Description
This is a presentation that highlights different types of bonds and various types of risks associated with them.
Fixed Income Securities
Group - II
1
SIBM - Finance (Group II)
A Fixed Income Security
? Is a security that offers a series of fixed interest
payments, and a fixed principal payment at
maturity
? Claim to a specified stream of income
? A loan, typically made by investors to a
corporation or government
? Prices not subject to wide fluctuations
Terminology of a Bond
? Par value: Face amount; paid at maturity
? Coupon interest rate: Stated interest rate. Multiply
by par value to get interest; Generally fixed
? Maturity: Years until bond must be repaid
? Issue date: Date when bond was issued
? Discount: Bond issued at value less than Par
Value/ trading at a discount to face value in
secondary market
? Premium: Bond that is priced higher than face
value
Cash Flow Determination
• Simple Cash Flow
? FV is the future value (i.e. cash flow expected in
the future)
? PV is the present value
? r is the rate of return
FV = PV (1 + r)
• Multiple Cash Flow
PV = Coupon
1
+ Coupon
2
+ …+ Coupon
T
+Par
(1 + r)
1
(1 + r)
2
(1 + r)
T
Types of Bonds
• Coupon (Fixed Interest)
• Zero Coupon - no periodic coupon payment
? Sold at discount; matures at par
? Also called „Pure Discount Bond?;
Types of Bonds
• Callable Bond
? allows issuer to repurchase bond at a specified call
price prior to maturity
? Call Date: date after which bond may be bought
back
? Typically bonds are available with call protection
initial time during which bonds are not callable
? Call Price: pre specified price; usually a premium
is paid
? Usually after falling rates
Types of Bonds
• Puttable Bond
? Allows an option to Buyer/Holder to sell bond
back to the issuer
? Usually after rising rates
• Convertible Bonds
? Gives an option to Buyer/Holder to exchange
bonds for pre specified # of shares after a pre
specified period of time
? Lower coupons & YTM
Types of Bonds
• Investment Grade Bonds rated BBB (S&P) or
Baa (Moody?s) and above
• Junk Bonds: speculative grade; rated below
investment grade, highly risky in nature
• Debenture - unsecured bonds, could be
convertible or non convertible
Types of Bonds
• International - Bonds issued in a country different
from borrower (eg: Resurgent India Bonds in the
US)
• Eurobond – Bonds issued in currency of one country
but sold in another
eg: Eurodollar bonds - dollar denominated sold
outside US
• Yankee Bonds –a bond denominated in U.S. dollars
and is publicly issued in the U.S. by foreign banks
and corporations
• Sukuk – the Arabic name for a financial certificate
but can be seen as an Islamic equivalent of bond
Types of Bonds
• STRIPS
? STRIPS (Separately Traded Interest and Principle
Securities) allow owner to register and sell interest
payments and principle an individual marketable
securities
? STRIPS are essentially longer term discount bonds
Example
Face Value = Rs 100
Rate of interest = 5% (annual)
Maturity = 3 years
Date of Payment of Interest – June 1
The following table shows how this one
bond can be stripped into 4 bonds
Types of Bonds
• TIPS
? Note that because bond payments are expressed in
a currency, their value in terms of purchasing
power is influenced by inflation (nominal = real +
inflation)
? To counter this, the treasury began issuing
inflation indexed securities.
? The face value of TIPS are continuously adjusted
according to changes in the CPI to protect
investors from inflation
Example
• A two year T-Note with a 5% annual coupon will
be worth Rs 96.23 if interest rates are equal to
7%
Types of Bonds
• Medium Term Notes
? A note that usually matures in five to 10 years.
? A corporate note continuously offered by a company to investors
through a dealer. Investors can choose from differing maturities,
ranging from nine months to 30 years.
? Notes range in maturity from one to 10 years. By knowing that a
note is medium term, investors have an idea of what its maturity
will be when they compare its price to that of other fixed-income
securities. All else being equal, the coupon rate on medium-term
notes will be higher than those achieved on short-term notes.
? This type of debt program is used by a company so it can have
constant cash flows coming in from its debt issuance; it allows a
company to tailor its debt issuance to meet its financing needs.
Medium-term notes allow a company to register with the SEC
only once, instead of every time for differing maturities.
15
Types of Risk Bondholders Face
• Interest Rate Risk
• Reinvestment Risk
• Default (Credit) Risk
• Inflation Risk
• Call Risk
• Liquidity Risk
Interest Rate Risk
• The risk that interest rates may change once the
bonds are issued
• When interest rates fall, bonds values rise and
vice versa
• Example
Face Value – 100, Coupon – 10%, Maturity of A –
5 years and B – 10 years, Current Interest Rates
– 7%
Reinvestment rate risk
• The risk that CFs will have to be reinvested in the
future at lower rates, reducing income.
• Example – Invest in a bond with a cumulative
interest on the following conditions
Face Value – Rs 100 , Maturity – 30 years
Rate of interest – 5%
Interest Rate Risk + Reinvestment Rate
Risk
• Long-term bonds: High interest rate risk, low
reinvestment rate risk.
• Short-term bonds: Low interest rate risk, high
reinvestment rate risk.
• Nothing is riskless!
Default (Credit) Risk
• Credit risk is the risk that the party that has
issued the bond or instrument will default on
payment of interest or principal
• It would most likely happen in the case of
bankruptcy
What factors affect default risk and
bond ratings?
• Financial performance
? Debt ratio
? Current ratios
• Provisions in the bond contract
? Secured versus unsecured debt
? Senior versus subordinated debt
? Guarantee provisions
? Sinking fund provisions
? Debt maturity
• Other factors
? Earnings stability
? Regulatory environment
? Potential product liability
? Accounting policies
Inflation Risk
• Because of their relative safety, bonds tend not to
offer extraordinarily high returns. That makes them
particularly vulnerable when inflation rises.
• Example
Treasury bond interest = 3.32%. If the rate of
inflation rises to, say, 4 percent, your investment is
not “keeping up with inflation.” In fact, you?d be
“losing” money because the value of the cash you
invested in the bond is declining. You?ll get your
principal back when the bond matures, but it will be
worth less.
Other Risk
? Call Risk
? Call risk refers to the risk that a bond may be
called when the investor does not want it to be
called.
• Liquidity Risk
? Investors may have difficulty finding a buyer when
they want to sell and may be forced to sell at a
significant discount to market value.
24
SIBM - Finance (Group II)
Bond Pricing
• Bond Pricing Fundamentals
1. Pricing a Coupon Bond
2. Pricing a Zero Coupon Bond
3. Pricing a Floater
4. Pricing a Callable/Puttable Bond
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SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Present Value of Cash Flows:
? P is the bond price
? C is the periodic coupon payment
? N is the number of years to maturity
? M is the (face value) payment at maturity
? y is the “risk-adjusted discount rate” (or yield to
maturity, or IRR)
( )
( ) ( ) ( ) ( )
N N 3 2
1
M
1
C
...
1
C
1
C
1
C
P
y y y y
y
+
+
+
+ +
+
+
+
+
+
=
26
SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Determining the Cash Flows
? Periodic Coupon Interest Payments
? Par Value at Maturity
• Determining the Required Yield
? Required Yield
? Theoretical arguments for using different yields to
discount
• Determining the Price
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SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Rates are different over time:
• Here, each spot rate r
n
is the discount rate for a
cash flow in year n that can be locked in today
• E.g., r
3
(3-year spot rate) is the rate the market uses
to value a single payment three years from today
P =
C
1+ r
1
( )
+
C
1 + r
2
( )
2
+
C
1 + r
3
( )
3
+... +
C
1+ r
N
( )
N
+
M
1+ r
N
( )
N
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SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Take a 3-year 10% coupon bond with face value = 1000, assuming annual
coupon payments:
? Spot rates: r
1
=10%, r
2
=12%, r
3
=14%
? Yield-to-Maturity
Price =
100
1.10 ( )
+
100
1.12 ( )
2
+
1100
1.14 ( )
3
= 913.1
( ) ( ) ( )
( ) ( ) ( )
% 7 . 13
137 . 1
1100
137 . 1
100
137 . 1
100
y 1
1100
y 1
100
1
100
913.1
3 2
3 2
=
+ + =
+
+
+
+
+
=
y
y
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SIBM - Finance (Group II)
1. Pricing a Coupon Bond
? Determining the Price when the Settlement Date
Falls Between Coupon Periods:
i = Periodic Interest Rates
period coupon in the days of No.
payment coupon next and Settlement between days of No.
W =
( ) ( ) ( ) ( ) ( )
w 1 - N w 1 - N W 2 W 1 W
1
M
1
C
...
1
C
1
C
1
C
P
+ + + +
+
+
+
+ +
+
+
+
+
+
=
i i i i i
30
SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Determining the Price when the Settlement Date
Falls Between Coupon Periods:
? Day Count Conventions
? Accrued Interest and Clean Price:
period coupon in the days of No.
date Settlement payment to coupon last from days of No.
* AI C =
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SIBM - Finance (Group II)
2. Pricing a Zero Coupon Bond
• Also the present value of expected cash flows:
? Incase of a Zero Coupon Bond the only cash flow
is the Maturity Value.
? Notice that YTM = the spot rate only for zero-
coupon bonds:
N N
N
y
M
r
M
) 1 ( ) 1 (
P
+
=
+
=
32
SIBM - Finance (Group II)
2. Pricing a Zero Coupon Bond
• Price of 3-year zero coupon bond with face value = 1000
? Spot rates: r
1
=10%, r
2
=12%, r
3
=14%
? Yield-to-Maturity
( )
675
14 . 1
1000
Price
3
= =
( )
% 14
y 1
1000
75 6
3
=
+
=
y
33
SIBM - Finance (Group II)
Relationship between Yield, Price,
Coupon, Time to Maturity
• Relationship Between required
Yield and Price at a given time:
• 20 year, 10% coupon Bond
34
SIBM - Finance (Group II)
Relationship between Yield, Price,
Coupon, Time to Maturity
• Relationship among Coupon
Rate, Required Yield and
Price at a given time:
? As yields in the marketplace
change, the only variable
that can change to
compensate an investor for
the new required yield in
the market is the price of
the bond.
? The capital appreciation
realized by holding the bond
to maturity represents a
form of interest to a new
investor to compensate for a
coupon rate that is lower
than the required yield.
35
SIBM - Finance (Group II)
Relationship between Yield, Price,
Coupon, Time to Maturity
• Time Path of a Bond:
? If Yield remains the same:
? As bond approaches
maturity, it becomes closer
to its par value
? And equals its par value at
Maturity
36
SIBM - Finance (Group II)
3. Pricing a Floater
• Floater:
Coupon Rate=Reference Rate+Quoted Margin
• Inverse Floater:
Coupon Rate=K-L*(Reference Rate)
Ex: 18% - 2.5*(three month LIBOR)
• The Price of a Floater depends on
? The spread over the reference rate
? Any restriction on resetting the coupon rate.
ex: Cap, Floor
37
SIBM - Finance (Group II)
3. Pricing a Floater
• Thus: Factors that affect a Floaters price are
1. Time Remaining to next coupon reset date
? The more time to next coupon reset date, the more it
behaves like a fixed-rate security – Greater potential
fluctuation.(example)
? For a floater in which the cap is not binding and the
required margin is not different from the quoted
margin, will trade at par.
SIBM - Finance (Group II)
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3. Pricing a Floater
2. Changes in the markets required margin
? The required margin depends on
-Margin Available in competitive funding Markets
-Credit Quality of the Issue
-Presence of a Call or Put option
-Liquidity of the Issue
SIBM - Finance (Group II)
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3. Pricing a Floater
3. Whether or not the cap or floor is reached
? Once the Cap is reached, the floater offers a below-
market coupon, thus the bond will trade at a
discount
? When a Cap or a float is reached, the bond is
effectively a fixed-rate security
SIBM - Finance (Group II)
40
4. Pricing a Callable Bond
• Price-Yield relationship for a Callable Bond
• Negative Convexity: Price appreciation will be less than the Price
depreciation for a large change in yield
• A bond can still trade ABOVE its call price even if it is highly likely
to be called
SIBM - Finance (Group II)
41
4. Pricing a Callable Bond
• Valuation Model:
? Hypothetical Zero Coupon Yield Curve
? By using the Bootstrapping Method we can
estimate the forward rates
SIBM - Finance (Group II)
42
4. Pricing a Callable Bond
1. Introducing Interest Rate Volatility
? This can be done by introducing a binomial
interest-rate tree
SIBM - Finance (Group II)
43
4. Pricing a Callable Bond
? Binomial Interest-Rate Tree
?r
1,H
= r
1,L
* e
2??t
? ? = Assumed Volatility of the One Year Forward
Rate
? r
1,L
= The Lower One Year Rate, one year from now
? r
1,H
= The Higher One Year Rate, one year from now
SIBM - Finance (Group II)
44
4. Pricing a Callable Bond
? Binomial Interest-Rate Tree
? Ex: Suppose that r
1,L
= 4.074% and ? = 10% per year
? Thus r
1,H
=
SIBM - Finance (Group II)
45
4. Pricing a Callable Bond
? Binomial Interest-Rate Tree
? In the Second Year there are 3 possibilities:
? Thus:
&
SIBM - Finance (Group II)
46
4. Pricing a Callable Bond
? Binomial Interest-Rate Tree
SIBM - Finance (Group II)
47
4. Pricing a Callable Bond
2. Determining the Value at a Node
? Future Cash Flows depends on:
1. The bond's value one year from now
2. The coupon payment one year from now
? Ex: Suppose that we are interested in the bond's
value at N
H
. The cash flow will be either the bond's
value at N
HH
plus the coupon payment or the
bond's value at N
HL
plus the coupon payment.
SIBM - Finance (Group II)
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4. Pricing a Callable Bond
2. Determining the Value at a Node
SIBM - Finance (Group II)
49
4. Pricing a Callable Bond
2. Determining the Value at a Node
? The present value of these two cash flows using
the one-year rate at the node, r*, is
? Thus the value at the node is:
SIBM - Finance (Group II)
50
4. Pricing a Callable Bond
3. Constructing the Binomial Tree
? Compute the value of a 4%, 2 Yr. bond, Market
Price = $100
SIBM - Finance (Group II)
51
4. Pricing a Callable Bond
1. Select a value for r
1
. Recall that r
1
is the lower one-
year forward rate one year from now. We arbitrarily
selected a value of 4.5%
2. Determine the corresponding value for the higher
one-year forward rate. This rate is related to the
lower one-year forward rate as follows: r
1
e
2?
3. Compute the bond?s value one year from now: In our
case $100 + $4 = $104
4. Compute the present value of this amount using the
higher forward rate of 5.496%. V
H
= $98.582
5. Compute the present value of the amount in 3 using
the lower forward rate of 4.5%. V
L
= $99.522
SIBM - Finance (Group II)
52
4. Pricing a Callable Bond
7. Add the coupon to V
H
and V
L
to get the cash flow at NH
and NL, respectively. In our example we have $102.582
for the higher rate and $103.522 for the lower rate.
8. Calculate the present value of the two values using
the one-year forward rate using r,. At this point in
the valuation, r, is the root rate, 3.50%. Therefore:
SIBM - Finance (Group II)
53
4. Pricing a Callable Bond
9. The average value thus calculated is $99.567
10. Compare this value with the price of the bond, if the
it matches then the r
1
used in this is the one we seek.
If not we have to find the r
1
by trial & error
11. By trial and error r
1
= 4.074%
12. We can use this info. to grow the tree & similarly
find the value for r
2
SIBM - Finance (Group II)
54
4. Pricing a Callable Bond
• Thus the tree formed can be used to value any
option – free bond, or any bond with option
• Arbitrage Free Tree
SIBM - Finance (Group II)
55
4. Pricing a Callable Bond
4. Valuing a callable bond
? 5.25% corporate bond with 3 years to maturity,
callable in one year at $100.
? V
t
= min[call price, PV(future cash flows)]
SIBM - Finance (Group II)
56
4. Pricing a Callable Bond
? The discounting process explained earlier is used to
calculate the value at the end of year 2
? The issuer calls the issue if the PV of future cash flows
exceeds the call price
? N
L
and N
LL
,th e values from the recursive valuation
formula ($101.001 at N
L
and $100.689 at N
LL
) exceed
the call price ($100) and therefore have been struck
out and replaced with $100.
? Each time a value derived from the recursive valuation
formula has been replaced, the process for finding the
values at that node is reworked starting with the
period to the right. The value for this callable bond is
$101.432.
SIBM - Finance (Group II)
57
Pricing a Puttable bond
• Similarly a Putable bond can valued using the
Binomial Tree
• V
t
= max[put price, PV(future cash flows)]
SIBM - Finance (Group II)
58
SIBM - Finance (Group
II)
59
60
Sensitivity analysis
61
Bond price
?Is always the present value of the
benefits associated with bond
discounted at yield
62
?At maturity, the value of any bond
must equal its par value.
?The value of a premium bond would
decrease to 1,000.
?The value of a discount bond would
increase to 1,000.
?A par bond stays at 1,000 if k
d
remains constant.
63
M
Bond price
Years remaining to Maturity
1,372
1,211
1,000
837
775
30 25 20 15 10 5 0
k
d
= 7%.
k
d
= 13%.
k
d
= 10%.
64
Example on bond price
? Suppose I have a, 100, 2 year T-Note with a 5%
annual coupon rate. If the annual market rate of
interest is 7%, how much is this bond worth?
65
? Suppose I have a, 100, 2 year T-Note with a 5%
annual coupon rate. If the annual market rate of
interest is 7%, how much is this bond worth?
(the semiannual coupon interest rate is 2.5%, the
semiannual market interest rate is 3.5%)
Example on bond price
66
Example on bond price
? Suppose I have a, 100, 2 year T-Note with a 5% annual coupon
rate. If the annual market rate of interest is 7%, how much is
this bond worth?
2.50/(1.035) = 2.42
2.50/(1.035)^2 = 2.33
2.50/(1.035)^3 = 2.25
+102.50/(1.035)^4 = 89.23
= 96.23
Note: This bond is currently selling at a discount.
67
Bond yields
? Coupon rate or coupon Yield
? Yield to Maturity (YTM)
? Current Yield
? Total Yield
? Yield on a Discounted Basis (YDB)
68
=
Annual coupon
Coupon rate
Par value
Coupon yield
?Yield is basically the rate of interest i.e.
rate attached with the coupon
69
? Suppose I have a bond of 100 face value having
current price of 96.23, with semiannual coupon of
2.50. How much is this bond yield?
Yield = (2.50 x 2)/100 = 5.0%
Example on coupon yield
70
Yield to maturity
?YTM is the rate of return earned on a
bond held to maturity. Also called
“promised yield.”
? The discount rate that equates a
bond’s price with the present value
of all future cash flows
? Also referred as investor’s required
or expected return on bond
71
What’s the YTM on a 10-year, 9%
annual coupon, 1,000 par value bond
that sells for 887?
90 90 90
0 1 9 10
k
d
=?
1,000
PV
1
.
.
.
PV
10
PV
M
887 Find k
d
that “works”!
...
72
10 -887 90 1000
N I/YR PV PMT FV
10.91
( ) ( ) ( )
V
INT
k
M
k
B
d
N
d
N
=
1 1
1
...
+
INT
1 + k
d
( ) ( ) ( )
887
90
1
1 000
1
1 10 10
=
k k
d d
+
90
1 + k
d
,
Find k
d
+ +
+ +
+ +
+ +
INPUTS
OUTPUT
...
73
2(10) 13/2 100/2
20 6.5 50 1000
N I/YR PV PMT FV
-834.72
Find the value of 10-year, 10% coupon,
semiannual bond if k
d
= 13%.
INPUTS
OUTPUT
74
Find YTM if price were 1,134.20.
10 -1134.2 90 1000
N I/YR PV PMT FV
7.08
Sells at a premium. Because
coupon = 9% > k
d
= 7.08%,
bond’s value > par.
INPUTS
OUTPUT
75
?If coupon rate < k
d
, bond sells at a
discount.
?If coupon rate = k
d
, bond sells at its
par value.
?If coupon rate > k
d
, bond sells at a
premium.
?If k
d
rises, price falls.
?Price = par at maturity.
76
Yield to maturity
? Assuming
• Investors purchased the bond at current price
• The bond is held until its maturity
• Coupons received intermittently will be
reinvested at the same rate
77
Measurement and management of IRR
? Increase in YTM results in depreciation of existing
portfolio. (i.e. higher the YTM, lower the price of an
existing security)
? At the end of each financial year, RBI prescribes the
YTM to be applied to the Govt.. Securities and the
bond portfolio of banks.
? Any sharp increase in YTM towards the close of a
financial year has the potential of a steep
depreciation which could wipe out the profits of a
bank during the entire year.
78
Other yields
Current yield =
Capital gains yield =
= YTM = +
Annual coupon pmt
Current price
Change in price
Beginning price
Exp total
return
Exp
Curr yld
Exp cap
gains yld
79
Find current yield and capital gains
yield for a 9%, 10-year bond when the
bond sells for 887 and YTM = 10.91%.
Current yield =
= 0.1015 = 10.15%.
90
887
As a useful approximation to YTM, the current yield is simply the
coupon payment as a percentage of the price.
80
YTM = Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= 10.91% - 10.15%
= 0.76%.
Total yield is the current yield plus any
capital gain/loss
81
Yield on a discount basis
?Yield on a discount basis is a commonly
used approximation for yield to maturity
for discount bonds.
YDB = FV – P ___360________
FV Days to Maturity
82
Example on YDB
?A T Bill with 28 days until maturity has a
bid YDB equal to .87%. What is the bid
price?
83
Example on YDB
?A T Bill with 28 days until maturity has a
bid YDB equal to .87%. What is the bid
price?
.87% = .0087 (annual rate)
.0087(28/360) = (.0007) (28 day rate)
P = (1 - .0007) $100 = $99.93 ($99:30)
84
Annualizing
?Likewise, if a 180 day T-Bill is selling for
97.56, then the annualized yield is
YTM = FV – P ___365_____
P Days to Maturity
= (100 -97.56) (365) = .05 (5%)
97.56 180
85
Reading the newspaper
Rate Maturity Bid Ask Chg. Ask Yld
7.25 May 08 101:20 101:21 -1 .74
86
Reading the newspaper
?Rate: Coupon Rate
?Maturity: Expiration Date
?Bid: Buying Price in 32nds
?Ask: Selling Price in 32nds
?Ask Yld: Current Yield Based on Ask
Price
87
Current
Price
P
r
i
c
e
Current Yield
Yield
Price/Yield Curve
Duration =
Slope of Price/Yield Curve
Convexity =
Change in Slope of Price/Yield Curve
Price yield relationship
88
Yield to call
?Effectively YTM for the time period
before call option can be exercised
89
A 10-year, 10% semiannual coupon,
1,000 par value bond is selling for
1,135.90 with an 8% yield to maturity.
It can be called after 5 years at 1,050.
What’s the bond’s nominal yield to
call (YTC)?
10 -1135.9 50 1050
N I/YR PV PMT FV
3.765 x 2 = 7.53%
INPUTS
OUTPUT
90
k
Nom
= 7.53% is the rate brokers would
quote. Could also calculate EFF% to
call:
EFF% = (1.03765)
2
- 1 = 7.672%.
This rate could be compared to monthly
mortgages, and so on.
91
If you bought bonds, would you be
more likely to earn YTM or YTC?
?Coupon rate = 10% vs. YTC = k
d
=
7.53%. Could raise money by selling
new bonds which pay 7.53%.
?Could thus replace bonds which pay
100/year with bonds that pay only
75.30/year.
?Investors should expect a call, hence
YTC = 7.5%, not YTM = 8%.
92
?In general, if a bond sells at a
premium, then if coupon > k
d
, so a
call is likely.
?So, expect to earn:
?YTC on premium bonds.
?YTM on par & discount bonds.
93
Market risk management
94
Duration
? Can be defined as the weighted average of the time
periods.
D t
PV CF
P
t
B
t
M
=
¸
(
¸
(
=
¿
( )
0
1
D w D
p i i
=
¿
95
?Duration of 4-year, 9% coupon Bond
with yield being 10%:
D t
PV CF
P
t
B
t
M
=
¸
(
¸
(
=
¿
( )
0 1
t CF
CF PV CF
P
t Weight
P D
t
t
t
t
B
B
( . )
( )
( )( )
. . .
. . .
. . .
. . .
. .
110
1 90 81818 0 084496 0 084496
2 90 74 348 0 076815 0153630
3 90 67 618 0 069832 0 209496
4 1090 744 485 0 768857 3075428
968 30 352
0
0
= =
96
Duration
?Duration is also a measure of a bond’s price
sensitivity to interest rate changes.
?This measure of duration is known as the
modified duration; the measure of duration as
a weighted average of the time periods is
known as Macaulay's duration.
D
P
YTM
P
YTM
B B
= ~ =
% %
%
A
A
A
A
0 0
c
97
Derivation
?Duration:
?Take derivative with respect to y:
P
CF
y
CF y
P CF y CF y CF y
B t
t
t
M
t
t
t
M
B
M
M
0
1 1
0 1
1
2
2
1
1
1 1 1
=
+
= +
= + + + + ··· + +
=
÷
=
÷ ÷ ÷
¿ ¿
( )
( )
( ) ( ) ( )
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + · ·· + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
98
Derivation
? Factor out
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + ·· · + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
÷ + = ÷
+
÷
( )
( )
1
1
1
1
1
y
y
( )
( )
dP
dy y
CF y CF y M CF y
dP
dy y
CF
y
CF
y
M
CF
y
dP
dy y
PV CF PV CF M PV CF
B
M
M
B
M
M
B
M
= ÷
+
+ + + + · · · + +
= ÷
+ +
+
+
+ · · · +
+
|
\
|
.
|
= ÷
+
+ + · · · +
÷ ÷ ÷
1
1
1 1 2 1 1
1
1
1
1
2
1 1
1
1
1 2
1
1
2
2
1
1
2
2
1 2
( )
( ) ( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( ) ( ) ( ) ( )
99
Derivation
Divide through by P:
dP
dy P
dP P
dy y
PV CF
P
PV CF
P
M
PV CF
P
B
B B
M
B
1 1
1
1 2
1
0
2
0 0
= = ÷
+
+ + · · · +
|
\
|
.
|
/
( )
( )
( )
( )
( )
( )
( )
Modified Duration
dP P
dy y
t
PV CF
P
t
M
t
B
= = ÷
+
|
\
|
.
|
=
¿
/
( )
( ) 1
1
1 0
100
Duration
D
P
YTM YTM
t
PV CF
P
B
t
B
t
M
= = ÷
+
¸
(
¸
(
=
¿
%
( )
( ) A
A
0
0
1
1
1
Modified Duration Macaulay s Duration '
Example
Modified Duration
:
( . )
( . ) . = ÷ = ÷
1
110
35 318
101
Duration
?Annualized Duration: Duration is defined in terms
of the length of the period between payments. If
the CFs are distributed annually, then duration is
in years; if CFs are semi-annual, then duration is
measured in half years. The convention is to
expressed duration as an annual measure. The
annualized duration is obtained by dividing duration
by the number of payments per year
:
Annualized Duration
Duration for n periods
n
=
÷
102
Duration
? Example: The duration in half-years for a 10-year, 9%
coupon bond selling at par (F= 100) and paying coupons
semiannually is -13 and its annualized duration is -6.5:
%
.
. ( . )
[ ( . /. )]
( . )
.
A
A
P
y
Annualized Duration
B
0
2 20 21
4 5
045
1
1
1045
20 100 4 5 045
1045
100
13
13
2
65
= ÷
÷
¸
(
¸
(
+
÷
= ÷
= ÷ = ÷
%
( )
[ ( / )]
( )
A
A
P
y
C
y y
M F C y
y
P
B
M M
B
0
2 1
0
1
1
1 1
= ÷
÷
+
¸
(
¸
(
+
÷
+
+
103
Duration
?Uses:
? Descriptive Parameter: Measure of a bond’s price sensitivity
to interest rate changes -- a measure of a bond’s volatility.
Note, duration is consistent with bond price relation:
volatility greater Duration Greater period Greater ¬ ¬
volatility greater Duration Greater Coupon Lower ¬ ¬
104
Duration
?Define Strategies: Use duration to define active
(speculative) and passive bond strategies.
?Examples:
?Rate-Anticipation Swap: Rates expected to decrease
across all maturities, go long in high duration bonds.
Rates expected to increase across all maturities, change
bond portfolio composition so that it has lower duration
bonds.
?Bond Immunization Strategy: Bond immunization is bond
strategy of minimizing market risk by buying a bond or a
portfolio of bonds with a duration equal to the certain fix D.
105
Duration limitation
? Estimate the percentage change in a bond’s price for a given
change in rates:
?For 10-year, 9% bond, an increase in the annualized yield
by 10BP (.09 to .0910) would lead to a .65% decrease in
price (the actual is .6476%). A 200BP increase (9% to
11%) would lead to an estimated price decrease of 13%;
the actual decrease, though, is only 12%.
%
( )
[ ]
% [ ] ( )
A
A
A A
P
YTM
Modified Duration
P Modified Duration YTM
B
B
=
=
% [ . ] (. . ) . AP
B
= ÷ ÷ = ÷ 6 5 0910 09 0065
% [ . ] (. . ) . AP
B
= ÷ ÷ = ÷ 6 5 11 09 13
106
Convexity
?Duration is a measure of the slope of the price-
yield curve at a given point -- first-order derivative.
?Convexity is a measure of the change in the slope
of the price-yield curve -- second-order derivative.
?Convexity measures how bowed-shaped the price-
yield curve is.
107
Convexity
? Property: The greater a bond’s convexity, the greater its capital
gains and the smaller its capital losses for given absolute
changes in yields.
YTM
P
B
0
y
0
P
B
0
YTM
y
1
y
2
K Gain
{
K Loss
{
y
0
y
1
y
2
K Gain
K Loss
{
{
-
-
-
-
-
-
y y y y
1 0 2 0
÷ = ÷
108
Derivation
?Convexity:
?Take derivative with respect to y:
P
CF
y
CF y
P CF y CF y CF y
B t
t
t
M
t
t
t
M
B
M
M
0
1 1
0 1
1
2
2
1
1
1 1 1
=
+
= +
= + + + + ··· + +
=
÷
=
÷ ÷ ÷
¿ ¿
( )
( )
( ) ( ) ( )
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + · ·· + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
109
Derivation
? Factor out
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + ·· · + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
÷ + = ÷
+
÷
( )
( )
1
1
1
1
1
y
y
( )
( )
dP
dy y
CF y CF y M CF y
dP
dy y
CF
y
CF
y
M
CF
y
dP
dy y
PV CF PV CF M PV CF
B
M
M
B
M
M
B
M
= ÷
+
+ + + + · · · + +
= ÷
+ +
+
+
+ · · · +
+
|
\
|
.
|
= ÷
+
+ + · · · +
÷ ÷ ÷
1
1
1 1 2 1 1
1
1
1
1
2
1 1
1
1
1 2
1
1
2
2
1
1
2
2
1 2
( )
( ) ( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( ) ( ) ( ) ( )
110
?Take the derivative of
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + · ·· + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
d P
dy
CF y CF y M M CF y
Divide through by P and ress as a summation
d P
dy P
d P
dy
Convexity
t t CF
y
P P
t t PV CF
y
B
M
M
B
B
B
B
t
t
t
M
B B
t
t
M
t
2
2 1
3
2
4 2
0
2
2
0
0
2
1
0 0
1
2
2 1 6 1 1 1
1
1
1 1
1
1
= + + + + ··· + + +
= = =
+
+
=
+
+
|
\
|
.
|
|
|
÷ ÷ ÷ +
+
= =
+
¿ ¿
( ) ( ) ( ) ( )
exp :
/
( )
( )
( ) ( )
( )
( )
A
|
Derivation
111
Convexity
?Measure:
Convexity
Slope P
y P
t t PV CF
y
B
B
t
t
t
M
= =
+
+
¸
(
¸
( +
=
¿
A
A
/ ( ) ( )
( )
0
0
2
1
1 1
1
Annualized Convexity
Convexity for n length
n
=
2
112
Convexity
?The convexity measure for a bond which
pays coupons each period and its principal
at maturity:
Convexity
C
y y
CM
y y
M M F C y
y
P
M M M
B
=
÷
+
¸
(
¸
(
÷
+
+
+ ÷
+
+ +
2
1
1
1
2
1
1
1
3 2 1 2
0
( ) ( )
( )[ ( / )]
( )
113
Convexity
?Example: The convexity in half-years for a 10-year,
9% coupon bond selling at par (F= 100) and paying
coupons semiannually is 225.43 and its annualized
convexity is 56.36:
Convexity
Annualized Convexity
=
÷
¸
(
¸
(
÷ +
÷
=
= =
2 45
045
1
1
1045
2 45 20
045 1045
20 21 100 45 045
1045
100
22543
22543
2
5636
3 20 2 21 22
2
( . )
. ( . )
( . )( )
(. ) ( . )
( )( )[ ( . /. )]
( . )
.
.
.
114
Convexity
Uses:
?Descriptive Parameter: Greater k-gains and
smaller k-losses the greater a bond’s convexity.
? Estimation of : Using Taylor Expansion, a better estimate of
price changes to discrete changes in yield than the duration
measure can be obtained by combining duration and
convexity measures.
% / % A A P y
B
115
Convexity
?Taylor Expansion:
? For 10-year, 9% bond, an increase in the annualized yield by
200 BP (9% to 11%) would lead to an estimated 11.87%
decrease in price using Taylor Expansion (the actual is
12%):
% [ ] [ ]( ) A A A P Modified Duration y Convexity y
B
= +
1
2
2
1187 . ) 02 (. ] 36 . 56 [
2
1
) 02 (. ] 5 . 6 [ %
2
÷ = + ÷ = A
B
P
116
Convexity
? Note: Using Taylor Expansion the percentage increases in
price are not symmetrical with the percentage decreases for
given absolute changes in yields.
y from to
P
B
|
= ÷ = ÷
9% 11%
6 5 02
1
2
56 36 02 1187
2
:
% [ . ] (. ) [ . ] (. ) . A
y from to
P
B
+
= ÷ ÷ ÷ =
9% 7%
6 5 02
1
2
56 36 02 1413
2
:
% [ . ] ( . ) [ . ] ( . ) . A
117
Summary:
118
Debt market
119
19,528
50,147
0
10,000
20,000
30,000
40,000
50,000
60,000
U
S
D
b
i
l
l
i
o
n
Total Equity Market Total Bond Market
120
23,998
6,376
19,265
0
5,000
10,000
15,000
20,000
25,000
U
S
D
b
i
l
l
i
o
n
Bonds issued by Financial Institutions Bonds issued by Corporates Bonds issued by Governments
121
19,528
50,147
155,731
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
160,000
U
S
D
b
i
l
l
i
o
n
Total Equity Market Total Bond Market Total Interest Rate Derivatives
122
What to see before making
investment?
123
EURO
0
50
100
150
200
250
300
350
Jän 01 Jul 01 Feb 02 Aug 02 Mär 03 Okt 03 Apr 04 Nov 04
B
a
s
i
s
p
u
n
k
t
e
Gesamt AAA
AA A
BBB
Credit risk
124
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
High Yields All Ratings Investment Grades
Credit default risk
125
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Investment Grades
126
127
128
129
Mortgage/Asset Backed Securities
? Mortgage Backed Securities (Mortgage Pass through securities)
are offered by Fannie Mae, Freddie Mac, and Ginnie Mae
? Payments for MBS come from portfolios of mortgages grouped
by loan characteristic (term, rate)
? MBS payments made up of monthly interest and principle
payments and, hence have no “balloon payment” at maturity
? As with callable bonds, MBS have an “embedded option” (the
option of the homeowner to prepay)
? Collateralized Mortgage Obligations (CMO) are derivatives of
MBS that attempt to avoid prepayment risk
doc_863238396.ppt
This is a presentation that highlights different types of bonds and various types of risks associated with them.
Fixed Income Securities
Group - II
1
SIBM - Finance (Group II)
A Fixed Income Security
? Is a security that offers a series of fixed interest
payments, and a fixed principal payment at
maturity
? Claim to a specified stream of income
? A loan, typically made by investors to a
corporation or government
? Prices not subject to wide fluctuations
Terminology of a Bond
? Par value: Face amount; paid at maturity
? Coupon interest rate: Stated interest rate. Multiply
by par value to get interest; Generally fixed
? Maturity: Years until bond must be repaid
? Issue date: Date when bond was issued
? Discount: Bond issued at value less than Par
Value/ trading at a discount to face value in
secondary market
? Premium: Bond that is priced higher than face
value
Cash Flow Determination
• Simple Cash Flow
? FV is the future value (i.e. cash flow expected in
the future)
? PV is the present value
? r is the rate of return
FV = PV (1 + r)
• Multiple Cash Flow
PV = Coupon
1
+ Coupon
2
+ …+ Coupon
T
+Par
(1 + r)
1
(1 + r)
2
(1 + r)
T
Types of Bonds
• Coupon (Fixed Interest)
• Zero Coupon - no periodic coupon payment
? Sold at discount; matures at par
? Also called „Pure Discount Bond?;
Types of Bonds
• Callable Bond
? allows issuer to repurchase bond at a specified call
price prior to maturity
? Call Date: date after which bond may be bought
back
? Typically bonds are available with call protection
initial time during which bonds are not callable
? Call Price: pre specified price; usually a premium
is paid
? Usually after falling rates
Types of Bonds
• Puttable Bond
? Allows an option to Buyer/Holder to sell bond
back to the issuer
? Usually after rising rates
• Convertible Bonds
? Gives an option to Buyer/Holder to exchange
bonds for pre specified # of shares after a pre
specified period of time
? Lower coupons & YTM
Types of Bonds
• Investment Grade Bonds rated BBB (S&P) or
Baa (Moody?s) and above
• Junk Bonds: speculative grade; rated below
investment grade, highly risky in nature
• Debenture - unsecured bonds, could be
convertible or non convertible
Types of Bonds
• International - Bonds issued in a country different
from borrower (eg: Resurgent India Bonds in the
US)
• Eurobond – Bonds issued in currency of one country
but sold in another
eg: Eurodollar bonds - dollar denominated sold
outside US
• Yankee Bonds –a bond denominated in U.S. dollars
and is publicly issued in the U.S. by foreign banks
and corporations
• Sukuk – the Arabic name for a financial certificate
but can be seen as an Islamic equivalent of bond
Types of Bonds
• STRIPS
? STRIPS (Separately Traded Interest and Principle
Securities) allow owner to register and sell interest
payments and principle an individual marketable
securities
? STRIPS are essentially longer term discount bonds
Example
Face Value = Rs 100
Rate of interest = 5% (annual)
Maturity = 3 years
Date of Payment of Interest – June 1
The following table shows how this one
bond can be stripped into 4 bonds
Types of Bonds
• TIPS
? Note that because bond payments are expressed in
a currency, their value in terms of purchasing
power is influenced by inflation (nominal = real +
inflation)
? To counter this, the treasury began issuing
inflation indexed securities.
? The face value of TIPS are continuously adjusted
according to changes in the CPI to protect
investors from inflation
Example
• A two year T-Note with a 5% annual coupon will
be worth Rs 96.23 if interest rates are equal to
7%
Types of Bonds
• Medium Term Notes
? A note that usually matures in five to 10 years.
? A corporate note continuously offered by a company to investors
through a dealer. Investors can choose from differing maturities,
ranging from nine months to 30 years.
? Notes range in maturity from one to 10 years. By knowing that a
note is medium term, investors have an idea of what its maturity
will be when they compare its price to that of other fixed-income
securities. All else being equal, the coupon rate on medium-term
notes will be higher than those achieved on short-term notes.
? This type of debt program is used by a company so it can have
constant cash flows coming in from its debt issuance; it allows a
company to tailor its debt issuance to meet its financing needs.
Medium-term notes allow a company to register with the SEC
only once, instead of every time for differing maturities.
15
Types of Risk Bondholders Face
• Interest Rate Risk
• Reinvestment Risk
• Default (Credit) Risk
• Inflation Risk
• Call Risk
• Liquidity Risk
Interest Rate Risk
• The risk that interest rates may change once the
bonds are issued
• When interest rates fall, bonds values rise and
vice versa
• Example
Face Value – 100, Coupon – 10%, Maturity of A –
5 years and B – 10 years, Current Interest Rates
– 7%
Reinvestment rate risk
• The risk that CFs will have to be reinvested in the
future at lower rates, reducing income.
• Example – Invest in a bond with a cumulative
interest on the following conditions
Face Value – Rs 100 , Maturity – 30 years
Rate of interest – 5%
Interest Rate Risk + Reinvestment Rate
Risk
• Long-term bonds: High interest rate risk, low
reinvestment rate risk.
• Short-term bonds: Low interest rate risk, high
reinvestment rate risk.
• Nothing is riskless!
Default (Credit) Risk
• Credit risk is the risk that the party that has
issued the bond or instrument will default on
payment of interest or principal
• It would most likely happen in the case of
bankruptcy
What factors affect default risk and
bond ratings?
• Financial performance
? Debt ratio
? Current ratios
• Provisions in the bond contract
? Secured versus unsecured debt
? Senior versus subordinated debt
? Guarantee provisions
? Sinking fund provisions
? Debt maturity
• Other factors
? Earnings stability
? Regulatory environment
? Potential product liability
? Accounting policies
Inflation Risk
• Because of their relative safety, bonds tend not to
offer extraordinarily high returns. That makes them
particularly vulnerable when inflation rises.
• Example
Treasury bond interest = 3.32%. If the rate of
inflation rises to, say, 4 percent, your investment is
not “keeping up with inflation.” In fact, you?d be
“losing” money because the value of the cash you
invested in the bond is declining. You?ll get your
principal back when the bond matures, but it will be
worth less.
Other Risk
? Call Risk
? Call risk refers to the risk that a bond may be
called when the investor does not want it to be
called.
• Liquidity Risk
? Investors may have difficulty finding a buyer when
they want to sell and may be forced to sell at a
significant discount to market value.
24
SIBM - Finance (Group II)
Bond Pricing
• Bond Pricing Fundamentals
1. Pricing a Coupon Bond
2. Pricing a Zero Coupon Bond
3. Pricing a Floater
4. Pricing a Callable/Puttable Bond
25
SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Present Value of Cash Flows:
? P is the bond price
? C is the periodic coupon payment
? N is the number of years to maturity
? M is the (face value) payment at maturity
? y is the “risk-adjusted discount rate” (or yield to
maturity, or IRR)
( )
( ) ( ) ( ) ( )
N N 3 2
1
M
1
C
...
1
C
1
C
1
C
P
y y y y
y
+
+
+
+ +
+
+
+
+
+
=
26
SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Determining the Cash Flows
? Periodic Coupon Interest Payments
? Par Value at Maturity
• Determining the Required Yield
? Required Yield
? Theoretical arguments for using different yields to
discount
• Determining the Price
27
SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Rates are different over time:
• Here, each spot rate r
n
is the discount rate for a
cash flow in year n that can be locked in today
• E.g., r
3
(3-year spot rate) is the rate the market uses
to value a single payment three years from today
P =
C
1+ r
1
( )
+
C
1 + r
2
( )
2
+
C
1 + r
3
( )
3
+... +
C
1+ r
N
( )
N
+
M
1+ r
N
( )
N
28
SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Take a 3-year 10% coupon bond with face value = 1000, assuming annual
coupon payments:
? Spot rates: r
1
=10%, r
2
=12%, r
3
=14%
? Yield-to-Maturity
Price =
100
1.10 ( )
+
100
1.12 ( )
2
+
1100
1.14 ( )
3
= 913.1
( ) ( ) ( )
( ) ( ) ( )
% 7 . 13
137 . 1
1100
137 . 1
100
137 . 1
100
y 1
1100
y 1
100
1
100
913.1
3 2
3 2
=
+ + =
+
+
+
+
+
=
y
y
29
SIBM - Finance (Group II)
1. Pricing a Coupon Bond
? Determining the Price when the Settlement Date
Falls Between Coupon Periods:
i = Periodic Interest Rates
period coupon in the days of No.
payment coupon next and Settlement between days of No.
W =
( ) ( ) ( ) ( ) ( )
w 1 - N w 1 - N W 2 W 1 W
1
M
1
C
...
1
C
1
C
1
C
P
+ + + +
+
+
+
+ +
+
+
+
+
+
=
i i i i i
30
SIBM - Finance (Group II)
1. Pricing a Coupon Bond
• Determining the Price when the Settlement Date
Falls Between Coupon Periods:
? Day Count Conventions
? Accrued Interest and Clean Price:
period coupon in the days of No.
date Settlement payment to coupon last from days of No.
* AI C =
31
SIBM - Finance (Group II)
2. Pricing a Zero Coupon Bond
• Also the present value of expected cash flows:
? Incase of a Zero Coupon Bond the only cash flow
is the Maturity Value.
? Notice that YTM = the spot rate only for zero-
coupon bonds:
N N
N
y
M
r
M
) 1 ( ) 1 (
P
+
=
+
=
32
SIBM - Finance (Group II)
2. Pricing a Zero Coupon Bond
• Price of 3-year zero coupon bond with face value = 1000
? Spot rates: r
1
=10%, r
2
=12%, r
3
=14%
? Yield-to-Maturity
( )
675
14 . 1
1000
Price
3
= =
( )
% 14
y 1
1000
75 6
3
=
+
=
y
33
SIBM - Finance (Group II)
Relationship between Yield, Price,
Coupon, Time to Maturity
• Relationship Between required
Yield and Price at a given time:
• 20 year, 10% coupon Bond
34
SIBM - Finance (Group II)
Relationship between Yield, Price,
Coupon, Time to Maturity
• Relationship among Coupon
Rate, Required Yield and
Price at a given time:
? As yields in the marketplace
change, the only variable
that can change to
compensate an investor for
the new required yield in
the market is the price of
the bond.
? The capital appreciation
realized by holding the bond
to maturity represents a
form of interest to a new
investor to compensate for a
coupon rate that is lower
than the required yield.
35
SIBM - Finance (Group II)
Relationship between Yield, Price,
Coupon, Time to Maturity
• Time Path of a Bond:
? If Yield remains the same:
? As bond approaches
maturity, it becomes closer
to its par value
? And equals its par value at
Maturity
36
SIBM - Finance (Group II)
3. Pricing a Floater
• Floater:
Coupon Rate=Reference Rate+Quoted Margin
• Inverse Floater:
Coupon Rate=K-L*(Reference Rate)
Ex: 18% - 2.5*(three month LIBOR)
• The Price of a Floater depends on
? The spread over the reference rate
? Any restriction on resetting the coupon rate.
ex: Cap, Floor
37
SIBM - Finance (Group II)
3. Pricing a Floater
• Thus: Factors that affect a Floaters price are
1. Time Remaining to next coupon reset date
? The more time to next coupon reset date, the more it
behaves like a fixed-rate security – Greater potential
fluctuation.(example)
? For a floater in which the cap is not binding and the
required margin is not different from the quoted
margin, will trade at par.
SIBM - Finance (Group II)
38
3. Pricing a Floater
2. Changes in the markets required margin
? The required margin depends on
-Margin Available in competitive funding Markets
-Credit Quality of the Issue
-Presence of a Call or Put option
-Liquidity of the Issue
SIBM - Finance (Group II)
39
3. Pricing a Floater
3. Whether or not the cap or floor is reached
? Once the Cap is reached, the floater offers a below-
market coupon, thus the bond will trade at a
discount
? When a Cap or a float is reached, the bond is
effectively a fixed-rate security
SIBM - Finance (Group II)
40
4. Pricing a Callable Bond
• Price-Yield relationship for a Callable Bond
• Negative Convexity: Price appreciation will be less than the Price
depreciation for a large change in yield
• A bond can still trade ABOVE its call price even if it is highly likely
to be called
SIBM - Finance (Group II)
41
4. Pricing a Callable Bond
• Valuation Model:
? Hypothetical Zero Coupon Yield Curve
? By using the Bootstrapping Method we can
estimate the forward rates
SIBM - Finance (Group II)
42
4. Pricing a Callable Bond
1. Introducing Interest Rate Volatility
? This can be done by introducing a binomial
interest-rate tree
SIBM - Finance (Group II)
43
4. Pricing a Callable Bond
? Binomial Interest-Rate Tree
?r
1,H
= r
1,L
* e
2??t
? ? = Assumed Volatility of the One Year Forward
Rate
? r
1,L
= The Lower One Year Rate, one year from now
? r
1,H
= The Higher One Year Rate, one year from now
SIBM - Finance (Group II)
44
4. Pricing a Callable Bond
? Binomial Interest-Rate Tree
? Ex: Suppose that r
1,L
= 4.074% and ? = 10% per year
? Thus r
1,H
=
SIBM - Finance (Group II)
45
4. Pricing a Callable Bond
? Binomial Interest-Rate Tree
? In the Second Year there are 3 possibilities:
? Thus:
&
SIBM - Finance (Group II)
46
4. Pricing a Callable Bond
? Binomial Interest-Rate Tree
SIBM - Finance (Group II)
47
4. Pricing a Callable Bond
2. Determining the Value at a Node
? Future Cash Flows depends on:
1. The bond's value one year from now
2. The coupon payment one year from now
? Ex: Suppose that we are interested in the bond's
value at N
H
. The cash flow will be either the bond's
value at N
HH
plus the coupon payment or the
bond's value at N
HL
plus the coupon payment.
SIBM - Finance (Group II)
48
4. Pricing a Callable Bond
2. Determining the Value at a Node
SIBM - Finance (Group II)
49
4. Pricing a Callable Bond
2. Determining the Value at a Node
? The present value of these two cash flows using
the one-year rate at the node, r*, is
? Thus the value at the node is:
SIBM - Finance (Group II)
50
4. Pricing a Callable Bond
3. Constructing the Binomial Tree
? Compute the value of a 4%, 2 Yr. bond, Market
Price = $100
SIBM - Finance (Group II)
51
4. Pricing a Callable Bond
1. Select a value for r
1
. Recall that r
1
is the lower one-
year forward rate one year from now. We arbitrarily
selected a value of 4.5%
2. Determine the corresponding value for the higher
one-year forward rate. This rate is related to the
lower one-year forward rate as follows: r
1
e
2?
3. Compute the bond?s value one year from now: In our
case $100 + $4 = $104
4. Compute the present value of this amount using the
higher forward rate of 5.496%. V
H
= $98.582
5. Compute the present value of the amount in 3 using
the lower forward rate of 4.5%. V
L
= $99.522
SIBM - Finance (Group II)
52
4. Pricing a Callable Bond
7. Add the coupon to V
H
and V
L
to get the cash flow at NH
and NL, respectively. In our example we have $102.582
for the higher rate and $103.522 for the lower rate.
8. Calculate the present value of the two values using
the one-year forward rate using r,. At this point in
the valuation, r, is the root rate, 3.50%. Therefore:
SIBM - Finance (Group II)
53
4. Pricing a Callable Bond
9. The average value thus calculated is $99.567
10. Compare this value with the price of the bond, if the
it matches then the r
1
used in this is the one we seek.
If not we have to find the r
1
by trial & error
11. By trial and error r
1
= 4.074%
12. We can use this info. to grow the tree & similarly
find the value for r
2
SIBM - Finance (Group II)
54
4. Pricing a Callable Bond
• Thus the tree formed can be used to value any
option – free bond, or any bond with option
• Arbitrage Free Tree
SIBM - Finance (Group II)
55
4. Pricing a Callable Bond
4. Valuing a callable bond
? 5.25% corporate bond with 3 years to maturity,
callable in one year at $100.
? V
t
= min[call price, PV(future cash flows)]
SIBM - Finance (Group II)
56
4. Pricing a Callable Bond
? The discounting process explained earlier is used to
calculate the value at the end of year 2
? The issuer calls the issue if the PV of future cash flows
exceeds the call price
? N
L
and N
LL
,th e values from the recursive valuation
formula ($101.001 at N
L
and $100.689 at N
LL
) exceed
the call price ($100) and therefore have been struck
out and replaced with $100.
? Each time a value derived from the recursive valuation
formula has been replaced, the process for finding the
values at that node is reworked starting with the
period to the right. The value for this callable bond is
$101.432.
SIBM - Finance (Group II)
57
Pricing a Puttable bond
• Similarly a Putable bond can valued using the
Binomial Tree
• V
t
= max[put price, PV(future cash flows)]
SIBM - Finance (Group II)
58
SIBM - Finance (Group
II)
59
60
Sensitivity analysis
61
Bond price
?Is always the present value of the
benefits associated with bond
discounted at yield
62
?At maturity, the value of any bond
must equal its par value.
?The value of a premium bond would
decrease to 1,000.
?The value of a discount bond would
increase to 1,000.
?A par bond stays at 1,000 if k
d
remains constant.
63
M
Bond price
Years remaining to Maturity
1,372
1,211
1,000
837
775
30 25 20 15 10 5 0
k
d
= 7%.
k
d
= 13%.
k
d
= 10%.
64
Example on bond price
? Suppose I have a, 100, 2 year T-Note with a 5%
annual coupon rate. If the annual market rate of
interest is 7%, how much is this bond worth?
65
? Suppose I have a, 100, 2 year T-Note with a 5%
annual coupon rate. If the annual market rate of
interest is 7%, how much is this bond worth?
(the semiannual coupon interest rate is 2.5%, the
semiannual market interest rate is 3.5%)
Example on bond price
66
Example on bond price
? Suppose I have a, 100, 2 year T-Note with a 5% annual coupon
rate. If the annual market rate of interest is 7%, how much is
this bond worth?
2.50/(1.035) = 2.42
2.50/(1.035)^2 = 2.33
2.50/(1.035)^3 = 2.25
+102.50/(1.035)^4 = 89.23
= 96.23
Note: This bond is currently selling at a discount.
67
Bond yields
? Coupon rate or coupon Yield
? Yield to Maturity (YTM)
? Current Yield
? Total Yield
? Yield on a Discounted Basis (YDB)
68
=
Annual coupon
Coupon rate
Par value
Coupon yield
?Yield is basically the rate of interest i.e.
rate attached with the coupon
69
? Suppose I have a bond of 100 face value having
current price of 96.23, with semiannual coupon of
2.50. How much is this bond yield?
Yield = (2.50 x 2)/100 = 5.0%
Example on coupon yield
70
Yield to maturity
?YTM is the rate of return earned on a
bond held to maturity. Also called
“promised yield.”
? The discount rate that equates a
bond’s price with the present value
of all future cash flows
? Also referred as investor’s required
or expected return on bond
71
What’s the YTM on a 10-year, 9%
annual coupon, 1,000 par value bond
that sells for 887?
90 90 90
0 1 9 10
k
d
=?
1,000
PV
1
.
.
.
PV
10
PV
M
887 Find k
d
that “works”!
...
72
10 -887 90 1000
N I/YR PV PMT FV
10.91
( ) ( ) ( )
V
INT
k
M
k
B
d
N
d
N
=
1 1
1
...
+
INT
1 + k
d
( ) ( ) ( )
887
90
1
1 000
1
1 10 10
=
k k
d d
+
90
1 + k
d
,
Find k
d
+ +
+ +
+ +
+ +
INPUTS
OUTPUT
...
73
2(10) 13/2 100/2
20 6.5 50 1000
N I/YR PV PMT FV
-834.72
Find the value of 10-year, 10% coupon,
semiannual bond if k
d
= 13%.
INPUTS
OUTPUT
74
Find YTM if price were 1,134.20.
10 -1134.2 90 1000
N I/YR PV PMT FV
7.08
Sells at a premium. Because
coupon = 9% > k
d
= 7.08%,
bond’s value > par.
INPUTS
OUTPUT
75
?If coupon rate < k
d
, bond sells at a
discount.
?If coupon rate = k
d
, bond sells at its
par value.
?If coupon rate > k
d
, bond sells at a
premium.
?If k
d
rises, price falls.
?Price = par at maturity.
76
Yield to maturity
? Assuming
• Investors purchased the bond at current price
• The bond is held until its maturity
• Coupons received intermittently will be
reinvested at the same rate
77
Measurement and management of IRR
? Increase in YTM results in depreciation of existing
portfolio. (i.e. higher the YTM, lower the price of an
existing security)
? At the end of each financial year, RBI prescribes the
YTM to be applied to the Govt.. Securities and the
bond portfolio of banks.
? Any sharp increase in YTM towards the close of a
financial year has the potential of a steep
depreciation which could wipe out the profits of a
bank during the entire year.
78
Other yields
Current yield =
Capital gains yield =
= YTM = +
Annual coupon pmt
Current price
Change in price
Beginning price
Exp total
return
Exp
Curr yld
Exp cap
gains yld
79
Find current yield and capital gains
yield for a 9%, 10-year bond when the
bond sells for 887 and YTM = 10.91%.
Current yield =
= 0.1015 = 10.15%.
90
887
As a useful approximation to YTM, the current yield is simply the
coupon payment as a percentage of the price.
80
YTM = Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= 10.91% - 10.15%
= 0.76%.
Total yield is the current yield plus any
capital gain/loss
81
Yield on a discount basis
?Yield on a discount basis is a commonly
used approximation for yield to maturity
for discount bonds.
YDB = FV – P ___360________
FV Days to Maturity
82
Example on YDB
?A T Bill with 28 days until maturity has a
bid YDB equal to .87%. What is the bid
price?
83
Example on YDB
?A T Bill with 28 days until maturity has a
bid YDB equal to .87%. What is the bid
price?
.87% = .0087 (annual rate)
.0087(28/360) = (.0007) (28 day rate)
P = (1 - .0007) $100 = $99.93 ($99:30)
84
Annualizing
?Likewise, if a 180 day T-Bill is selling for
97.56, then the annualized yield is
YTM = FV – P ___365_____
P Days to Maturity
= (100 -97.56) (365) = .05 (5%)
97.56 180
85
Reading the newspaper
Rate Maturity Bid Ask Chg. Ask Yld
7.25 May 08 101:20 101:21 -1 .74
86
Reading the newspaper
?Rate: Coupon Rate
?Maturity: Expiration Date
?Bid: Buying Price in 32nds
?Ask: Selling Price in 32nds
?Ask Yld: Current Yield Based on Ask
Price
87
Current
Price
P
r
i
c
e
Current Yield
Yield
Price/Yield Curve
Duration =
Slope of Price/Yield Curve
Convexity =
Change in Slope of Price/Yield Curve
Price yield relationship
88
Yield to call
?Effectively YTM for the time period
before call option can be exercised
89
A 10-year, 10% semiannual coupon,
1,000 par value bond is selling for
1,135.90 with an 8% yield to maturity.
It can be called after 5 years at 1,050.
What’s the bond’s nominal yield to
call (YTC)?
10 -1135.9 50 1050
N I/YR PV PMT FV
3.765 x 2 = 7.53%
INPUTS
OUTPUT
90
k
Nom
= 7.53% is the rate brokers would
quote. Could also calculate EFF% to
call:
EFF% = (1.03765)
2
- 1 = 7.672%.
This rate could be compared to monthly
mortgages, and so on.
91
If you bought bonds, would you be
more likely to earn YTM or YTC?
?Coupon rate = 10% vs. YTC = k
d
=
7.53%. Could raise money by selling
new bonds which pay 7.53%.
?Could thus replace bonds which pay
100/year with bonds that pay only
75.30/year.
?Investors should expect a call, hence
YTC = 7.5%, not YTM = 8%.
92
?In general, if a bond sells at a
premium, then if coupon > k
d
, so a
call is likely.
?So, expect to earn:
?YTC on premium bonds.
?YTM on par & discount bonds.
93
Market risk management
94
Duration
? Can be defined as the weighted average of the time
periods.
D t
PV CF
P
t
B
t
M
=
¸
(
¸
(
=
¿
( )
0
1
D w D
p i i
=
¿
95
?Duration of 4-year, 9% coupon Bond
with yield being 10%:
D t
PV CF
P
t
B
t
M
=
¸
(
¸
(
=
¿
( )
0 1
t CF
CF PV CF
P
t Weight
P D
t
t
t
t
B
B
( . )
( )
( )( )
. . .
. . .
. . .
. . .
. .
110
1 90 81818 0 084496 0 084496
2 90 74 348 0 076815 0153630
3 90 67 618 0 069832 0 209496
4 1090 744 485 0 768857 3075428
968 30 352
0
0
= =
96
Duration
?Duration is also a measure of a bond’s price
sensitivity to interest rate changes.
?This measure of duration is known as the
modified duration; the measure of duration as
a weighted average of the time periods is
known as Macaulay's duration.
D
P
YTM
P
YTM
B B
= ~ =
% %
%
A
A
A
A
0 0
c
97
Derivation
?Duration:
?Take derivative with respect to y:
P
CF
y
CF y
P CF y CF y CF y
B t
t
t
M
t
t
t
M
B
M
M
0
1 1
0 1
1
2
2
1
1
1 1 1
=
+
= +
= + + + + ··· + +
=
÷
=
÷ ÷ ÷
¿ ¿
( )
( )
( ) ( ) ( )
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + · ·· + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
98
Derivation
? Factor out
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + ·· · + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
÷ + = ÷
+
÷
( )
( )
1
1
1
1
1
y
y
( )
( )
dP
dy y
CF y CF y M CF y
dP
dy y
CF
y
CF
y
M
CF
y
dP
dy y
PV CF PV CF M PV CF
B
M
M
B
M
M
B
M
= ÷
+
+ + + + · · · + +
= ÷
+ +
+
+
+ · · · +
+
|
\
|
.
|
= ÷
+
+ + · · · +
÷ ÷ ÷
1
1
1 1 2 1 1
1
1
1
1
2
1 1
1
1
1 2
1
1
2
2
1
1
2
2
1 2
( )
( ) ( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( ) ( ) ( ) ( )
99
Derivation
Divide through by P:
dP
dy P
dP P
dy y
PV CF
P
PV CF
P
M
PV CF
P
B
B B
M
B
1 1
1
1 2
1
0
2
0 0
= = ÷
+
+ + · · · +
|
\
|
.
|
/
( )
( )
( )
( )
( )
( )
( )
Modified Duration
dP P
dy y
t
PV CF
P
t
M
t
B
= = ÷
+
|
\
|
.
|
=
¿
/
( )
( ) 1
1
1 0
100
Duration
D
P
YTM YTM
t
PV CF
P
B
t
B
t
M
= = ÷
+
¸
(
¸
(
=
¿
%
( )
( ) A
A
0
0
1
1
1
Modified Duration Macaulay s Duration '
Example
Modified Duration
:
( . )
( . ) . = ÷ = ÷
1
110
35 318
101
Duration
?Annualized Duration: Duration is defined in terms
of the length of the period between payments. If
the CFs are distributed annually, then duration is
in years; if CFs are semi-annual, then duration is
measured in half years. The convention is to
expressed duration as an annual measure. The
annualized duration is obtained by dividing duration
by the number of payments per year
: Annualized Duration
Duration for n periods
n
=
÷
102
Duration
? Example: The duration in half-years for a 10-year, 9%
coupon bond selling at par (F= 100) and paying coupons
semiannually is -13 and its annualized duration is -6.5:
%
.
. ( . )
[ ( . /. )]
( . )
.
A
A
P
y
Annualized Duration
B
0
2 20 21
4 5
045
1
1
1045
20 100 4 5 045
1045
100
13
13
2
65
= ÷
÷
¸
(
¸
(
+
÷
= ÷
= ÷ = ÷
%
( )
[ ( / )]
( )
A
A
P
y
C
y y
M F C y
y
P
B
M M
B
0
2 1
0
1
1
1 1
= ÷
÷
+
¸
(
¸
(
+
÷
+
+
103
Duration
?Uses:
? Descriptive Parameter: Measure of a bond’s price sensitivity
to interest rate changes -- a measure of a bond’s volatility.
Note, duration is consistent with bond price relation:
volatility greater Duration Greater period Greater ¬ ¬
volatility greater Duration Greater Coupon Lower ¬ ¬
104
Duration
?Define Strategies: Use duration to define active
(speculative) and passive bond strategies.
?Examples:
?Rate-Anticipation Swap: Rates expected to decrease
across all maturities, go long in high duration bonds.
Rates expected to increase across all maturities, change
bond portfolio composition so that it has lower duration
bonds.
?Bond Immunization Strategy: Bond immunization is bond
strategy of minimizing market risk by buying a bond or a
portfolio of bonds with a duration equal to the certain fix D.
105
Duration limitation
? Estimate the percentage change in a bond’s price for a given
change in rates:
?For 10-year, 9% bond, an increase in the annualized yield
by 10BP (.09 to .0910) would lead to a .65% decrease in
price (the actual is .6476%). A 200BP increase (9% to
11%) would lead to an estimated price decrease of 13%;
the actual decrease, though, is only 12%.
%
( )
[ ]
% [ ] ( )
A
A
A A
P
YTM
Modified Duration
P Modified Duration YTM
B
B
=
=
% [ . ] (. . ) . AP
B
= ÷ ÷ = ÷ 6 5 0910 09 0065
% [ . ] (. . ) . AP
B
= ÷ ÷ = ÷ 6 5 11 09 13
106
Convexity
?Duration is a measure of the slope of the price-
yield curve at a given point -- first-order derivative.
?Convexity is a measure of the change in the slope
of the price-yield curve -- second-order derivative.
?Convexity measures how bowed-shaped the price-
yield curve is.
107
Convexity
? Property: The greater a bond’s convexity, the greater its capital
gains and the smaller its capital losses for given absolute
changes in yields.
YTM
P
B
0
y
0
P
B
0
YTM
y
1
y
2
K Gain
{
K Loss
{
y
0
y
1
y
2
K Gain
K Loss
{
{
-
-
-
-
-
-
y y y y
1 0 2 0
÷ = ÷
108
Derivation
?Convexity:
?Take derivative with respect to y:
P
CF
y
CF y
P CF y CF y CF y
B t
t
t
M
t
t
t
M
B
M
M
0
1 1
0 1
1
2
2
1
1
1 1 1
=
+
= +
= + + + + ··· + +
=
÷
=
÷ ÷ ÷
¿ ¿
( )
( )
( ) ( ) ( )
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + · ·· + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
109
Derivation
? Factor out
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + ·· · + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
÷ + = ÷
+
÷
( )
( )
1
1
1
1
1
y
y
( )
( )
dP
dy y
CF y CF y M CF y
dP
dy y
CF
y
CF
y
M
CF
y
dP
dy y
PV CF PV CF M PV CF
B
M
M
B
M
M
B
M
= ÷
+
+ + + + · · · + +
= ÷
+ +
+
+
+ · · · +
+
|
\
|
.
|
= ÷
+
+ + · · · +
÷ ÷ ÷
1
1
1 1 2 1 1
1
1
1
1
2
1 1
1
1
1 2
1
1
2
2
1
1
2
2
1 2
( )
( ) ( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( ) ( ) ( ) ( )
110
?Take the derivative of
dP
dy
CF y CF y M CF y
B
M
M
= ÷ + + ÷ + + · ·· + ÷ +
÷ ÷ ÷ +
( ) ( ) ( ) ( ) ( ) ( )
( )
1 1 2 1 1
1
2
2
3 1
d P
dy
CF y CF y M M CF y
Divide through by P and ress as a summation
d P
dy P
d P
dy
Convexity
t t CF
y
P P
t t PV CF
y
B
M
M
B
B
B
B
t
t
t
M
B B
t
t
M
t
2
2 1
3
2
4 2
0
2
2
0
0
2
1
0 0
1
2
2 1 6 1 1 1
1
1
1 1
1
1
= + + + + ··· + + +
= = =
+
+
=
+
+
|
\
|
.
|
|
|
÷ ÷ ÷ +
+
= =
+
¿ ¿
( ) ( ) ( ) ( )
exp :
/
( )
( )
( ) ( )
( )
( )
A
|
Derivation
111
Convexity
?Measure:
Convexity
Slope P
y P
t t PV CF
y
B
B
t
t
t
M
= =
+
+
¸
(
¸
( +
=
¿
A
A
/ ( ) ( )
( )
0
0
2
1
1 1
1
Annualized Convexity
Convexity for n length
n
=
2
112
Convexity
?The convexity measure for a bond which
pays coupons each period and its principal
at maturity:
Convexity
C
y y
CM
y y
M M F C y
y
P
M M M
B
=
÷
+
¸
(
¸
(
÷
+
+
+ ÷
+
+ +
2
1
1
1
2
1
1
1
3 2 1 2
0
( ) ( )
( )[ ( / )]
( )
113
Convexity
?Example: The convexity in half-years for a 10-year,
9% coupon bond selling at par (F= 100) and paying
coupons semiannually is 225.43 and its annualized
convexity is 56.36:
Convexity
Annualized Convexity
=
÷
¸
(
¸
(
÷ +
÷
=
= =
2 45
045
1
1
1045
2 45 20
045 1045
20 21 100 45 045
1045
100
22543
22543
2
5636
3 20 2 21 22
2
( . )
. ( . )
( . )( )
(. ) ( . )
( )( )[ ( . /. )]
( . )
.
.
.
114
Convexity
Uses:
?Descriptive Parameter: Greater k-gains and
smaller k-losses the greater a bond’s convexity.
? Estimation of : Using Taylor Expansion, a better estimate of
price changes to discrete changes in yield than the duration
measure can be obtained by combining duration and
convexity measures.
% / % A A P y
B
115
Convexity
?Taylor Expansion:
? For 10-year, 9% bond, an increase in the annualized yield by
200 BP (9% to 11%) would lead to an estimated 11.87%
decrease in price using Taylor Expansion (the actual is
12%):
% [ ] [ ]( ) A A A P Modified Duration y Convexity y
B
= +
1
2
2
1187 . ) 02 (. ] 36 . 56 [
2
1
) 02 (. ] 5 . 6 [ %
2
÷ = + ÷ = A
B
P
116
Convexity
? Note: Using Taylor Expansion the percentage increases in
price are not symmetrical with the percentage decreases for
given absolute changes in yields.
y from to
P
B
|
= ÷ = ÷
9% 11%
6 5 02
1
2
56 36 02 1187
2
:
% [ . ] (. ) [ . ] (. ) . A
y from to
P
B
+
= ÷ ÷ ÷ =
9% 7%
6 5 02
1
2
56 36 02 1413
2
:
% [ . ] ( . ) [ . ] ( . ) . A
117
Summary:
118
Debt market
119
19,528
50,147
0
10,000
20,000
30,000
40,000
50,000
60,000
U
S
D
b
i
l
l
i
o
n
Total Equity Market Total Bond Market
120
23,998
6,376
19,265
0
5,000
10,000
15,000
20,000
25,000
U
S
D
b
i
l
l
i
o
n
Bonds issued by Financial Institutions Bonds issued by Corporates Bonds issued by Governments
121
19,528
50,147
155,731
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
160,000
U
S
D
b
i
l
l
i
o
n
Total Equity Market Total Bond Market Total Interest Rate Derivatives
122
What to see before making
investment?
123
EURO
0
50
100
150
200
250
300
350
Jän 01 Jul 01 Feb 02 Aug 02 Mär 03 Okt 03 Apr 04 Nov 04
B
a
s
i
s
p
u
n
k
t
e
Gesamt AAA
AA A
BBB
Credit risk
124
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
High Yields All Ratings Investment Grades
Credit default risk
125
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Investment Grades
126
127
128
129
Mortgage/Asset Backed Securities
? Mortgage Backed Securities (Mortgage Pass through securities)
are offered by Fannie Mae, Freddie Mac, and Ginnie Mae
? Payments for MBS come from portfolios of mortgages grouped
by loan characteristic (term, rate)
? MBS payments made up of monthly interest and principle
payments and, hence have no “balloon payment” at maturity
? As with callable bonds, MBS have an “embedded option” (the
option of the homeowner to prepay)
? Collateralized Mortgage Obligations (CMO) are derivatives of
MBS that attempt to avoid prepayment risk
doc_863238396.ppt