example (Cont…)
? Thus the clean price at the time of the bond going ex-dividend is 1140.4910 – 42.5543 = $1097.9367 ? The clean price is therefore greater than the exdividend dirty price.
?This represents the fact that the seller has to compensate the buyer because while the buyer is entitled to his share of the next coupon the entire amount will be received by the seller.
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Example (Cont…)
?The fraction of the next coupon that is payable to the buyer is 0.09x1000 10 _________ x ____ = $2.4457 2 184 ?Hence the buyer has to pay 1097.9367 – 2.4457 = $1095.4910 which is the ex-dividend dirty price.
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Yield Measures
?The yield or the rate of return from a bond can and is computed in various ways. ?We will discuss various yield measures and their relative merits and demerits.
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The Current Yield
?This is very commonly reported. ?Although it is technically very unsatisfactory. ?It relates the annual coupon payment to the current market price.
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Example of the Current Yield
?A 15 year 15% coupon bond is currently selling for $800. ?The current yield is given by
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Current Yield (Cont…)
?If you buy this bond for $800 and hold it for one year you will earn an interest income of $150.
?So your interest yield is 18.75%
?However, if you sell it after one year you will either make a Capital Gain or a Capital Loss.
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Current Yield (Cont…)
?What is a Capital Gain?
?If the price at the time of sale is higher than the price at which the bond was bought, the profit is termed as a Capital Gain. ?Else if there is a loss, it is termed a Capital Loss.
?The current yield does not take such gains and losses into account.
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Current Yield (Cont…)
? One question is: ?Should the current yield be based on the dirty price or the clean price ? The advantage of using the clean price is that the current yield will stay constant till the yield changes. ?However if the dirty price is used it will give rise to a
sawtooth pattern.
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Current Yield (Cont…)
?The current yield is used to estimate the cost of or profit from holding the bond. ?If short-term rates are higher than the current yield, the bond is said to involve a running cost.
?This is known as negative carry or negative funding.
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Simple YTM
?This yield measure attempts to rectify the shortcomings of the current yield by taking into account capital gains and losses. ?The assumption made is that capital gains and losses accrue evenly over the life of the bond.
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Simple YTM (Cont…)
?The formula is: Simple YTM = C M-P __ + ____ P PXN/2
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Simple YTM (Cont…)
?For the 15 year bond that we considered earlier
Simple YTM = 150 1000-800 _____+_________ = 20.42% 800 15 x 800
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Simple YTM (Cont…)
?The problem with the simple YTM is that it does not take into account the compound interest that can be earned by reinvesting the coupons. ?This will obviously increase the overall return from the bond.
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Yield to Maturity (YTM)
?The YTM is the interest rate that equates the present value of the cash flows from the bond (assuming that the bond is held to maturity), to the price of the bond. ?It is exactly analogous to the concept of the Internal Rate of Return (IRR) used in project valuation.
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YTM (Cont…)
?Consider a bond that makes an annual coupon of C on a semi-annual basis. ?The face value is M, the price is P, and the number of coupons remaining is N.
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YTM (Cont…)
?The YTM is the value of y that satisfies the following equation.
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YTM (Cont…)
? The YTM is a solution to a non-linear equation. ? We generally require a financial calculator or a computer to calculate it. ? However it is fairly simple to compute the YTM in the case of a coupon paying bond with exactly two periods to maturity.
?In such a case it is simply a solution to a quadratic equation.
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YTM for a Zero Coupon Bond
?The YTM is easy to compute in the case of zero coupon bonds. ?Consider a ZCB with a face value of $1,000, maturing after 5 years. ?The current price is $500. ?The YTM is the solution to
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Features of YTM
?The YTM calculation takes into account all the coupon payments ?As well as any capital gains/losses that accrue to an investor who buys and holds a bond to maturity.
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Sources of Returns From a Bond
?A bondholder can expect to receive income from the following sources. ?Firstly there are coupon payments which are typically paid every six months. ?There will be a capital gain/loss when a bond matures or is called before maturity or is sold before maturity.
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Returns From a Bond (Cont…)
? The YTM calculation assumes that the bond is held to maturity. ? Finally when a coupon is received it will have to be reinvested till the time the bond eventually matures or is sold or is called.
?Once again the YTM calculation assumes that the bond is held till maturity. ?The reinvestment income is nothing but interest on interest.
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YTM
?A satisfactory measure of the yield should take into account all the three sources of income. ?The current yield measure considers only the coupon for the first year. ?All the other factors are totally ignored.
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YTM (Cont…)
?The YTM calculation takes into account all the three sources of income. ?However it makes two key assumptions.
?Firstly it assumes that the bond is held till maturity. ?Secondly it assumes that all intermediate coupons are reinvested at the YTM itself.
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YTM (Cont…)
?The latter assumption is built in to the mathematics of the YTM calculation. ?The YTM is called a Promised Yield. ?It is Promised because in order to realize it you have to satisfy both the above conditions. ?If either of the two conditions is violated you may not get what was promised.
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The Re-investment Assumption
?Consider a bond that pays a semi-annual coupon of $C/2. ?Let r be the annual rate of interest at which these coupons can be re-invested. ?r would be dependent on the market rate of interest that is prevailing when the coupon is received, and need not be equal to y, the YTM, or c, the coupon rate.
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Reinvestment (Cont…)
?For ease of exposition we will assume that r is a constant for the life of the bond. ?However, in practice, it is likely that each coupon may have to be reinvested at a different rate of interest. ?Thus each coupon can be re-invested at a rate of r/2 per six monthly period.
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Reinvestment (Cont…)
?The coupon stream is an annuity. ?The final payoff from re-investment is the future value of this annuity. ?The future value is
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Reinvestment (Cont…)
?The future value represents the sum of all the coupons which are reinvested (which in this case is the principal), plus the interest from re-investment. ?The total value of coupons that are reinvested is
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Re-investment (Cont…)
?The interest on interest is therefore
The YTM Calculation assumes that r/2 = y/2.
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Reinvestment in Action
?Consider an L&T bond with 10 years to maturity. ?The face value is Rs 1,000. ?It pay a semi-annual coupon at the rate of 10% per annum. ?The YTM is 12% per annum. ?Price can be calculated to be Rs 885.295.
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Reinvestment in Action (Cont…)
?Assume that the semi-annual interest payments can be reinvested at a six monthly rate of 6%, which corresponds to a nominal annual rate of 12%. ?The total coupon income = 50 x 20 = 1000
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Reinvestment in Action (Cont…)
?Interest on interest gotten by reinvesting the coupons
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Reinvestment in Action (Cont…)
?Finally in the end you will get back the face value of Rs 1,000. ?So the total cash flow at the end = 1000 + 839.3 + 1000 = 2839.3 ?To get this income, the bondholder has to make an initial investment of 885.295.
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Reinvestment in Action (Cont…)
?So what is the effective rate of return? ?It is the value of i that satisfies the following equation
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Reinvestment in Action (Cont…)
?So the rate of return is 6% on a semiannual basis or 12% on a nominal annual basis, which is exactly the same as the YTM. ?So how was this return achieved? ?Only by being able to reinvest all the coupons at a nominal annual rate of 12%, compounded on a semi-annual basis.
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The Significance of the Reinvestment Rate
?The reinvestment rate affects only the interest on interest income. ?The other two sources are unaffected. ?If r > y, then the investor’s interest on interest income would be higher, and the return on investment, i, would be greater than the YTM, y.
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The Reinvestment Rate (Cont…)
? On the contrary, if r < y, then the interest on interest income would be lower, and the rate of return, i, would be less than the YTM, y. ? So if you buy a bond by paying a price which corresponds to a given YTM, you will realize that YTM only if ? You hold the bond till maturity ? You are able to reinvest all the intermediate coupons at the YTM.
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Reinvestment Risk
?One of the risks faced by an investor is that the future reinvestment rates may be less than the YTM which was in effect at the time the bond was purchased.
?This risk is called Reinvestment Risk. ?The degree of reinvestment risk depends on the time to maturity as well as the quantum of the coupon.
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Reinvestment Risk (Cont…)
?For a bond with a given YTM, and a coupon rate, the greater the time to maturity, the more dependent is the total return from the bond on the reinvestment income. ?Thus everything else remaining constant, the longer the term to maturity, the greater is the reinvestment risk.
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Reinvestment Risk (Cont…)
?For a bond with a given maturity and YTM, the higher the coupon rate, the more dependent is the total return on the reinvestment income. ?Thus everything else remaining the same, the larger the coupon rate, the greater is the reinvestment risk.
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Reinvestment Risk (Cont…)
?Thus premium bonds will be more vulnerable to such risks than bonds selling at par. ?Correspondingly, discount bonds will be less vulnerable than bonds selling at par.
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Zero Coupon Bonds and Reinvestment Risk
? If a zero coupon bond is held to maturity, there will be no reinvestment risk, because there are no coupons to reinvest. ? Thus if a ZCB is held to maturity, the actual rate of return will be equal to the promised YTM. ? If the risk is lower or absent, the return should also be less. ? Thus a ZCB will command a higher price than an otherwise similar Plain Vanilla bond.
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The Realized Compound Yield
? We will continue with the assumption that the bond is held till maturity. ? But we will make an explicit assumption about the rate at which the coupons can be reinvested. ? That is, unlike in the case of the YTM, we will no longer take it for granted that intermediate cash flows can be reinvested at the YTM.
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Illustration
?Let us reconsider the L&T bond. ?Assume that intermediate coupons can be reinvested at 7% for six months, or at a nominal annual rate of 14%. ?The total coupon income and the final face value payment will remain the same, but the reinvestment income will change.
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Illustration (Cont…)
?The interest on interest
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Illustration (Cont…)
?So the final amount received = 1000 + 1049.75 + 1000 = 3049.75 ?The initial investment is once again 885.295 ?Therefore, the rate of return is given by
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Illustration (Cont…)
?This is the rate of return for six months. ?The nominal annual return is 6.38 x 2 = 12.76%, which is greater than the YTM of 12%. ?The RCY is greater than the YTM, because we assumed that the reinvestment rate was greater than the YTM.
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Illustration (Cont…)
?Had we assumed the reinvestment rate to be less than the YTM, the RCY would have turned out to be less than the YTM. ?The RCY can be an ex-ante or an ex-post measure. ?Ex-ante means that we make an assumption about the reinvestment rate and then calculate the RCY.
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Illustration (Cont…)
?Ex-post means that we take into account the actual rate at which we have been able to reinvest and calculate the RCY.
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The Horizon Return
?Let us now relax both the assumptions which were used to calculate the YTM. ?Firstly the investor need not hold the bond until maturity. ?Secondly he may not be able to reinvest the coupons at the YTM.
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The Horizon Return (Cont…)
?Now the return will depend on three sources – the coupons received, the reinvestment income, and the price at which the bond is sold prior to maturity. ?The sale price of the bond would depend on the prevailing market yield at that point in time, and need not equal the face value.
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Illustration
?Assume that an investor with a 7 year investment horizon buys the L&T bond that we discussed earlier. ?He will get coupons for 14 periods (not 20). ?The total coupon income will be ?50x14 = 700 ?We will assume that the reinvestment rate is expected to be 7% per six monthly period.
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Illustration (Cont…)
?We will also assume that the investor expects the YTM after 7 years to be 12% per annum. ?The first step is to calculate the expected price at the time of sale. ?At that point in time the bond will have 3 years to maturity.
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Illustration (Cont…)
?The price using a YTM of 12% can be shown to be Rs 950.865. ?The interest on interest
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Illustration (Cont…)
?The total terminal cash flow = 700 + 427.50 + 950.865 = 2,078.365
? The initial investment as before is 885.295
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Illustration (Cont…)
?The nominal annual rate of return is 6.29x2 = 12.58% ?This is the Horizon Yield. ?Once again, it can be calculated ex-post or ex-ante.
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Yield to Call (YTC)
?This measure of the rate of return is used for callable bonds. ?The YTC is the yield that will make the present value of the cash flows from the bond equal to the price, assuming the bond is held till the call date. ?In principle a bond can have many possible call dates.
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YTC (Cont…)
?In practice the cash flows are usually taken only till the first call date, although they can easily be taken to any subsequent call date. ?The YTC is given by the equation
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YTC (Cont…)
? N* is the number of coupons till the call date. ? M* is the price at which the bond is expected to be recalled. ? M* need not equal the face value. ? In practice companies pay as much as one year’s coupon as a Call Premium at the time of recall. ? If so, M* = M + C
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Illustration (Cont…)
?Let us assume that the L&T bond is a callable bond and that the first call date is 7 years away. ?Assume that a call premium of Rs 100 will be paid if the bond is recalled.
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Illustration (Cont…)
?The YTC is the solution to the following equation
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Illustration (Cont…)
?The solution comes out to be 6.74%. ?So the YTC on an annual basis is 13.48%. ?The YTC is very important for Premium Bonds. ?The very fact that a bond is selling at a premium, indicates that the coupon is greater than the yield, and that therefore there is a greater chance of recall.
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The Yield to Worst
?In practice the investors compute the YTC for every possible call date. ?They then compute the YTM as well. ?The lowest of all possible values is called the Yield to Worst.
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Portfolio Yield
?Consider a case where you hold a portfolio or a collection of bonds. ?You cannot simply calculate the yield from the portfolio as a weighted average of the YTMs of the individual bonds.
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Portfolio Yield (Cont…)
?You have to first compute the cash flows from the portfolio, and then find that interest rate which will make the present value of the cash flows equal to the sum of the prices of the component bonds.
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Illustration
?Consider a person who buys a TELCO bond and a Ranbaxy bond. ?The TELCO bond has a time to maturity of 5 years, face value of 1000, and pays coupons semi-annually at the rate of 10% per annum. ?The YTM is 12% per annum.
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Illustration (Cont…)
?The Ranbaxy bond has a face value of 1000, time to maturity of 4 years, and pays a coupon of 10% per annum semiannually. ?The YTM is 16% per annum. ?Consider a portfolio consisting of one bond of each company. ?What is the portfolio yield?
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Illustration (Cont…)
?The first step is to calculate the two prices. ?The price of the TELCO bond can be shown to be 926.405. ?The price of the Ranbaxy bond can be shown to be 827.63. ?The total initial investment is therefore ?1,754.035
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The Cash Flow Table
Period
0 1 2 3 4 5
Investment
(1754.035)
Inflow from TELCO
50 50 50 50 50
Inflow from Ranbaxy
50 50 50 50 50
Total
(1754.035) 100 100 100 100 100
6
7 8 9
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50
50 50 50
50
50 1050
100
100 1100 50
10
1050
1050
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Illustration (Cont…)
?Using a financial calculator or a spread sheet, the portfolio yield can be calculated to be 13.76%.
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Duration
?Long term bonds are more susceptible to changes in yield than shorter term bonds ?Take two bonds with a face value of 1,000 ?Both pay a 10% coupon on a semi-annual basis ?YTM is 10% in both cases ?Bond A has a time to maturity of 5 years ?Bond B has a time to maturity of 10 years
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Duration (Cont…)
?Both bonds will obviously sell at par
?Since coupon = YTM = 10%
?Now assume that the YTM increases to 12%
?Price of bond A = 926.40 ?Price of bond B = 885.30 ?Price of A has declined by 7.34% ?Price of B has declined by 11.47%
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Duration (Cont…)
? The longer term bond is more impacted by the price change ? Why?
?The PV of a cash value is
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Duration (Cont…)
?The larger the value of t, the greater is the impact of a change in the YTM
?A 10 year bond has most of its cash flows coming in at later points as compared to a 5 year bond ?Thus its price is more vulnerable to changes in the yield
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Duration (Cont…)
?However the issue is not so simple. ?Consider a 5 year Zero with a face value of $1,000
?At 10% price = 613.91 ?At 12% price = 558.39 ?The price decline is 9.04%
?Why is a 5 year Zero more price sensitive than a 5 year coupon bond?
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Duration (Cont…)
?A coupon paying bond is
?A series of cash flows arising at 6 monthly intervals ?It is a portfolios of Zeroes ?Time to maturity only takes cognizance of the last cash flow ?The effective time to maturity
?Should be an average of the times to maturity of the component zeroes
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Duration (Cont…)
?What about a 5 year Zero?
?It gives rise to a single cash flow ?Its stated time to maturity is the same as its effective time to maturity
?It is obvious why the 5 year Zero is more price sensitive
?Its effective time to maturity is greater
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Duration (Cont…)
?Duration is a measure of the effective term to maturity of a Plain Vanilla bond
?It is a weighted average of the terms to maturity of the component cash flows ?The weights are the fractions of the total present value of the bond that is contributed by the cash flow
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Illustration
?Consider a 5 year 10% coupon paying bond ?With a face value of $1,000 ?YTM = 10%
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Illustration (Cont…)
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Illustration (Cont…)
?The weighted average time to maturity is
?8.1078 semi-annual periods ?Or 4.0539 years
?The weighted average time to maturity of a 5 year Zero is 5 years ?Thus a 5 years Zero is more price sensitive
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Duration (Cont…)
? The relationship between the duration of a bond and the rate of change of the percentage change in price is
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Duration (Cont…)
?Thus the rate of change of the percentage change in price is a function
?Of the duration of the bond ?And not its time to maturity
?Thus it is duration and not time to maturity that accurately captures the relationship between the change in yield and the corresponding price change.
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doc_229451536.pptx
Different types of bonds, difference between debt and equity, bonds with embedded options, yield to maturity, bond valuation, zero coupon bonds, how treasury auction is done, STRIPS, floating rate bonds, callable bonds, puttable bonds, convertible bonds, exchangeable bonds, different types of risks, YTM of zero coupon bond, significance of reinvestment risk, yield to call.
Part-06
1/30/2013
Part-02 An Introduction to Fixed Income Securities
1
Basics
?What is debt?
?It is a financial claim.
?Who issues it?
?The borrower of funds
?For whom it is a liability
?Who holds it?
?The lender of funds
?For whom it is an asset
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Basics (Cont…)
?What is the difference between debt and equity?
?Debt does not confer ownership rights on the holder. ?It is merely an IOU
?A promise to pay interest at periodic intervals ?And to repay the principal at a prespecified maturity date.
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Basics (Cont…)
?It usually has a finite life span ?The interest payments are contractual obligations
?Borrowers are required to make payments irrespective of their financial performance ?Interest payments have to be made before any dividends can be paid to equity holders. ?In the event of liquidation
• The claims of debt holders must be settled first • Only then can equity holders be paid.
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Fixed Income Securities
?Why are bonds and debentures termed as Fixed Income Securities
?Once the rate of interest is set at the onset of the period for which it is due
?It is not a function of the profitability of the firm
?Thus even floating rate bonds are fixed income securities
?Failure to pay the promised interest will tantamount to default
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Basics (Cont…)
?Bonds may be secured or unsecured
?Unsecured dent securities are termed as Debentures in the US ?Unsecured implies that no specific assets have been earmarked as collateral ?Secured debt issues require the firm to earmark specific assets as collateral
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Basics (Cont…)
?Debt securities may be negotiable or nonnegotiable
?Negotiable securities can be traded in the secondary market
?Can be endorsed by one party in favor of another
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Plain Vanilla & Bells and Whistles
? The most basic form of a bond is called the Plain Vanilla version.
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Plain Vanilla (Cont…)
? This is true for all securities, not just for bonds. ? More complicated versions are said to have `Bells and Whistles’ attached.
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Plain Vanilla (Cont…)
?Floating rate bonds are similar to conventional bonds
?The difference is that the interest rate does no remain fixed ?It varies from period to period based on the benchmark to which it is linked
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Bonds With Embedded Options
?Convertible bonds can be converted to shares of stock ?Callable bonds can be prematurely retired by the issuer ?Putable bonds can be prematurely surrendered by the holders
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Face Value
?It is the principal value underlying the bond.
?It is the amount payable by the borrower to the last holder at maturity. ?It is the amount on which the periodic interest payments are calculated. ?A.K.A as
?Par Value ?Redemption Value ?Maturity Value ?Principal Value
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Term to Maturity
?It is the time remaining in the life of the bond.
?It represents the length of time for which interest has to be paid as promised. ?It represents the length of time after which the face value will be repaid. ?A.K.A as
?Maturity ?Term
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Coupon
?The coupon payment is the periodic interest payment that has to be made by the borrower.
?The coupon rate when multiplied by the face value gives the dollar value of the coupon. ?Most bonds pays coupons on a semi-annual basis. ?In the earlier days bonds were accompanied by a booklet of post-dated coupons ?Each coupon could be detached and redeemed on the corresponding coupon payment date
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Example of Coupon Calculation
?Consider a bond with a face value of $1000. ?The coupon rate is 8% per annum paid semi-annually.
?So the bond holder will receive
1000 x 0.08 ___ = $40 every six months. 2
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Yield to Maturity (YTM)
? Yield to maturity is the rate of return for an investor if he buys the bond at the prevailing market price and holds it till maturity. ? In order to get the YTM, two conditions must be satisfied.
?The bond must be held till maturity. ?All coupon payments received before maturity must be reinvested at the YTM.
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YTM (Cont…)
?At any point in time the YTM may be
?Greater than ?Less than or ?Equal to the Coupon Rate
?YTM is the IRR of a bond
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Value of a Bond
? A bond holder gets a stream of contractually promised payments. ? The value of the bond is the value of this stream of cash flows. ? However you cannot simply add up cash flows arising at different points in time.
?Cash flows have to be discounted before being added.
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Price versus Yield
?Price versus yield is a chicken and egg story
?We cannot say which comes first.
?If we know the yield that is required we can quote a price accordingly. ?Similarly, once we acquire the asset at a certain price, we can work out the corresponding yield.
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Bond Valuation
?A bond is an instrument that will pay identical coupons every period, usually every six months, and will then repay the face value at maturity. ?The periodic cash flows obviously constitute an annuity. ?The terminal face value is a lump sum payment.
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Bond Valuation (Cont…)
? Consider a bond that pays a semi-annual coupon of $C/2, and which has a face value of $M. ? Assume that there are N coupons left, and that we are standing on a coupon payment date.
?That is, we are assuming that the next coupon is exactly six months away.
? The required annual yield is y, which implies that the semi-annual yield is y/2.
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Bond Valuation (Cont…)
?The present value of the coupon stream is:
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Bond Valuation (Cont…)
?The present value of the face value is:
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Bond Valuation (Cont…)
? So the price of the bond is:
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Illustration
?IBM has issued a bond with a face value of $1,000. ?The coupon is 8% per year to be paid on July 15 and January 15 every year. ?Assume that today is 15 July 2002 and that the bond matures on 15 January 2022. ?The required yield is 10% per annum.
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Illustration (Cont…)
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Par, Discount & Premium Bonds
? In the above example, the price of the bond is less than the face value of $1,000. ? Such a bond is called a Discount Bond, since it is trading at a discount from the face value. ? The reason why it is trading for less than the face value is because the required yield of 10% is greater than the rate of 8% that the bond is paying by way of interest.
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Par, Discount & Premium Bonds (Cont…)
? If the required yield were to equal the coupon rate, the bond would sell for $1,000. ? Such bonds are said to be trading at Par. ? If the required yield were to be less than the coupon rate the price will exceed the face value. ? Such bonds are called Premium Bonds, since they are trading at a premium over the face value.
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Par Discount and Premium (Cont…)
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Par Discount and Premium (Cont…)
?If c = y, P = M
?Thus if the coupon is equal to the YTM, the bond will always sell at Par
?It can be shown that the bond price is a monotonically increasing function of the coupon
?Obviously if the coupon is less than the YTM the price will be less than the face value ?If the coupon is greater than the YTM the price will be in excess of the face value
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Par Premium and Discount (Cont…)
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Par Premium and Discount (Cont…)
?Why would a bond trade at a premium or a discount?
?The price of a bond is the PV of all the cash flows emanating from it ?If YTM = coupon the return demanded by investors will be equal to the rate offered by the issuer
?Obviously the bond will sell at PAR
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Par Premium and Discount (Cont…)
?What if the YTM is less than the coupon
?Assume c = 10% while YTM = 8% ?An investor will be willing to pay more than the face value ?The price would be bid up to a level where the YTM is equal to 8%
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Par Premium and Discount (Cont…)
?On the other hand what if YTM is greater than the coupon
?Assume coupon = 8% while YTM = 10% ?Investors will only pay less than the face value ?The price will be driven down to a level where the yield is exactly 10%
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Evolution of The Price
?Consider the change in price of a bond from one coupon date to another assuming that the YTM is constant
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Evolution (Cont…)
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Evolution (Cont…)
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Evolution (Cont…)
?If y = c, then ?P = 0 ?Thus if the YTM remains constant, the price of a par bond will remain at par as we go from one coupon date to the next ?If the YTM > Coupon, ?P > 0
?Thus a discount bond will steadily increase in price as we go from one coupon date to another
?If YTM < Coupon ?P < 0
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?A premium bond will steadily decline in price as we go from one coupon date to another
38
Illustration
?Consider a bond with 10 years to maturity and a par value of 1,000
?YTM is 8% per annum ?Coupon = 6% per annum ?Price = 864.10
?If we move 6-M ahead the price will be 868.66 if the YTM were to remain constant
?Obviously since it is a discount bond the price has increased
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Illustration (Cont…)
?Now consider a bond with 10 years to maturity and a face value of 1,000
?YTM = 8% ?Coupon = 10% ?Price = 1135.90
?Six months later if the yield were to remain constant the price will be 1131.34
?Obviously the price has declined
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Zero Coupon Bonds
? A Plain Vanilla bond pays coupon interest every period, typically every six months, and repays the face value at maturity. ? A Zero Coupon Bond on the other hand does not pay any coupon interest. ? It is issued at a discount from the face value and repays the principal at maturity. ? The difference between the price and the face value constitutes the interest for the buyer.
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Illustration
?Microsoft is issuing zero coupon bonds with 5 years to maturity and a face value of $10,000. ?If you want a yield of 10% per annum, what price will you pay? ?The price of the bond is the present value of a single cash flow of $10,000, discounted at 10%.
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Illustration (Cont…)
?In practice, we usually discount the face value using a semi-annual rate of y/2, where y in this case is 10%. ?This is to facilitate comparisons with conventional bonds which pay coupon interest every six months.
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Zero Coupon Bonds (Cont…)
?Zero coupon bonds are called Zeroes by traders. ?They are also referred to as Deep Discount Bonds. ?They should not be confused with Discount Bonds, which are Plain Vanilla bonds which are trading at a discount from the face value.
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Zero Coupon Bonds (Cont…)
?A zero coupon bond can never sell at a premium
?It will always trade at a discount prior to maturity ?At maturity it will trade at par
?Can a zero coupon bond give rise to a capital gain or a loss?
?If it is bought and held to maturity there will obviously be a capital gain
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Zero Coupon Bonds (Cont…)
?If a zero coupon bond is sold prior to maturity there may be a capital gain or a capital loss ?Consider a bond with 10 years to maturity
?The YTM at the time of purchase was 10% ?The cost was $376.90 ?A year later it is sold at a prevailing YTM of 12% ?The corresponding price is $350.35 ?Obviously there is a capital loss
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Treasury Securities
?They are fully backed by the federal government of the issuing nation. ?Consequently they are devoid of credit risk or the risk of default. ?The interest rate on such securities is used as a benchmark for setting rates on other kinds of debt.
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U.S. Treasury Securities
?The Treasury issues three categories of marketable securities. ?T-bills are discount securities
?They are issued at a discount from their face values and do not pay interest.
?T-notes and T-bonds are sold at face value and pay interest periodically.
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U.S. Treasury Securities (Cont…)
?T-bills are issued with a original time to maturity of one year or less.
?Consequently they are Money market instruments. ?They have maturities of either 1, 3, 6, or 12 months at the time of issue.
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US. Treasury Securities (Cont…)
?T-notes and T-bonds have a time to maturity exceeding one year at the time of issue.
?They are therefore capital market instruments. ?T-bonds have an original maturity in excess of 10 years, extending up to 30 years.
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U.S. Treasury Securities (Cont…)
?T-notes are similar to T-bonds except that their terms to maturity range from one to ten years.
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U.S. Treasury Securities (Cont…)
?At times an issue may be followed later by a further issue with the same remaining time to maturity and the same coupon
?The issuance of further tranches is termed as a Re-opening.
?Six months ago a 10-year note was issued with a coupon of 8% per annum. ?Today if a note with 9 ½ years to maturity and a coupon of 8% issued it will add to the pool that is already trading in the market ?Thus it is a re-opening of an existing issue
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U.S. Treasury Securities (Cont…)
?The secondary market is liquid and transparent and trades take place through banks and primary dealers. ?Securities are also listed on the NYSE to accommodate overseas investors who may be permitted by regulations to trade only in listed securities.
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U.S. Treasury Securities (Cont…)
?Settlement is arranged through FEDWIRE, which is the Federal Reserve’s wire transfer system
?Foreign investors need to arrange for a local custodian with access to FEDWIRE.
?Three month and six month bills are issued on a weekly basis. ?One year bills are issued every month.
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U.S. Treasury Securities (Cont…) Issue of T-notes and Bonds
Issue 2 Year Frequency Monthly Auction Month Every month
3, 10 Year
5 Year 30 Year
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Quarterly
Monthly
Feb, May, Aug, Nov Every month
Semi-annually Feb and Aug
55
U.S. Treasury Securities (Cont…)
?Interest from these instruments is exempt from state income taxes. ?Guidelines of Mutual Reciprocity.
?Federal bonds are exempt from state taxes ?Bonds issued by state governments are exempt from federal taxes ?The exemption applies only to interest income. ?Capital gains are taxable at normal rates.
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FEDWIRE
? It is an RTGS (Real Time Gross Settlement) Funds transfer system
?Operated by the Federal Reserve Banks ?Electronically transfers funds between more than 8900 participants ?It is the primary US network for large-value or timecritical domestic and international payments ?The average daily value of transfers = 2.3 trillion USD ?Daily average number of payments = 532,000
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Primary Dealers
? Who is a primary dealer?
?A PD is a bank or securities broker-dealer that directly deals in U.S. government securities with the Federal Reserve Bank of New York. ?As of November 2007 there are 20 primary dealers, down from a number of 44 in 1988.
? The most important reason is consolidation. ? That is many firms have merged or refocused their core lines of business.
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Primary Dealers (Cont…)
?The FED requires primary dealers to participate meaningfully in both open market operations as well as Treasury Auctions. ?The current list of primary dealers is as follows.
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List of Primary Dealers
? BNP Paribas Securities ? Banc of America Securities ? Barclays Capital Inc. ? Cantor Fitzgerald & Co. ? Citigroup Global Markets ? Credit Suisse Securities ? Daiwa Capital Markets America ? Deutsche Bank Securities ? Goldman, Sachs & Co. ? HSBC Securities (USA)
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? Jefferies & Company, Inc. ? J.P. Morgan Securities LLC ? Mizuho Securities USA Inc. ? Morgan Stanley & Co. Incorporated ? Nomura Securities International, Inc. ? RBC Capital Markets Corporation ? RBS Securities Inc. ? UBS Securities LLC.
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Primary Dealers (Cont…)
?These dealers purchase the vast majority of Treasury securities sold at Treasury auctions and resell them to the public ?They also account for over 70% of FOREX trading volume
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Primary Dealers in India
? Deutsche Securities ? ICICI Securities Primary Dealership ? IDBI Gilts ? Morgan Stanley India Primary Dealer ? Nomura Fixed Income Securities ? PNB Gilts ? SBI DFHI ? Kotak Mahindra Bank ? Standard Chartered Bank ? Axis Bank
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? ABN AMRO ? Bank of America ? Bank of Baroda ? Canara Bank ? Citibank ? Corporation Bank ? HDFC Bank ? STCI Primary Dealer ? HSBC ? JP Morgan Chase
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Treasury Auctions
?The U.S. Treasury sells bills, notes, and bonds by way of a competitive auction process. ?Most of the treasury securities are bought by primary dealers. ?Individual investors who submit noncompetitive bids participate on a much smaller scale.
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Treasury Auctions (Cont…)
?The auction process begins with a public announcement by the Treasury giving the following information.
?Offering amount ?Description of the offering ?Strips information
?Is the security eligible for stripping
?Procedures for submission of bids; minimum bid amount; and payment terms
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Treasury Auctions (Cont…)
?Description of the offering includes:
?Term and type of security ?CUSIP number ?Auction date ?Issue date ?Dated date ?Maturity date ?Interest payment dates
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Treasury Auctions (Cont…)
? Bids may be:
? Competitive ? Non-competitive
? Small investors and individuals generally submit noncompetitive bids
? The bidder merely indicates the quantity sought ? The price is determined by the auction process ? A non-competitive bidder may not bid for more than $5MM worth of securities in a bill or bond auction
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Treasury Auctions (Cont…)
? Primary dealers who bid for their accounts or on behalf of their clients usually submit large competitive bids
?These bids indicate not only the quantity that is sought ?But also the maximum price that the bidder is prepared to pay if it is a price based auction ?Or the minimum yield that the bidder is prepared to accept if it is a yield based auction
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Treasury Auctions (Cont…)
?Bidders are forbidden from bidding both competitively and non-competitively for the same account in the same auction. ?Competitive bidders can submit multiple bids
?But no bidder may receive more than 35% of the security being sold.
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Treasury Auctions (Cont…)
?Bids are submitted in terms of discount rates for bills
?Stated in 3 decimal places ?In 0.005 percent increments
?In note and bond auctions
?They are expressed as yields up to 3 decimal places ?In 0.001 percent increments
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Treasury Auctions (Cont…)
?Competitive bids are accepted till 1:00 p.m. EST on the day of the auction ?The deadline for non-competitive bids is 12:00 EST on the auction date
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Treasury Auctions (Cont…)
? Once the bids are received the Treasury will net out the total amount of non-competitive bids and will begin allocating the balance to competitive bidders. ? There are two ways in which securities can be allotted
?The multiple price/yield auction mechanism ?The uniform price/yield auction mechanism
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Illustration
?Assume that the Treasury is offering 15 billion dollars worth of T-bonds. ?2 billion dollars worth of non-competitive bids have been received. ?So 13 billion dollars worth of bonds are available to be offered to the competitive bidders.
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Illustration (Cont…)
?Assume that there are six competitive bidders who have submitted the following yields.
?The bids have been arranged in ascending order of yield. ?Had it been a price based auction the bids would have been arranged in descending order of price.
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Illustration (Cont…)
Bidder Alpha Beta Gamma Delta Charlie
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Bid Yield 5.370 5.372 5.373 5.375 5.375 5.380
Bid Amount 3.0 bn 3.0 bn 4.0 bn 3.0 bn 2.0 bn 2.0 bn
Aggregate Amount 3.0 bn 6.0 bn 10 bn 13 bn 15 bn 17 bn
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Tango
Illustration (Cont…)
?The aggregate demand equals the amount on offer at a yield of 5.375. ?A multiple yield auction will lead to the following allocation.
?Alpha will get 3 bn at a yield of 5.370 ?Beta will get 3 bn at 5.372 ?Gamma will get 4 bn at 5.373
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Illustration (Cont…)
?By the time we reach a yield of 5.375 we have only 3 bn left to allocate. ?There is a demand of 5 bn at this yield
?3 bn from Delta and 2 bn from Charlie.
?So there will be pro-rata allocation
?3/5 of 3 bn or 1.8 bn will go to Delta ?2/5 of 3 bn or 1.2 bn will go to Charlie
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Illustration (Cont…)
?The highest yield that is accepted at the auction is called the Stop Yield
?In this case it is 5.375
?The ratio of bids received to the amount awarded is known as the bid to cover ratio
?The higher the ratio the stronger is the auction
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Illustration (Cont…)
?The difference between the average yield of all accepted bids and the stop yield is called the tail of the auction. ?A multiple price/yield auction is also known as a discriminatory auction
?Since each successful bidder is allotted at the price/yield bid by him or her.
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Illustration (Cont…)
? The second type of auction is called a uniform price/yield auction. ? In our case aggregate demand is equal to the supply at a yield of 5.375%. ? Consequently everyone who bid less will be allotted the quantities sought by them at this yield. ? The two bidders at 5.375 will also be awarded at this yield but on a pro-rata basis.
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Illustration (Cont…)
?Those who bid more than 5.375 will get nothing and are said to be shutout of the auction. ?Since 1999 the U.S. Treasury has been conducting only uniform yield auctions.
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Treasury Auctions (Cont…)
? The auction results are released to the public within two hours of the auction. ? The following information is made public:
?The amount of bids received ?The total bids accepted ?The bid to cover ratio ?High, low and median bids ?The issue price
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Illustration-I: A Real Treasury Auction
? Announcement date: 2 August ? Offering amount: $ 10 billion ? Term and type of security:
?4 ¾ year note (reopening of a 5 year note) ?Series: E 2005 ?CUSIP No.: 912827 6D9 ?Auction date: 8 August 2000 ?Issue date: 15 August 2000 ?Dated date: 15 May 2000 ?Maturity date: 15 May 2005
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Illustration-I (Cont…)
?Interest rate: 6 3/4 % ?Amount currently outstanding: $15.426 billion ?Yield: To be determined at the auction ?Interest payment dates: 15 November and 15 May ?Minimum bid amounts and multiples: $ 1,000 ?Premium or discount: To be determined at the auction
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Analysis
? This auction is a re-opening of a 5 year note issued on 15 May 2000.
?Consequently the securities being issued have 4 ¾ years to maturity.
? Although the auction is announced on 2 August the actual auction date is 8 August. ? The securities will however be issued only on 15 August. ? The dated date is 15 May which is when the original 5 year security was issued.
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Analysis (Cont…)
? The dated date is different from the issue date because the issue is being reopened. ? The maturity date is 15 May 2005. ? The interest rate or the coupon is known since the security is already trading in the market. ? The yield will be determined at the auction.
?Consequently the issue price and the premium/discount with respect to the face value will also be determined at the auction.
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Illustration-II
? Auction announcement date: 2 August ? Offering amount: 10 billion ? Term and type of security: 10 year note ? Series: C 2010 ? CUSIP No.: 912827 6J6 ? Auction date: 9 August 2000 ? Issue date: 15 August 2000 ? Dated date: 15 August 2000 ? Maturity date: 15 August 2010
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Illustration-II (Cont…)
? Interest rate: Determined based on the highest accepted competitive bid ? Amount currently outstanding: Not applicable ? Yield: Determined at auction ? Interest payment dates: 15 Feb and 15 August ? Minimum bid amounts and multiples: $ 1,000 ? Premium/discount: To be determined at the auction
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Analysis
? This auction represents a fresh issue of a 10 year T-note ? The coupon rate is unknown at the outset since it will be fixed based on the bids received.
?Assume that the market clearing yield is 4.920% ?The coupon will be set after rounding down the winning bid to the nearest multiple of 1/8th which in this case is 4.875%.
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Zero Coupon Treasury Securities
? The Treasury per se does not issue zero coupon securities. ? But there exist two types of treasury based zero coupon securities. ? The principle behind both forms is the same.
?Take a large quantity of a T-note or bond and separate all the coupons from each other and from the principal. ?Sell the entitlement to each cash flow separately.
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Zero…(Cont…)
?Take the case of a two-year T-note. ?It can be separated into five zero coupon securities maturing after:
?6 months ?12 months ?18 months ?24 months
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Zero…(Cont…)
?Earlier investment banks used to buy regular coupon bonds from the Treasury and then separate the cash flows themselves. ?Each cash flow was then sold separately as a zero coupon bond. ?Such issues are called trademarks.
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Zero…(Cont…)
? The issue of trademarks has now ceased. ? This is because investment banks can now create such instruments in concert with the Treasury itself. ? These zero coupon bonds are known as STRIPS – Separate Trading of Registered Interest and Principal of Securities.
?These are not issued or sold by the Treasury ?The market is made by investment banks. ?But such issues are considered to be an obligation of the Treasury.
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Trademark Products
?Some of the older trademark products which have not yet matured continue to trade. ?The process of issuing trademarks was begun by Merrill Lynch and Salomon Brothers in 1982. ?These securities are synthetic zero coupon Treasury receipts.
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Trademarks (Cont…)
? The process of separating each coupon payment as well as the principal and selling securities backed by them is referred to as Coupon Stripping. ? The receipts issued in the process are not created by the Treasury. ?But the underlying asset in the bank custody account is an obligation of the Treasury. ?Thus the cash flows from the underlying asset are guaranteed.
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Trademarks (Cont…)
?Merrill Lynch marketed its Treasury receipts as Treasury Income Growth Receipts – TIGRS for short. ?Salomon Brothers called its receipts as Certificates of Accrual on Treasury Securities – CATS for short. ?Lehman Brothers offered Lehman Investment Opportunities Notes or LIONS for short.
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Trademarks (Cont…)
?These securities are called trademarks because each is associated with a particular investment banking firm. ?They are called Animal Products for obvious reasons. ?This segment of the financial market was also referred to as the Zoo.
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Trademarks (Cont…)
? Receipts created by one firm were rarely traded by others.
?So the secondary market was illiquid.
? What is the motivation for investment banks to create such products? ? In practice arbitrage is possible when a Treasury coupon security is purchased at a price that is lower than what could be obtained by selling each cash flow separately.
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Trademarks (Cont…)
?The initial reason for the popularity of these securities was tax related. ?Under the then US law, the discount on a bond purchase could be treated as a capital loss.
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Illustration
?Assume that an investor could buy a 30 year zero for $8. ?He could then deduct $92 from his taxable income per $100 of par value ?At the same time he was guaranteed a payoff of $100 after 30 years
?This loophole was plugged in 1982.
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STRIPS
?The Treasury launched this programme in 1985 to facilitate the stripping of designated Treasury securities.
?All new T-bonds and notes with a maturity of 10 years or more are eligible. ?The zeroes created in the process are direct obligations of the U.S. government. ?They are cleared through the Federal Reserve’s book-entry system.
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STRIPS (Cont…)
?On dealer quote sheets and vendor screens, STRIPS are identified as follows.
Cash Flow Source Coupon Symbol ci
Principal from T-bond bp Principal from T-note np
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STRIPS (Cont…)
?The mechanism of issue is as follows.
?A dealer who owns a bond or note can ask the FRB where it is held
?To replace it with an equivalent set of STRIPS representing each payment as a separate security. ?Each of these securities can be traded independently of others.
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STRIPS (Cont…)
?Most coupon and principal payments fall on the same set of dates ?These are
?15 February ?15 May ?15 August ?15 November
?So a lot of bonds would have coupons on the same date.
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STRIPS (Cont…)
?All these interest payments would be converted in to the same security
?Regardless of the bond they were stripped from ?Consequently coupon payments are said to be fungible ?Principal payments falling on the same date are not fungible
?They have different CUSIP numbers
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STRIPS (Cont…)
?In 1987 the Treasury started to allow dealers to reverse the process
?This is called STRIPS RECONSTUTUTION
?How does this work?
?If a dealer owns STRIPS representing all the coupon and principal payments of a bond
?The FED can on request convert these holdings into a single position in the corresponding bond
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Floating Rate Bonds
? In the case of a Plain Vanilla Bond, the coupon rate that is specified at the outset, is valid for the life of the bond. ? In the case of a Floating Rate bond, the coupon rate is reset at the beginning of every period, and is therefore valid for only the next six months. ? Thus when you buy such a bond, the coupon will be known only for the first six months. Subsequent coupons will be unknown.
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Floaters
? For instance the rate on a floating rate bond, also called a Floater, may be specified as LIBOR + 50b.p. in which case the spread is positive. ? Or it may be specified as LIBOR – 30b.p., in which case the spread is negative. ? The rate of interest on a floater will move directly with changes in the benchmark. ? Thus if LIBOR rises, the rate will increase, whereas if LIBOR falls, the rate will decrease.
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Inverse Floaters
? In the case of an inverse floater the coupon varies inversely with the benchmark. ? For instance the rate on an inverse floater may be specified as 10% - LIBOR. ? In this case as LIBOR rises, the coupon will decrease, whereas as LIBOR falls, the coupon will increase.
?In this case a floor has to be specified for the coupon.
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Inverse Floaters (Cont…)
?In the absence of a floor the coupon can become negative in principle.
?In the above case, if LIBOR were to exceed 10%, then we would be confronted with the spectre of a negative coupon.
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Callable Bonds
? In the case of such a bond, the issuer has the right to call back the bond prematurely.
?He can buy it back from the holder before maturity by paying him the face value.
? In this case the option is with the issuer, and so he has to pay a price for it.
?This compensation will manifest itself as a lower price for the bond as compared to a Plain Vanilla Bond.
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Callable Bond (Cont…)
?Since prices and yields are inversely related a lower price means a higher yield.
?Thus buyers of callable bonds demand a higher yield from them as compared to buyers of otherwise similar plain vanilla bonds. ?This is because a buyer of a callable bond is exposed to cash flow uncertainty.
?That is, he can never be sure as to when a bond will be recalled.
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Callable Bonds (Cont…)
?When will a callable bond be recalled?
?Obviously when interest rates or required yields are falling. ?Under such conditions, the issuer can call back the bonds and issue fresh bonds with a lower coupon. ?However this is precisely the scenario when a holder would like to hold on to his bonds, since they are yielding a higher rate of interest.
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Callable Bond (Cont…)
? Thus the call provision works in favour of the borrower and against the lender.
?Hence it is not surprising that callable bonds command a lower price.
? The way to look at it is as follows
?At the time of issue a callable bond has to carry a higher coupon than an equivalent Plain Vanilla Bond ?Subsequently a callable with a given coupon will have a lower price than a Plain Vanilla with the same coupon.
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Callable Bonds (Cont…)
?A bond may be discretely callable or continuously callable ?A discretely callable bond may be recalled only at certain pre-specified dates
?For instance the coupon dates over a period of the bond’s life
?A continuously callable bond may be called at any time after it becomes callable
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Callable Bond (Cont…)
?Freely callable bonds can be called at any time.
?Thus they offer the lender no protection.
?Deferred Callable Bonds on the other hand do offer some protection.
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Callable Bonds (Cont…)
?This is because they have a Call Protection Period during which they cannot be recalled.
?For instance if a bond with 20 years to maturity has a call protection period of 10 years, then it cannot be recalled for the first 10 years.
?After that, it will of course become freely callable.
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Callable Bond (Cont…)
?In practice when a bond is recalled, the issuer will pay the lender not just the face value, but usually also one year’s coupon.
?This additional amount is called the Call Premium. ?The call premium acts as a sweetener
?That is it makes such bonds more attractive to potential investors.
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Callable Bond (Cont…)
?One of the risks in a callable bond is therefore reinvestment risk
?That is, the bond will be called back when market rates are low and consequently the proceeds will have to be invested at a lower rate of interest.
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Callable Bond (Cont…)
?Second, the price appreciation potential for a callable bond in a declining interest rate environment is limited.
?This is because the market will increasingly expect the bond to be redeemed at the call price as rates fall.
?This is referred to as Price Compression.
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Callable Bond (Cont…)
?Given the reinvestment risk and price compression why would any investor want to hold such a bond.
?If he receives sufficient compensation in the form of a higher yield he may be willing to take the risk.
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Puttable Bonds
?Such bonds give the lender or the bondholder, the right to return the bond prematurely, and take back the face value.
?The option in such cases is with the bondholders or the lenders, and consequently they have to pay an option premium.
?This will manifest itself as a higher bond price, as compared to that of an otherwise similar plain vanilla bond.
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Puttable Bonds (Cont…)
?A higher bond price obviously means a lower yield. ?When will such a put option be exercised?
?Obviously when interest rates are rising. ?Under such conditions holders can return the bonds and buy fresh bonds with a higher coupon rate. ?This is precisely the scenario when the issuers would prefer that the holders hold on to the bonds.
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Puttable Bonds (Cont…)
?Since the put option works in favour of the holder and against the issuer, such bonds are characterized by higher prices or lower yields.
?At the time of issue a puttable will carry a lower coupon than an equivalent Plain Vanilla ?Subsequently a puttable will carry a higher price than a Plain Vanilla with the same coupon.
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Puttable Bonds (Cont…)
?The price at which a bond can be sold back by the holder acts as a floor price for the bond when interest rates rise. ?Since the holders can always return the bonds to the issuer at this price, they will never sell them to anyone else at a lower price.
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Convertible Bonds
?A conversion provision, if present in the bond, grants the bondholder the right to convert the bond into a predetermined number of shares of common stock of the issuer.
?It is therefore a Plain Vanilla corporate bond with a call option to buy the common stock of the issuer.
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Convertible Bonds (Cont…)
? The number of shares of common stock that a bondholder will receive if he converts the bond is called the Conversion Ratio.
?The conversion privilege may extend for all or only some portion of the bond’s life. ?The stated conversion ratio may also decline over time. ?The conversion ratio is always adjusted proportionately for stock splits and stock dividends.
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Convertible Bonds (Cont…) Illustration
? ABC Corporation has issued the following bond
?Maturity = 10 years ?Coupon rate = 8% ?Conversion ratio = 40 ?Face value = $1,000 ?Current market price = $900 ?Current share price = $20 ?Dividends per share = $1
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Convertible Bonds (Cont…)
?The conversion price = 1000 ------- = $25 40 ?The conversion value of a convertible bond is the value if it is converted immediately.
?Conversion value = Share price x Conversion Ratio
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Convertible Bond (Cont…)
?The minimum price of a convertible bond is the greater of:
?Its conversion value or ?Its value as a bond without the conversion option .
?This is also called the straight value of the bond.
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Convertible Bond (Cont…)
?To estimate the straight value we must determine the required yield on a nonconvertible bond with the same credit rating and similar investment characteristics.
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130
Convertible Bond (Cont…)
?In our case the conversion value is
?$20 x 40 = $800
?To determine the straight value we have to obtain the YTM of a comparable straight bond.
?Assume it is 10%.
? Straight value = 40PVIFA(5,20)+1000PVIF(5,20)
= $875.38
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Exchangeable Bonds
? These are a category of convertible bonds where the holder gets the shares of a different company when he converts the bonds.
? For instance if IBM were to issue convertible bonds, the holders would get shares of IBM if they were to convert. ? On the other hand, if IBM were to issue exchangeable bonds, the holders would get shares of another company, say Hewlett Packard.
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Exchangeable Bonds (Cont…)
?Exchangeable bonds may be issued by firms which own blocks of shares of another company and intend to sell them eventually.
?They may like to defer the sale and issue such bonds, because they may perceive a rise in the value of the shares. ?It may also be the case that they desire to defer their capital gains tax liability.
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Risks Inherent in Bonds
?What is risk? ?Risk is the possibility of loss arising due to the uncertainty regarding the outcome of a transaction. ?All bonds are exposed to one or more sources of risk.
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Credit Risk
? This risk refers to the possibility of default by the borrower. ? That is, it refers to the risk that coupon payments and/or principal payments may not be forthcoming as promised. ? Except for Treasury securities, which are backed by the full faith and credit of the Federal government, all debt securities are exposed to credit risk of varying magnitudes.
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Credit Evaluation
? At the time of issue, it is the issuer’s responsibility to provide accurate information about his financial soundness and creditworthiness. ? This is provided in the Offer Document or the Prospectus. ? But every potential investor cannot be expected to be able to properly evaluate the creditworthiness of a borrower. ? Thus in practice we have credit rating agencies.
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Credit Rating Agencies
? Such agencies specialize in evaluating the credit quality of a bond at the time of issue. ? They also monitor the issuing company, throughout the life of the bond, and modify their recommendations if required. ? The main rating agencies in the U.S. are
? Moody’s Investors Service ? Standard and Poor’s Corporation ?and Fitch Ratings.
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Rating Criteria
?Ratings are based on an in-depth analysis of the issuer’s financial condition and management ?And the specific source of revenue that has been specified as collateral for the bond.
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Investment Grade Ratings
Credit Risk
Highest Quality High Quality Upper Medium Medium
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Moody’s Ratings Aaa
Aa
S&P’s Ratings AAA
AA
Fitch’s Ratings AAA
AA
A
Baa
A
BBB
A
BBB
139
Non Investment Grade Ratings
Credit Risk
Somewhat Speculative
Moody’s
Ba
S&P
BB
Fitch
BB
Speculative
Highly Speculative Most Speculative Imminent Default Default
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B
Caa Ca C C
B
CCC CC C D
B
CCC CC C D
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Changes in Ratings
?Ratings can change over the course of time. ?If a rating change is being contemplated, the agency will signal its intentions.
?S&P will place the security on Credit Watch. ?Moody’s on Under Review. ?Fitch on Rating Watch.
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Bond Insurance
?A company can have its issue insured in order to enhance its credit quality.
?An insurance premium will have to be paid, but the coupon rate will come down. ?The insurance company will then guarantee the timely payment of the principal and interest.
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List of Specialist Insurance Companies
American Municipal Bond Assurance Corporation (AMBAC) ACA Financial Guaranty Asset Guaranty Insurance Company AXA Re Finance Capital Guaranty Insurance Company Capital Reinsurance Company Enhance Reinsurance Company Financial Guaranty Insurance Company Financial Security Assurance
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Insured Bonds
?Insured bonds receive the same rating as the insurance company, which is based on the insurer’s capital and claims-paying ability. ?In the U.S., the buyer of an uninsured bond can separately buy insurance for it on his own.
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Liquidity Risk
?This risk refers to the possibility that the market may be illiquid or thin at a time when the asset holder wants to buy or sell the security. ?A liquid market is characterized by the presence of a sizeable number of buyers and sellers at any point in time.
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Illiquid Markets
?In illiquid markets, potential buyers will have to offer a large premium over the fair value of an asset in order to acquire it, whereas potential sellers will have to accept large discounts at the time of sale. ?Illiquid markets are characterized by large bid-ask spreads, because trades will be few and far between.
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Interest Rate Risk
?The interest rate or yield is the key variable of interest in debt markets. ?The yield is the fundamental variable that drives the market. ?Interest rate risk refers to the fact that rates may move in an adverse fashion from the standpoint of the holder of the debt instrument.
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Interest Rate Risk
?Interest rate risk impacts fixed income securities in two ways.
?Firstly, all bonds with the exception of zeroes pay coupons
?These have to be reinvested.
?Reinvestment risk is the risk that market rates of interest may decline by the time a coupon is received.
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Interest Rate Risk (Cont…)
?If so, the coupon will have to be reinvested at a lower than anticipated rate of interest. ?Secondly a bond may not be held to maturity.
?If it is sold prior to maturity, it will have to be at the prevailing market price
?This will be inversely related to the prevailing yield.
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Interest Rate Risk (Cont…)
?Market Risk or Price Risk, is the risk that interest rates may be higher than anticipated at the time of sale, in which case the bond will have to be sold at a lower than anticipated price. ?The two risks work in opposite directions.
?Reinvestment risk arises because rates may fall subsequently ?Market risk arises because rates may rise subsequently.
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Inflation Risk
?Inflation refers to the erosion in the purchasing power of money. ?Most bonds promise fixed cash flows in dollar terms. ?Inflation risk is the risk that the purchasing power of money may have eroded by more than what was anticipated, by the time the cash flow from the bond is received.
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Inflation Risk (Cont…)
?High inflation will reduce the effective or Real rate of interest. ?The interest rate in monetary terms is called the Nominal Rate of interest. ?The Real Rate, on the other hand, is the nominal rate adjusted for changes in the purchasing power.
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Indexed Bonds
?These are bonds whose coupons are linked to a price index. ?Price indices are used as barometers of changes in the purchasing power of a currency. ?If inflation is high, so will be the index level and vice versa.
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Indexed Bonds (Cont…)
?Thus indexed bonds will offer higher cash flows during times of high inflation ?And relatively lower cash flows during periods of lower inflation
?This will ensure that the cash flow in real terms is kept at a virtually constant level.
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Timing Risk
? In the case of Plain Vanilla bonds, there is no uncertainty regarding the times to receipt of the cash flows. ? However, callable bonds can be recalled at any time. ? For a callable bond holder there is cash flow uncertainty, since he is unsure as to how many periods he is going to get coupons for, and also as to when the face value will be repaid.
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Timing Risk (Cont…)
?Thus holders of callable bonds will demand a premium for bearing this risk.
?That is why callable bonds trade at a lower price than otherwise comparable plain vanilla bonds.
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Foreign Exchange Risk
?This risk arises when the cash flows from a bond are denominated in a foreign currency. ?If the foreign currency depreciates in value with respect to the home currency, the returns will be lower than anticipated.
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Illustration
? A bond promises to pay a coupon of $10 every six months. ? Assume that the rate of exchange is Rs 50 per dollar.
?So an Indian bondholder will expect to receive Rs 500 every six months.
? However, what if the exchange rate at the time of the coupon payment is Rs 45.
?If so, he will receive only Rs 450.
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Valuation in between Coupon Dates
?While valuing a bond we assumed that we were standing on a coupon payment date.
?This is a significant assumption because it implies that the next coupon is exactly one period away.
?What should be the procedure if the valuation date is in between two coupon payment dates?
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The Procedure for Treasury Bonds
?Calculate the actual number of days between the date of valuation and the next coupon date.
?Include the next coupon date. ?But do not include the starting date.
?Let us call this interval N1.
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Treasury Bonds (Cont…)
?Calculate the actual number of days between the coupon date preceding the valuation date and the following coupon date.
?Once again include the ending date but exclude the starting date.
?Let us call this time interval as N2.
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Treasury Bonds (Cont…)
?The next coupon is then k periods away where
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Illustration
?There is a Treasury bond with a face value of $1,000. ?The coupon rate is 8% per annum, paid on a semi-annual basis. ?The coupon dates are 15 July and 15 January. ?The maturity date is 15 January 2022. ?Today is 15 September 2002.
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No. of Days Till the Next Coupon Date
Month No. of Days
September
October November December January TOTAL
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15
31 30 31 15 122
164
No. of Days between Coupon Dates
Month July August September October November December January TOTAL No. of Days 16 31 30 31 30 31 15 184
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Treasury Bonds (Cont…)
?K = 122/184 = .6630 ?This method is called the Actual/Actual method and is often pronounced as the Ack/Ack method. ?It is the method used for Treasury bonds in the U.S.
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The Valuation Equation
?Wall Street professionals will then price the bond using the following equation.
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Valuation
?In our example
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The Treasury Method
?There is a difference between the Wall Street approach and the approach used by the Treasury to value T-bonds.
?The difference is that the Treasury uses a simple interest approach for the fractional first period.
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The Treasury Method (Cont…)
? The Treasury will thus use the following equation.
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The Treasury Method (Cont…)
?The Treasury approach will always give a lower price because for a fractional period the simple interest approach will always give a larger discount factor than the compound interest approach.
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The 30/360 PSA Approach
? The Actual/Actual method is applicable for Treasury bonds in the U.S. ? For corporate bonds in the U.S. we use what is called the 30/360 PSA method.
?In this method the number of days between successive coupon dates is always taken to be 180. ?That is each month is considered to be of 30 days.
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The 30/360 Approach (Cont…)
?The number of days from the date of valuation till the next coupon date is calculated as follows. ?The start date is defined as ?D1 = (month1, day1,year1) ?The ending date is defined as ?D2 = (month2,day2,year2)
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The 30/360 Approach (Cont…)
?The number of days is then calculated as ?360(year2 – year1) + 30(month2 – month1) + (day2 – day1)
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Additional Rules
?If day1 = 31 then set day1 = 30 ?If day1 is the last day of February, then set day1 = 30 ?If day1 = 30 or has been set equal to 30, then if day2 = 31, set day2 = 30
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Examples of Calculations
Start Date
Jan-01-86 Jan-15-86 Feb-15-86 Jul-15-86 Nov-01-86 Dec-15-86 Dec-31-86 Feb-01-88 1/30/2013
End Date
Feb-01-86 Feb-01-86 Apr-01-86 Sep-15-86 Mar-01-87 Dec-31-86 Feb-01-87 Mar-01-88
Actual Days Days Based on 30/360 31 30 17 16 45 46 62 60 120 120 16 16 31 31 29 30 176
Pricing of A Corporate Bond
?Let us assume that the bond considered earlier was a corporate bond rather than a Treasury bond.
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Pricing (Cont…)
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30/360 ISDA
?The difference between 30/360 PSA and 30/360 ISDA is that the additional rule pertaining to the last day of February is not applicable.
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30/360 SIA
?The additional rules for this convention are the following.
?If day1 = 31, then set day1 = 30. ?If day1 is the last day of February and the bond pays a coupon on the last day of February then set day1 = 30. ?If day1 = 30 or has been set equal to 30, then if day2 = 31, set day2 = 30.
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30/360 European Convention
?In this convention, if day2 = 31, then it is always set equal to 30. ?So the additional rules are: ?If day1 = 31 then set day1 = 30 ?If day2 = 31 then set day2 = 30
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Examples of Calculations
Start Date End Date Actual Days Days Based on 30/360E
Mar-31-86
Dec-31-86
275
270
Dec-15-86
Dec-31-86
16
15
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Actual/365 Convention
?The difference between this and the Actual/Actual method is that the denominator in this convention will consist of 365 even in leap years.
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Actual/365 Japanese
?This is used for Japanese Government Bonds (JGBs) ?It is similar to the Actual/365 method. ?The only difference is that in this case, the extra day in February is ignored in leap years, while calculating both the numerator and the denominator.
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Actual/365 ISDA
? This day count convention is identical to the Actual/365 convention for a coupon period that does not include days falling within a leap year. ? However for a coupon period that includes days falling within a leap year, the day count is given by: #of days falling within the leap year ______________________________ + 366 #of days not falling within the leap year _________________________________ 365
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Actual/360 Convention
?This is a simple variant of Actual/365. ?This is the convention used for money market instruments in most countries.
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Global Conventions
Country Japan Japan Japan UK UK UK US Security T-bills JGBs Other Bonds Fixed rate gilts Index linked gilts Strips T-bills Convention Act/365 Japanese Act/365 Japanese Act/365 Japanese Act/Act Act/Act Act/Act Act/360
US
US India
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T-notes and T-bonds
Other bonds Government bonds Corporate bonds
Act/Act
30/360 PSA 30E/360
187
India
Act/365
Accrued Interest
? The price of a bond is the present value of all the cash flows that the buyer will receive when he buys the bond.
?Thus the seller is compensated for all the cash flows that he is parting with.
? This compensation includes the amount due for the fact that the seller is parting with the entire next coupon, although he has held it for a part of the current coupon period.
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Accrued Interest (Cont…)
?This compensation is called Accrued Interest. ?Let us denote the sale date by t; the previous coupon date by t1; and the following coupon date by t2 ?The accrued interest is given by
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Accrued Interest (Cont…)
?Both the numerator and the denominator are calculated according to the conventions discussed above.
?That is for U.S. Treasury bonds the Actual/Actual method is used, whereas for U.S. corporate bonds the 30/360 method is used.
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Why Accrued Interest?
?Why should we calculate the accrued interest if it is already included in the price calculation?
?The answer is that the quoted bond price does not include accrued interest. ?That is, quoted prices are net of accrued interest.
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Why Accrued Interest? (Cont…)
?The rationale is as follows. ?On July 15 the price of the Treasury bond using a YTM of 10% is $829.83. ?On September 15 the price using a yield of 10% is $843.5906.
?Since the required yield on both the days is the same, the increase in price is entirely due to the accrued interest.
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Why Accrued Interest (Cont…)
?On July 15 the accrued interest is zero. ?This is true because on a coupon payment date, the accrued interest has to be zero. ?On September 15 the accrued interest is
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Why Accrued Interest? (Cont…)
? The price net of accrued interest is ? $843.5906 - $13.4783 = $830.1123$, which is very close to the price of $829.83 that was observed on July 15. ? We know that as the required yield changes, so will the price. ? If the accrued interest is not subtracted from the price before being quoted, then we would be unsure as to whether the observed price change is due to a change in the market yield or is entirely due to accrued interest.
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Why Accrued Interest? (Cont…)
?However if prices are reported net of accrued interest, then in the short run, observed price changes will be entirely due to changes in the market yield.
?Consequently bond prices are always reported after subtracting the accrued interest.
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Clean versus Dirty Prices
?Quoted bond prices are called clean or add-interest prices. ?When a bond is purchased in addition to the quoted price, the accrued interest has also to be paid. ?The total price that is paid is called the dirty price or the full price.
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Negative Accrued Interest
? One logical question is
?Can the accrued interest be negative? ?That is, can there be cases where the seller of the bond has to pay accrued interest to the buyer.
? The answer is yes.
?In markets where bonds trade ex-dividend the dirty price will fall by the present value of the next coupon on the ex-dividend date and the dirty price will be less than the clean price.
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Example
?Take a T-bond that matures on 15 July 2021. ?It pays a 9% coupon semi-annually on 15 January and 15 July every year. ?The face value is 1000 and the YTM is 8%. ?Assume that we are on 5 January 2002 which is the ex-dividend date.
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Example (Cont…)
? Using the Actual/Actual convention we can calculate k to be 0.0543.
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Example (Cont…)
?The moment the bond goes ex-dividend the dirty price will fall by the present value of the forthcoming coupon, because the buyer will be no longer entitled to it.
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Example (Cont…)
? Thus the ex-dividend dirty price is
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Example (Cont…)
?This is the amount payable by the person who buys the bond an instant after it goes ex-dividend. ?The accrued interest an instant before the bond goes ex-dividend is: 0.09x1000 174 ________ x ____ = $ 42.5543 2 184
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Example (Cont…)
? Thus the clean price at the time of the bond going ex-dividend is 1140.4910 – 42.5543 = $1097.9367 ? The clean price is therefore greater than the exdividend dirty price.
?This represents the fact that the seller has to compensate the buyer because while the buyer is entitled to his share of the next coupon the entire amount will be received by the seller.
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Example (Cont…)
?The fraction of the next coupon that is payable to the buyer is 0.09x1000 10 _________ x ____ = $2.4457 2 184 ?Hence the buyer has to pay 1097.9367 – 2.4457 = $1095.4910 which is the ex-dividend dirty price.
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Yield Measures
?The yield or the rate of return from a bond can and is computed in various ways. ?We will discuss various yield measures and their relative merits and demerits.
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The Current Yield
?This is very commonly reported. ?Although it is technically very unsatisfactory. ?It relates the annual coupon payment to the current market price.
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Example of the Current Yield
?A 15 year 15% coupon bond is currently selling for $800. ?The current yield is given by
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Current Yield (Cont…)
?If you buy this bond for $800 and hold it for one year you will earn an interest income of $150.
?So your interest yield is 18.75%
?However, if you sell it after one year you will either make a Capital Gain or a Capital Loss.
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Current Yield (Cont…)
?What is a Capital Gain?
?If the price at the time of sale is higher than the price at which the bond was bought, the profit is termed as a Capital Gain. ?Else if there is a loss, it is termed a Capital Loss.
?The current yield does not take such gains and losses into account.
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Current Yield (Cont…)
? One question is: ?Should the current yield be based on the dirty price or the clean price ? The advantage of using the clean price is that the current yield will stay constant till the yield changes. ?However if the dirty price is used it will give rise to a
sawtooth pattern.
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Current Yield (Cont…)
?The current yield is used to estimate the cost of or profit from holding the bond. ?If short-term rates are higher than the current yield, the bond is said to involve a running cost.
?This is known as negative carry or negative funding.
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Simple YTM
?This yield measure attempts to rectify the shortcomings of the current yield by taking into account capital gains and losses. ?The assumption made is that capital gains and losses accrue evenly over the life of the bond.
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Simple YTM (Cont…)
?The formula is: Simple YTM = C M-P __ + ____ P PXN/2
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Simple YTM (Cont…)
?For the 15 year bond that we considered earlier
Simple YTM = 150 1000-800 _____+_________ = 20.42% 800 15 x 800
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Simple YTM (Cont…)
?The problem with the simple YTM is that it does not take into account the compound interest that can be earned by reinvesting the coupons. ?This will obviously increase the overall return from the bond.
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Yield to Maturity (YTM)
?The YTM is the interest rate that equates the present value of the cash flows from the bond (assuming that the bond is held to maturity), to the price of the bond. ?It is exactly analogous to the concept of the Internal Rate of Return (IRR) used in project valuation.
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YTM (Cont…)
?Consider a bond that makes an annual coupon of C on a semi-annual basis. ?The face value is M, the price is P, and the number of coupons remaining is N.
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YTM (Cont…)
?The YTM is the value of y that satisfies the following equation.
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YTM (Cont…)
? The YTM is a solution to a non-linear equation. ? We generally require a financial calculator or a computer to calculate it. ? However it is fairly simple to compute the YTM in the case of a coupon paying bond with exactly two periods to maturity.
?In such a case it is simply a solution to a quadratic equation.
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YTM for a Zero Coupon Bond
?The YTM is easy to compute in the case of zero coupon bonds. ?Consider a ZCB with a face value of $1,000, maturing after 5 years. ?The current price is $500. ?The YTM is the solution to
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Features of YTM
?The YTM calculation takes into account all the coupon payments ?As well as any capital gains/losses that accrue to an investor who buys and holds a bond to maturity.
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Sources of Returns From a Bond
?A bondholder can expect to receive income from the following sources. ?Firstly there are coupon payments which are typically paid every six months. ?There will be a capital gain/loss when a bond matures or is called before maturity or is sold before maturity.
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Returns From a Bond (Cont…)
? The YTM calculation assumes that the bond is held to maturity. ? Finally when a coupon is received it will have to be reinvested till the time the bond eventually matures or is sold or is called.
?Once again the YTM calculation assumes that the bond is held till maturity. ?The reinvestment income is nothing but interest on interest.
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YTM
?A satisfactory measure of the yield should take into account all the three sources of income. ?The current yield measure considers only the coupon for the first year. ?All the other factors are totally ignored.
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YTM (Cont…)
?The YTM calculation takes into account all the three sources of income. ?However it makes two key assumptions.
?Firstly it assumes that the bond is held till maturity. ?Secondly it assumes that all intermediate coupons are reinvested at the YTM itself.
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YTM (Cont…)
?The latter assumption is built in to the mathematics of the YTM calculation. ?The YTM is called a Promised Yield. ?It is Promised because in order to realize it you have to satisfy both the above conditions. ?If either of the two conditions is violated you may not get what was promised.
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The Re-investment Assumption
?Consider a bond that pays a semi-annual coupon of $C/2. ?Let r be the annual rate of interest at which these coupons can be re-invested. ?r would be dependent on the market rate of interest that is prevailing when the coupon is received, and need not be equal to y, the YTM, or c, the coupon rate.
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Reinvestment (Cont…)
?For ease of exposition we will assume that r is a constant for the life of the bond. ?However, in practice, it is likely that each coupon may have to be reinvested at a different rate of interest. ?Thus each coupon can be re-invested at a rate of r/2 per six monthly period.
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Reinvestment (Cont…)
?The coupon stream is an annuity. ?The final payoff from re-investment is the future value of this annuity. ?The future value is
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Reinvestment (Cont…)
?The future value represents the sum of all the coupons which are reinvested (which in this case is the principal), plus the interest from re-investment. ?The total value of coupons that are reinvested is
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Re-investment (Cont…)
?The interest on interest is therefore
The YTM Calculation assumes that r/2 = y/2.
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Reinvestment in Action
?Consider an L&T bond with 10 years to maturity. ?The face value is Rs 1,000. ?It pay a semi-annual coupon at the rate of 10% per annum. ?The YTM is 12% per annum. ?Price can be calculated to be Rs 885.295.
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Reinvestment in Action (Cont…)
?Assume that the semi-annual interest payments can be reinvested at a six monthly rate of 6%, which corresponds to a nominal annual rate of 12%. ?The total coupon income = 50 x 20 = 1000
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Reinvestment in Action (Cont…)
?Interest on interest gotten by reinvesting the coupons
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234
Reinvestment in Action (Cont…)
?Finally in the end you will get back the face value of Rs 1,000. ?So the total cash flow at the end = 1000 + 839.3 + 1000 = 2839.3 ?To get this income, the bondholder has to make an initial investment of 885.295.
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Reinvestment in Action (Cont…)
?So what is the effective rate of return? ?It is the value of i that satisfies the following equation
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236
Reinvestment in Action (Cont…)
?So the rate of return is 6% on a semiannual basis or 12% on a nominal annual basis, which is exactly the same as the YTM. ?So how was this return achieved? ?Only by being able to reinvest all the coupons at a nominal annual rate of 12%, compounded on a semi-annual basis.
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The Significance of the Reinvestment Rate
?The reinvestment rate affects only the interest on interest income. ?The other two sources are unaffected. ?If r > y, then the investor’s interest on interest income would be higher, and the return on investment, i, would be greater than the YTM, y.
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The Reinvestment Rate (Cont…)
? On the contrary, if r < y, then the interest on interest income would be lower, and the rate of return, i, would be less than the YTM, y. ? So if you buy a bond by paying a price which corresponds to a given YTM, you will realize that YTM only if ? You hold the bond till maturity ? You are able to reinvest all the intermediate coupons at the YTM.
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Reinvestment Risk
?One of the risks faced by an investor is that the future reinvestment rates may be less than the YTM which was in effect at the time the bond was purchased.
?This risk is called Reinvestment Risk. ?The degree of reinvestment risk depends on the time to maturity as well as the quantum of the coupon.
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Reinvestment Risk (Cont…)
?For a bond with a given YTM, and a coupon rate, the greater the time to maturity, the more dependent is the total return from the bond on the reinvestment income. ?Thus everything else remaining constant, the longer the term to maturity, the greater is the reinvestment risk.
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Reinvestment Risk (Cont…)
?For a bond with a given maturity and YTM, the higher the coupon rate, the more dependent is the total return on the reinvestment income. ?Thus everything else remaining the same, the larger the coupon rate, the greater is the reinvestment risk.
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Reinvestment Risk (Cont…)
?Thus premium bonds will be more vulnerable to such risks than bonds selling at par. ?Correspondingly, discount bonds will be less vulnerable than bonds selling at par.
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Zero Coupon Bonds and Reinvestment Risk
? If a zero coupon bond is held to maturity, there will be no reinvestment risk, because there are no coupons to reinvest. ? Thus if a ZCB is held to maturity, the actual rate of return will be equal to the promised YTM. ? If the risk is lower or absent, the return should also be less. ? Thus a ZCB will command a higher price than an otherwise similar Plain Vanilla bond.
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The Realized Compound Yield
? We will continue with the assumption that the bond is held till maturity. ? But we will make an explicit assumption about the rate at which the coupons can be reinvested. ? That is, unlike in the case of the YTM, we will no longer take it for granted that intermediate cash flows can be reinvested at the YTM.
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Illustration
?Let us reconsider the L&T bond. ?Assume that intermediate coupons can be reinvested at 7% for six months, or at a nominal annual rate of 14%. ?The total coupon income and the final face value payment will remain the same, but the reinvestment income will change.
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Illustration (Cont…)
?The interest on interest
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Illustration (Cont…)
?So the final amount received = 1000 + 1049.75 + 1000 = 3049.75 ?The initial investment is once again 885.295 ?Therefore, the rate of return is given by
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Illustration (Cont…)
?This is the rate of return for six months. ?The nominal annual return is 6.38 x 2 = 12.76%, which is greater than the YTM of 12%. ?The RCY is greater than the YTM, because we assumed that the reinvestment rate was greater than the YTM.
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Illustration (Cont…)
?Had we assumed the reinvestment rate to be less than the YTM, the RCY would have turned out to be less than the YTM. ?The RCY can be an ex-ante or an ex-post measure. ?Ex-ante means that we make an assumption about the reinvestment rate and then calculate the RCY.
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Illustration (Cont…)
?Ex-post means that we take into account the actual rate at which we have been able to reinvest and calculate the RCY.
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The Horizon Return
?Let us now relax both the assumptions which were used to calculate the YTM. ?Firstly the investor need not hold the bond until maturity. ?Secondly he may not be able to reinvest the coupons at the YTM.
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The Horizon Return (Cont…)
?Now the return will depend on three sources – the coupons received, the reinvestment income, and the price at which the bond is sold prior to maturity. ?The sale price of the bond would depend on the prevailing market yield at that point in time, and need not equal the face value.
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Illustration
?Assume that an investor with a 7 year investment horizon buys the L&T bond that we discussed earlier. ?He will get coupons for 14 periods (not 20). ?The total coupon income will be ?50x14 = 700 ?We will assume that the reinvestment rate is expected to be 7% per six monthly period.
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Illustration (Cont…)
?We will also assume that the investor expects the YTM after 7 years to be 12% per annum. ?The first step is to calculate the expected price at the time of sale. ?At that point in time the bond will have 3 years to maturity.
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Illustration (Cont…)
?The price using a YTM of 12% can be shown to be Rs 950.865. ?The interest on interest
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Illustration (Cont…)
?The total terminal cash flow = 700 + 427.50 + 950.865 = 2,078.365
? The initial investment as before is 885.295
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Illustration (Cont…)
?The nominal annual rate of return is 6.29x2 = 12.58% ?This is the Horizon Yield. ?Once again, it can be calculated ex-post or ex-ante.
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Yield to Call (YTC)
?This measure of the rate of return is used for callable bonds. ?The YTC is the yield that will make the present value of the cash flows from the bond equal to the price, assuming the bond is held till the call date. ?In principle a bond can have many possible call dates.
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YTC (Cont…)
?In practice the cash flows are usually taken only till the first call date, although they can easily be taken to any subsequent call date. ?The YTC is given by the equation
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YTC (Cont…)
? N* is the number of coupons till the call date. ? M* is the price at which the bond is expected to be recalled. ? M* need not equal the face value. ? In practice companies pay as much as one year’s coupon as a Call Premium at the time of recall. ? If so, M* = M + C
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Illustration (Cont…)
?Let us assume that the L&T bond is a callable bond and that the first call date is 7 years away. ?Assume that a call premium of Rs 100 will be paid if the bond is recalled.
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Illustration (Cont…)
?The YTC is the solution to the following equation
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Illustration (Cont…)
?The solution comes out to be 6.74%. ?So the YTC on an annual basis is 13.48%. ?The YTC is very important for Premium Bonds. ?The very fact that a bond is selling at a premium, indicates that the coupon is greater than the yield, and that therefore there is a greater chance of recall.
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The Yield to Worst
?In practice the investors compute the YTC for every possible call date. ?They then compute the YTM as well. ?The lowest of all possible values is called the Yield to Worst.
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Portfolio Yield
?Consider a case where you hold a portfolio or a collection of bonds. ?You cannot simply calculate the yield from the portfolio as a weighted average of the YTMs of the individual bonds.
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Portfolio Yield (Cont…)
?You have to first compute the cash flows from the portfolio, and then find that interest rate which will make the present value of the cash flows equal to the sum of the prices of the component bonds.
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Illustration
?Consider a person who buys a TELCO bond and a Ranbaxy bond. ?The TELCO bond has a time to maturity of 5 years, face value of 1000, and pays coupons semi-annually at the rate of 10% per annum. ?The YTM is 12% per annum.
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Illustration (Cont…)
?The Ranbaxy bond has a face value of 1000, time to maturity of 4 years, and pays a coupon of 10% per annum semiannually. ?The YTM is 16% per annum. ?Consider a portfolio consisting of one bond of each company. ?What is the portfolio yield?
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Illustration (Cont…)
?The first step is to calculate the two prices. ?The price of the TELCO bond can be shown to be 926.405. ?The price of the Ranbaxy bond can be shown to be 827.63. ?The total initial investment is therefore ?1,754.035
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The Cash Flow Table
Period
0 1 2 3 4 5
Investment
(1754.035)
Inflow from TELCO
50 50 50 50 50
Inflow from Ranbaxy
50 50 50 50 50
Total
(1754.035) 100 100 100 100 100
6
7 8 9
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50 50 50
50
50 1050
100
100 1100 50
10
1050
1050
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Illustration (Cont…)
?Using a financial calculator or a spread sheet, the portfolio yield can be calculated to be 13.76%.
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Duration
?Long term bonds are more susceptible to changes in yield than shorter term bonds ?Take two bonds with a face value of 1,000 ?Both pay a 10% coupon on a semi-annual basis ?YTM is 10% in both cases ?Bond A has a time to maturity of 5 years ?Bond B has a time to maturity of 10 years
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Duration (Cont…)
?Both bonds will obviously sell at par
?Since coupon = YTM = 10%
?Now assume that the YTM increases to 12%
?Price of bond A = 926.40 ?Price of bond B = 885.30 ?Price of A has declined by 7.34% ?Price of B has declined by 11.47%
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Duration (Cont…)
? The longer term bond is more impacted by the price change ? Why?
?The PV of a cash value is
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Duration (Cont…)
?The larger the value of t, the greater is the impact of a change in the YTM
?A 10 year bond has most of its cash flows coming in at later points as compared to a 5 year bond ?Thus its price is more vulnerable to changes in the yield
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Duration (Cont…)
?However the issue is not so simple. ?Consider a 5 year Zero with a face value of $1,000
?At 10% price = 613.91 ?At 12% price = 558.39 ?The price decline is 9.04%
?Why is a 5 year Zero more price sensitive than a 5 year coupon bond?
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Duration (Cont…)
?A coupon paying bond is
?A series of cash flows arising at 6 monthly intervals ?It is a portfolios of Zeroes ?Time to maturity only takes cognizance of the last cash flow ?The effective time to maturity
?Should be an average of the times to maturity of the component zeroes
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Duration (Cont…)
?What about a 5 year Zero?
?It gives rise to a single cash flow ?Its stated time to maturity is the same as its effective time to maturity
?It is obvious why the 5 year Zero is more price sensitive
?Its effective time to maturity is greater
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Duration (Cont…)
?Duration is a measure of the effective term to maturity of a Plain Vanilla bond
?It is a weighted average of the terms to maturity of the component cash flows ?The weights are the fractions of the total present value of the bond that is contributed by the cash flow
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Illustration
?Consider a 5 year 10% coupon paying bond ?With a face value of $1,000 ?YTM = 10%
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Illustration (Cont…)
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Illustration (Cont…)
?The weighted average time to maturity is
?8.1078 semi-annual periods ?Or 4.0539 years
?The weighted average time to maturity of a 5 year Zero is 5 years ?Thus a 5 years Zero is more price sensitive
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Duration (Cont…)
? The relationship between the duration of a bond and the rate of change of the percentage change in price is
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Duration (Cont…)
?Thus the rate of change of the percentage change in price is a function
?Of the duration of the bond ?And not its time to maturity
?Thus it is duration and not time to maturity that accurately captures the relationship between the change in yield and the corresponding price change.
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doc_229451536.pptx