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0.8750 2.6250

898.39

0.8396

3 1,070

1.oooo

$1,026.73 2.8107

This 3-year bondвЂ™s duration is a little over 2.8 years. Although duration is expressed in years, think of

it as a percentage change. Thus, 2.8 years means this particular bond will gain (lose) 2.8 percent of its

value for each 1percentage drop (rise) in interest rates. Note, however, that duration will not tell you

anything about the credit quality or yield of your bonds.

Interest Rate Elasticity

A bondвЂ™s interest rate elasticity (E) is defined as

Percentage change in bond price

E=

Percentage change in YTM

Since bond prices and YTMs always move inversely, the elasticity will always be a negative number.

Any bondвЂ™s elasticity can be determined directly with the above formula. Knowing the duration

coefficient (D), e can calculate the E using the following simple formula:

w

YTM

(-l)E = D

(1+

EXAMPLE 7.22 Using the same date in Example 7.21, the elasticity is calculated as follows:

(-1) E = 2.8107 [0.06/(1.06)] = 0.1591, which means that the bond will lose or gain 15.91% of principal value

for each 1percentage point move in interest rates.

Review Questions

1. refers to the variability of associated with a given investment.

2. Expected rate of return is the of possible returns from a given investment, with

the weights being

3. The smaller the standard deviation, the вЂњtighterвЂќ the and, thus, the lower the

of the investment.

,the greater the risk of the security.

4. The higher the coefficient of

5. depends on in demand, sales price, input prices, and so on.

6. refers to the change in a stockвЂ™s price that results from changes in the stock

market as a whole.

7. Total risk is the sum of and

RISK, RETURN, AND VALUATION

184 [CHAP. 7

8. Portfolio risk can be reduced by

= -1.0 means that assets A and B have a(n)

9. PAB

,equation shows that the required rate of return on a

10. The or ?

security is equal to the risk-free rate plus

of an assetвЂ™s expected future

11. The valuation process involves finding the

cash flows using the investorвЂ™s required rate of return.

yield and

12. The expected rate of return on a stock is the sum of

yield.

computes the value of a common stock when dividends are expected

13. The

to grow at a constant rate.

, and

14. The three cases of dividend growth are: 9

, divided by the

15. The one-period return on stock investment is dividends plus

beginning price.

is an index of systematic risk.

16.

includes any number of

17. Unlike the Capital Asset Pricing Model (CAPM), the

risk factors.

18. There are two ways to measure interest rate risk of a bond: one is and the other

is the interest rate elasticity.

Answers: (1)Risk, expected return (or earnings); (2) weighted average, probabilities; (3) probability distribution,

risk; (4) variation; ( 5 ) Business risk, variability; (6) Market risk; (7) unsystematic risk, systematic risk; (8)

diversification; (9) perfectly negative correlation; (10) capital asset pricing model (CAPM), security market line

(SML), risk premium; (11)present value; (12) dividend, capital gain; (13) Gordon growth model; (14) zero growth,

a

constant growth, supernormal growth; (15) capital gain; (16) Beta; (17) Arbitrage Pricing Model (APM); duration

or MacaulayвЂ™s duration coefficient.

Solved Problems

ExpectedReturn and Standard Deviation. Assuming the following probability distribution of the

71

.

possible returns, calculate the expected return (F) and the standard deviation ( U ) of the

returns.

Return (rr)

Probability ( p r )

-20%

0.1

5%

0.2

0.3 10%

25 %

0.4

185

RISK, RETURN, AND VALUATION

CHAP. 71

SOLUTION

It is convenient to set up the following table:

w ( % ) 0 - 1 -9(%) (ri- '

)

F (r,- iI2Pf(OIO)

rd0/0) PI

-32

-20 102.4

1,024

-2

0.1

-7

5 49 9.8

0.2 1

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