bond theorems

8/3/2019 Bond Theorems

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BOND VALUATIONTHEOREMS


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IntroductionA bond is a loan, typically made by investors toa corporation or government.The value of a bond depends upon three factors:-1.Coupon Rate2. Years to Maturity3. Expected yield to Maturity (or) RequiredRate of Return.On the basis of this Bond Valuation theoremshave been evolved.


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Characteristics of Bond Prices The cash flows on a bond are constant (fixed income).

A bonds market price changes in responseto the market interest rate.

When market rates increase, the fixed

payments from the bond are worth less so theprice falls.If rates decrease, the fixed payments are nowworth more.


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Example - Annual Coupon

4

1000 10 year bond paying a 10% annual coupon

What is the value when the interest rate is 10%?

If r = 11%?

If r = 9%?

00.1000)10.1(

1000)10.1(

1110.

100 10100 B

11.941)11.1(

1000

)11.1(

11

11.

10010100

B

18.1064)09.1(

1000

)09.1(

11

09.

10010100

B


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Bond Theorems Price and interest rates move inversely .A decrease in interest rates raises bondprices by more than a correspondingincrease in rates lowers price .Price volatility is inversely related tocoupon .Price volatility is directly related to

maturity .Price volatility increases at a diminishingrate as maturity increases.


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THEOREM 1

If the market price of the bond increases, the yieldwould decline and vice versa.

MARKET PRICE YIELD

MARKET PRICE YIELD


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Bond A Bond B

Par Value Rs. 100 Rs.100

Coupon Rate 10 % 10 %Maturity Period 2 yrs 2 yrs

Market Price Rs.874.75 Rs.1035.66

Yield 18 % 8 %


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Illustration of Bond Theorems A decrease in interest rates raises bond prices by more than acorresponding increase in rates lowers price . This is known asconvexity .

$0

$500

$1,000

$1,500

$2,000

$2,500

$3,000

4% 6% 8% 10% 12% 14% 16%

Interest Rate

B o n d P r i c e

30 yr, 15%30 yr, 10%20 yr, 10%10 yr, 10%

30 yr, 5%


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Illustration of Bond Theorems

Price volatility is inversely related tocoupon .

-40%

-20%

0%

20%

40%

60%

80%

100%

4% 6% 8% 10% 12% 14% 16%

Interest Rate

P r i c e V o l a t i l i t y

( | %

C h a n g e f r o m

p a r | )

30 yr, 5%30 yr, 10%30 yr, 15%


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Price volatility is directly related tomaturity .

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

4% 6% 8% 10% 12% 14% 16%

Interest Rate

P r i c e V o l a t i l i t y ( | %

C h a n g e f r o m p a r | )

30 yr, 10%20 yr, 10%10 yr, 10%


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Price volatility increases at a diminishingrate as maturity increases.Illustration of Bond Theorems

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0 5 10 15 20 25 30

Years to Maturiy

P e r c e n t a

g e P r i c e

C h a n g e

5% Interest Rate

10% Interest Rate

15% Interest Rate


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Duration Theorems: A Summary I. The duration of a zero coupon bond always equals itstime to maturity.

II. The lower the coupon rate the longer the duration,other things held constant.

III. The longer the maturity, the longer the duration, other

things held constant.

IV. The lower the yield to maturity, the longer theduration, other things held constant


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bond theorems

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