Description
An event study of seleceted firms (Wipro, ITC, Aegis logistics, L&T ltd, Sterlite Industries, EIL) on their share price around stock dividends
Bond Pricing
Price Quotations
• Quoted Price : Clean price is quoted
• Clean Price: Does not include interest
• Accrued Interest
• Invoice Price= Clean Price + Accrued Interest
Period Coupon in Days Total
Payment Coupen Last Since Days
2
Coupon Annual
AI × =
Day Count Conventions
Basis Day count basis Remark
0 or omitted US (NASD) 30/360
February=30
1 Actual/actual
2 Actual/360
3 Actual/365
In India used for T-Bills ,
CD, CP and Corporate
Bonds
4 European 30/360
February=28/29
In India used for Dated
Securities
Day Count under 30/360
Convention
) ( 30 ) ( 360 ) (
1 2 1 2 1 2
D D M M Y Y
Days
÷ + × ÷ + × ÷
=
Two Parameters of Bond Pricing
• Yield
• Price
?Yield (or YTM) is equivalent to IRR
?Price is equivalent to PV.
?Both are two sides of the same coin.
Return on Bond Investment: Yield
• Is it always better to purchase a higher coupon
bond (say 12% p.a.) than a low coupon bond
(say 3.5% p.a.)?
• What is yield? How is it different from Coupon
Rate?
• While investing money in fixed income
securities, should we give more importance to
yield rate or coupon rate?
Why Yield is different from Coupon
Rate
• Bonds are not always sold at par. Neither in
secondary market, nor always in primary
market.
• Therefore, yield depends on buying prices.
• Where coupon rate is pre-decided (fixed or
floating), yield keeps changing according to
market conditions.
Current Yield
Price
Coupon Annual
Yield Current =
Yield-to-Maturity
• It is IRR of the bond investment, with a
assumption that bond is held till maturity.
?It is assumed here that the coupon payments can
be reinvested at an interest rate equal to YTM.
i' ' period for Coupon c
maturity to Term n
Baond the of Price P
: where
) 1 (
...
) 1 ( ) 1 (
i
2
2 1
=
÷ ÷ =
=
+
+
+
+
+
= ¬
=
n
n
y
RV c
y
c
y
c
P
y YTM
YTM: Important Relationship
Price = Par Value: YTM= Current Yield=Coupon Rate
Price> Par Value: YTM<Current Yield<Coupon Rate
Price < Par Value YTM>Current Yield<Coupon Rate
Yield-to-Call
• In case of a callable bond YTM is not a good
indicator of expected bond return.
• A bond is likely to be called if current market
yield (interest rate) is less then the Coupon
Rate.
• Yield-to-Call is calculated for a assumed call
date; generally for:
– First call date
– First par call date.
Example
• A 8.5% Corporate Bond is trading today at
1020 (FV 1000) , It has a exact three years’
term to maturity, but company has an option
to call it after 1 year at Rs. 1010. Coupon is
paid annually. Find out:
– CY
– YTM
– YTC
Realized Yield
• YTM analysis is subject to reinvestment risk.
• If the bond is not held till maturity, investment
is also subject to price risk.
• The realized return is the actual rate of return
from an investment for a given horizon based
on actual reinvestment income and actual
selling price of the bond.
Example
• An investor purchased 500, 7.5% bond with 3
years’ remaining term-to-maturity at Rs 95.
What is its YTM.
• He received first coupon after 6 month and
reinvested the money for six month at the
interest rate of 3.5% p.a. . He also received
second coupon after 1 year and sold the
investment on the same date at Rs. 96. What
is his realized yield.
Yield and Law of One Price
• If two securities, X and Y, are otherwise similar
(risk, cash-flow pattern) both should have
same yield.
…Yield and Law of One Price
• If the yield of security X is higher than that of
security Y; it implies that security X has higher
risk or some undesirable attributes.
• Higher yield is required to compensate for
higher risk or some undesirable attributes.
…Yield and Law of One Price
• Corporate bonds give higher yield than Treasury Bonds.
• Corporate Bonds with good credit rating give low yield
than Junk Bonds.
• Bonds with longer maturity, generally, give higher yield
than bonds of shorter maturity. (WHY?)
• Ceteris paribus, Bonds with higher coupon rate give
lower yield (WHY).
• A Bond with higher liquidity will give lower yield
• A Callable bond gives higher yield than a non-callable
Bond
Price of a Bond
Price of a Bond
• WHY DOES A PERSON PAY FOR BOND?
• BECAUSE IT GIVES FUTURE STREAM OF CASHFLOWS.
• Therefore, the value of a bond should be equal
to present value of future cashflows.
YTM or rate discount y
value redemption RV
period i of coupon c
bond of price P
where
) 1 (
...
) 1 ( ) 1 (
th
i
2
2
1
1
=
=
=
=
+
+
+ +
+
+
+
=
n
n
y
RV c
y
c
y
c
P
Price of a bond depends on…
• Required yield
/ YTM
• Coupon (c)
• Term-to-Maturity
) , , ( n c y f P = ¬
Required Yield /Rate of Discounting
• Required yield is the minimum YTM,
demanded by the investors to invest in the
bond.
• Determined on the basis of YTM of the
comparable bonds.
For your Discussion
• Why do yield rates/ interest rates change in
the market?
• How do the macro-economic variables
(including fiscal and monetary policies) affect
the yield rates/interest rates?
?Price and yield are inversely related with each
other.
?When interest rate decreases bond prices go up. When
interest rate increases bond prices come down.
?The relationship is not linear
It is Convex
Relationship between
Yield and Price.
0
50
100
150
200
250
0.0% 2.0% 4.0% 6.0% 8.0% 10.0%
P
r
i
c
e
Yield
What does convexity of Yield-Price
Relationship imply
0
100
200
300
400
500
600
700
1% 7% 13% 20% 30% 50%
P
R
I
C
E
(
R
s
.
)
YIELD
RELATION BETWEEN BOND VALUATION AND BOND YIELD
CONVEX SHAPE OF
THE CURVE
GAINS BECOME
GREATER!!
LOSSES
BECOME
SMALLER!!
Convexity depends on Maturity
• Higher the Maturity : Higher the Convexity
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200.0
1 2 3 4 5 6 7 8 9
P
r
i
c
e
Term to Maturity
5 year
10 yera
15 year
20 year
25 year
30 year
Relationship between
Coupon and Price
? FOR A GIVEN MATURITY PERIOD AND GIVEN YTM, WE
OBSERVE THE FOLLOWING RELATION BETWEEN BOND PRICE
AND COUPON RATE:
?As coupon increases, the price of bond
increases LINEARLY.
linear is fuction this , of e given valu a for
) y 1 (
1
1
y
1
c
P
Coupon in change rupee one for Price in Change
y
n |
|
.
|
\
|
+
÷ =
c
c
=
=
0.00
20.00
40.00
60.00
80.00
100.00
120.00
0% 5% 10% 15%
P
r
i
c
e
Coupon
Coupon-Price Relationship
|
|
.
|
\
|
+
÷ =
n
) y 1 (
1
1
y
1
Coupon in change rupee one for Price in Change
Yield-Price-Coupon Relationship
• When yield is equal to coupon rate, bond is
priced at par value.
• When the yield is below the coupon rate the
bond will be priced at premium to its par
value.
• When the yield is above the coupon rate the
bond will be priced at discount to its par
value.
? Zero coupon bond is always sold at discount.
0
50
100
150
200
250
0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0%
P
r
i
c
e
Yield
Coupon =6.00%
Par Value=Rs. 100
Term-to-Maturity and Price
• On maturity the prices of a bond converse to
its par value/ redemption value
• Bond selling at Premium:
?Longer the maturity - Higher the price
• Bond selling at Discount:
? Longer the maturity - Lower the Price
80.00
85.00
90.00
95.00
100.00
105.00
110.00
1
-
J
u
n
-
0
9
1
-
S
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-
0
9
1
-
D
e
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9
1
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M
a
r
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0
1
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J
u
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0
1
-
S
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p
-
1
0
1
-
D
e
c
-
1
0
1
-
M
a
r
-
1
1
1
-
J
u
n
-
1
1
1
-
S
e
p
-
1
1
1
-
D
e
c
-
1
1
1
-
M
a
r
-
1
2
1
-
J
u
n
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1
2
1
-
S
e
p
-
1
2
1
-
D
e
c
-
1
2
1
-
M
a
r
-
1
3
1
-
J
u
n
-
1
3
1
-
S
e
p
-
1
3
1
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D
e
c
-
1
3
1
-
M
a
r
-
1
4
1
-
J
u
n
-
1
4
Time Path of the Price of a Bond with
Par Value = Rs 100,
Date of Maturity 30 June 2014.
Price of a bond changes with time!!!
• If a bond is being sold at premium at present, its price
will decrease over time; and
• if it is being sold at a discount, then its price will
increase over a period of time.
doc_588722038.pptx
An event study of seleceted firms (Wipro, ITC, Aegis logistics, L&T ltd, Sterlite Industries, EIL) on their share price around stock dividends
Bond Pricing
Price Quotations
• Quoted Price : Clean price is quoted
• Clean Price: Does not include interest
• Accrued Interest
• Invoice Price= Clean Price + Accrued Interest
Period Coupon in Days Total
Payment Coupen Last Since Days
2
Coupon Annual
AI × =
Day Count Conventions
Basis Day count basis Remark
0 or omitted US (NASD) 30/360
February=30
1 Actual/actual
2 Actual/360
3 Actual/365
In India used for T-Bills ,
CD, CP and Corporate
Bonds
4 European 30/360
February=28/29
In India used for Dated
Securities
Day Count under 30/360
Convention
) ( 30 ) ( 360 ) (
1 2 1 2 1 2
D D M M Y Y
Days
÷ + × ÷ + × ÷
=
Two Parameters of Bond Pricing
• Yield
• Price
?Yield (or YTM) is equivalent to IRR
?Price is equivalent to PV.
?Both are two sides of the same coin.
Return on Bond Investment: Yield
• Is it always better to purchase a higher coupon
bond (say 12% p.a.) than a low coupon bond
(say 3.5% p.a.)?
• What is yield? How is it different from Coupon
Rate?
• While investing money in fixed income
securities, should we give more importance to
yield rate or coupon rate?
Why Yield is different from Coupon
Rate
• Bonds are not always sold at par. Neither in
secondary market, nor always in primary
market.
• Therefore, yield depends on buying prices.
• Where coupon rate is pre-decided (fixed or
floating), yield keeps changing according to
market conditions.
Current Yield
Price
Coupon Annual
Yield Current =
Yield-to-Maturity
• It is IRR of the bond investment, with a
assumption that bond is held till maturity.
?It is assumed here that the coupon payments can
be reinvested at an interest rate equal to YTM.
i' ' period for Coupon c
maturity to Term n
Baond the of Price P
: where
) 1 (
...
) 1 ( ) 1 (
i
2
2 1
=
÷ ÷ =
=
+
+
+
+
+
= ¬
=
n
n
y
RV c
y
c
y
c
P
y YTM
YTM: Important Relationship
Price = Par Value: YTM= Current Yield=Coupon Rate
Price> Par Value: YTM<Current Yield<Coupon Rate
Price < Par Value YTM>Current Yield<Coupon Rate
Yield-to-Call
• In case of a callable bond YTM is not a good
indicator of expected bond return.
• A bond is likely to be called if current market
yield (interest rate) is less then the Coupon
Rate.
• Yield-to-Call is calculated for a assumed call
date; generally for:
– First call date
– First par call date.
Example
• A 8.5% Corporate Bond is trading today at
1020 (FV 1000) , It has a exact three years’
term to maturity, but company has an option
to call it after 1 year at Rs. 1010. Coupon is
paid annually. Find out:
– CY
– YTM
– YTC
Realized Yield
• YTM analysis is subject to reinvestment risk.
• If the bond is not held till maturity, investment
is also subject to price risk.
• The realized return is the actual rate of return
from an investment for a given horizon based
on actual reinvestment income and actual
selling price of the bond.
Example
• An investor purchased 500, 7.5% bond with 3
years’ remaining term-to-maturity at Rs 95.
What is its YTM.
• He received first coupon after 6 month and
reinvested the money for six month at the
interest rate of 3.5% p.a. . He also received
second coupon after 1 year and sold the
investment on the same date at Rs. 96. What
is his realized yield.
Yield and Law of One Price
• If two securities, X and Y, are otherwise similar
(risk, cash-flow pattern) both should have
same yield.
…Yield and Law of One Price
• If the yield of security X is higher than that of
security Y; it implies that security X has higher
risk or some undesirable attributes.
• Higher yield is required to compensate for
higher risk or some undesirable attributes.
…Yield and Law of One Price
• Corporate bonds give higher yield than Treasury Bonds.
• Corporate Bonds with good credit rating give low yield
than Junk Bonds.
• Bonds with longer maturity, generally, give higher yield
than bonds of shorter maturity. (WHY?)
• Ceteris paribus, Bonds with higher coupon rate give
lower yield (WHY).
• A Bond with higher liquidity will give lower yield
• A Callable bond gives higher yield than a non-callable
Bond
Price of a Bond
Price of a Bond
• WHY DOES A PERSON PAY FOR BOND?
• BECAUSE IT GIVES FUTURE STREAM OF CASHFLOWS.
• Therefore, the value of a bond should be equal
to present value of future cashflows.
YTM or rate discount y
value redemption RV
period i of coupon c
bond of price P
where
) 1 (
...
) 1 ( ) 1 (
th
i
2
2
1
1
=
=
=
=
+
+
+ +
+
+
+
=
n
n
y
RV c
y
c
y
c
P
Price of a bond depends on…
• Required yield
/ YTM • Coupon (c)
• Term-to-Maturity
) , , ( n c y f P = ¬
Required Yield /Rate of Discounting
• Required yield is the minimum YTM,
demanded by the investors to invest in the
bond.
• Determined on the basis of YTM of the
comparable bonds.
For your Discussion
• Why do yield rates/ interest rates change in
the market?
• How do the macro-economic variables
(including fiscal and monetary policies) affect
the yield rates/interest rates?
?Price and yield are inversely related with each
other.
?When interest rate decreases bond prices go up. When
interest rate increases bond prices come down.
?The relationship is not linear
It is Convex
Relationship between
Yield and Price.
0
50
100
150
200
250
0.0% 2.0% 4.0% 6.0% 8.0% 10.0%
P
r
i
c
e
Yield
What does convexity of Yield-Price
Relationship imply
0
100
200
300
400
500
600
700
1% 7% 13% 20% 30% 50%
P
R
I
C
E
(
R
s
.
)
YIELD
RELATION BETWEEN BOND VALUATION AND BOND YIELD
CONVEX SHAPE OF
THE CURVE
GAINS BECOME
GREATER!!
LOSSES
BECOME
SMALLER!!
Convexity depends on Maturity
• Higher the Maturity : Higher the Convexity
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200.0
1 2 3 4 5 6 7 8 9
P
r
i
c
e
Term to Maturity
5 year
10 yera
15 year
20 year
25 year
30 year
Relationship between
Coupon and Price
? FOR A GIVEN MATURITY PERIOD AND GIVEN YTM, WE
OBSERVE THE FOLLOWING RELATION BETWEEN BOND PRICE
AND COUPON RATE:
?As coupon increases, the price of bond
increases LINEARLY.
linear is fuction this , of e given valu a for
) y 1 (
1
1
y
1
c
P
Coupon in change rupee one for Price in Change
y
n |
|
.
|
\
|
+
÷ =
c
c
=
=
0.00
20.00
40.00
60.00
80.00
100.00
120.00
0% 5% 10% 15%
P
r
i
c
e
Coupon
Coupon-Price Relationship
|
|
.
|
\
|
+
÷ =
n
) y 1 (
1
1
y
1
Coupon in change rupee one for Price in Change
Yield-Price-Coupon Relationship
• When yield is equal to coupon rate, bond is
priced at par value.
• When the yield is below the coupon rate the
bond will be priced at premium to its par
value.
• When the yield is above the coupon rate the
bond will be priced at discount to its par
value.
? Zero coupon bond is always sold at discount.
0
50
100
150
200
250
0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0%
P
r
i
c
e
Yield
Coupon =6.00%
Par Value=Rs. 100
Term-to-Maturity and Price
• On maturity the prices of a bond converse to
its par value/ redemption value
• Bond selling at Premium:
?Longer the maturity - Higher the price
• Bond selling at Discount:
? Longer the maturity - Lower the Price
80.00
85.00
90.00
95.00
100.00
105.00
110.00
1
-
J
u
n
-
0
9
1
-
S
e
p
-
0
9
1
-
D
e
c
-
0
9
1
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M
a
r
-
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0
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J
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1
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p
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1
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M
a
r
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1
1
1
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u
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1
1
1
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1
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S
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1
3
1
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D
e
c
-
1
3
1
-
M
a
r
-
1
4
1
-
J
u
n
-
1
4
Time Path of the Price of a Bond with
Par Value = Rs 100,
Date of Maturity 30 June 2014.
Price of a bond changes with time!!!
• If a bond is being sold at premium at present, its price
will decrease over time; and
• if it is being sold at a discount, then its price will
increase over a period of time.
doc_588722038.pptx