стр. 89 |

I I

I I

Beta

0.6 1.0 1.4

B

Portfolio C

A

Fig. 7-3

(c) A lower expected return for the market portfolio would change the slope of the market line

downward, as is shown in Fig. 7-4.

I

Beta

Fig. 7-4

190 RISK, RETURN, AND VALUATION [CHAP. 7

CAPM. During a 5-year period, the relevant results for the aggregate market are that the rf

71

.2

(risk-free rate) is 8percent and the r, (return on market) is 14percent. For that period, the results

of four portfolio managers are as follows:

Portfolio Manager Average Return (%) Beta

A 13 0.80

B 14 1.OS

C 17 1.25

D 13 0.90

( a ) Calculate the expected rate of return for each portfolio manager and compare the actual

returns with the expected returns. (b) Based upon your calculations, select the manager with the

best performance. ( c ) What are the critical assumptions in the capital asset pricing model

(CAPM)? What are the implications of relaxing these assumptions? (CFA, adapted.)

SOLUTION

( a ) Use the CAPM equation:

= rf + b(rm- rf)

rj

The expected rates of return are as follows:

Difference

between

Actual and

Expected

Actual

Average

Portfolio

Return (Yo) Returns (Oh)

Return ('10)

Manager Expected Return (%)

r A = 8% + O.80(140/, - 8%) = 12.8 +0.2

A 13 13

r B = 8% + I.OS(14Yo - 8%) = 14.3 -0.3

14 14

B

TC = 8% + 1.25(14% - 8%)= 15.5

17 17 +1.5

C

TD = 8% + O.9O(14% - 8%) = 13.4 -0.4

D 13 13

(6) Portfolio managers A and C did better than expected, since A exceeded the expected return by 1.56

percent (0.2% c 12.8%) and C bettered the expected return by 9.68 percent (1.5% + 15.5%). C

therefore showed the best performance.

(c) The critical assumptions in CAPM are perfect capital markets and homogeneous expectations.

Relaxation of the perfect capital markets assumption results in limitations to the effectiveness of

predicting and computing expected return on stock. Certain securities may have values and expected returns

that are not entirely explained by the security market line. Residual risk may be important, particularly

where bankruptcy costs are significant. When expectations of market participants are not homogeneous,

each investor has his or her own capital market line. The important thing to stress, however, is that in market

equilibrium, there still will exist an implied risk-return trade-off for securities where risk is represented by

the undiversifiable risk, as opposed to the total risk of the security.

71

.3 Value of Bond. Trooper Corporation has a bond issue with a coupon rate of 10 percent per year

and 5 years remaining until maturity. The par value of the bond is $l,OOO. What is the value of

the bond when the going rate of interest is (a) 6 percent; (b) 10percent; and (c) 12 percent? The

bond pays interest annually.

SOLUTION

Annual interest = 10% X $1,000 = $100

V = C - I +- M

" $100 $100 $100 $loo0

=-+++...+++

(1 + r)5 (1 + r)5

(1 +r)" (1 +r)I (1 + r ) 2

i - 1 (1 +r)'

WO(

$100(PVIFA,,) + $1, PVIF,,)

=

191

RISK, RETURN, AND VALUATION

CHAP. 71

+

(4 Value $lOO(PVIFA6%,5) $1,00O(PVIF˜%˜˜)

=

= $100(4.2124) + $1,000(0.7473) = $421.24 + $747.30 = $1,168.54

+ $1,000(PVIFlo%,s)

Value $100(PVIFA˜o˜,˜)

=

(6)

= $100(3.7908) + $1,000(0.6209) = $379.08 + $620.90 = $999.98

(4 Value = $lOO(PVIFA12%5)+ $1,000(PVIF12%,5)

= $100(3.6048) + $1,000(0.5674) = $360.48 + $567.40 = $927.88

Value of Bond. Assume the same data and questions as in Problem 7.13, except that in this

7.14

problem, the bond pays interest semiannually.

SOLUTION

$100

-= $50

Semiannual interest =

2

Number of periods = 5 years X 2 = 10 periods

2n

M

N2

V=C-

+

,= 1 (1 + d2)' (1+ r/2)2"

$50

+ $1,000

$50

- $50

+ ...

--

(1 + r/2) (1 + r/2)2 (1 + r/2)1В° (1 + r/2)'O

+

= $50(PVIFAr/˜,m) $1,000(PVIFrn.i0)

стр. 89 |