Principles of Finance 6e Chapter 11
Besley/Brigham
11-1
CHAPTER 11
ANSWERS
11-2 a. The probability distribution for complete certainty is a vertical line.
11-3 Events that affect a single firm or a group of firms are defined as the components of unsystematic
risk. Such events include changes in manufacturing methods, changes in management, labor
11-4 Systematic risk is the “relevant” risk because it cannot be diversified away. Unsystematic, or firm-
11-5 The statement is true, because the portion of total risk that is unsystematic can be diversified away
0.83.
11-7 a. No, it is not riskless. The portfolio would be free of default risk and liquidity risk, but inflation
could erode the portfolio’s purchasing power. If the actual inflation rate is greater than that
11-8 a. The expected return on a life insurance policy is calculated just as for a common stock. Each
outcome is multiplied by its probability of occurrence, and then these products are summed.
For example, suppose a one-year term policy pays $10,000 at death, and the probability of the
policyholder’s death in that year is 2 percent. Then, there is a 98 percent probability of zero
return and a 2 percent probability of $10,000:
Chapter 11 Principles of Finance 6e
Besley/Brigham
11-2
b. There is a perfect negative correlation between the returns on the life insurance policy and the
c. People are generally risk-averse. Therefore, they are willing to pay a premium to decrease the
11-9 The risk premium on a high beta stock would increase more.
11–10 At least theoretically, it is possible to combine two stocks that are perfectly negatively correlated to
produce a portfolio that has no risk. For example, see Figure 11-5 in the chapter. However, it would
11-11 False. The amount of the risk premium changes by the amount of the beta coefficient. For example,
when β = 1.0 and β = 2.0, the respective risk premiums for the investment are:
Example: Suppose that rRF = 4% and rM = 11%. Using this information, we have
Principles of Finance 6e Chapter 11
Besley/Brigham
11-3
____________________________________________________________
SOLUTIONS
11-1
r
ˆ
= 0.2(-5%) + 0.3(10%) + 0.5(30%) = 17.0%
11-5 r = 5% + (12% – 5%)1.5 = 15.5%
11-8 CVD = 8.0%/10.0% = 0.8
11-9 rZR = rRF + (rRF – rM)β
11–10 Portfolio beta:
Investment Weight Beta Portfolio beta
Chapter 11 Principles of Finance 6e
Besley/Brigham
(1) (2) (3) (4) = (2) x (3)
$ 400,000 0.40 1.5 0.6
rRF = 3% and rM – rRF = 7%.
Investment Beta rj = rRF + (rM – rRF)βj Weight
$ 400,000 1.5 13.5% 0.40
11–11 a.
M
r
ˆ
= (0.3)(15%) + (0.4)(9%) + (0.3)(18%) = 13.5%.
6.22%
0.29 =
3.85%
=
CV S
11-5
11–14 a.
R
r
ˆ
= 0.5 (–2%) + 0.1 (10%) + 0.4 (15) = 6.0%
Alternative computation: Compute the portfolio return for each possible stock outcome.
Returns
Probability Stock R Stock S 50/50 Portfolio
0.5 –2% 20% 9.0% = 0.5 (–2%) + 0.5 (20%)
c.
=
−===
n
1i
i
2
i
2) r
ˆ
(rσ σ deviation Standard Pr
8.12%6632.41.632
6%)0.4(15%6%)0.1(10%6%)2%0.5( σ222
R
==++=
−+−+−−=
Chapter 11 Principles of Finance 6e
Besley/Brigham
11-6
d.
r
ˆ
σ
Return
Risk
CV variation of tCoefficien ===
e. In this case, because the standard deviation for the two-stock portfolio is close to zero, we
11-15 rK = rRF + (rM – rRF)β
11-16 βold = 1.2; there are five stocks in the portfolio
If one stock with β = 2.0 is sold, then the portfolio’s beta would change
11-17 βold = 1.5; portfolio value = $400,000; β of the four stocks that remain after selling one stock that
currently makes up 25 percent of the portfolio is 1.8; thus,
11-7
11-18 Alternative solutions:
1. Old portfolio beta = 1.12 = (0.05)β1 + (0.05)β2 +…+ (0.05)β20
11-19 a. rB = rRF + (rM – rRF)βB
14% = 8% + (11% – 8%)βB
11–20 a. rX = rRF + (rM – rRF)βX = 9% + (14% – 9%)1.3 = 15.5%.
(2) rRF decreases to 8%; RPM does not change:
rX = rRF + (RPM)βX = 8% + (5%)1.3 = 14.5%.
rM = rRF + (RPM)βM = 8% + (5%)1.0 = 13.0%.
Chapter 11 Principles of Finance 6e
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11-8
11–21 We know that βR = 1.50, βS = 0.75, rM = 15%, rRF = 9%.
11–22 Portfolio beta:
Stock Investment Weight Beta Portfolio beta
(1) (2) (3) (4) (5) = (3) x (4)
A $ 400,000 0.10 1.50 0.150
rRF = 6% and rM – rRF = 8%.
Stock Investment Beta rj = 6% + (8%)βj Weight
A $ 400,000 1.50 18.0% 0.10
11-23 Following is information about Investment A, Investment B, and Investment C:
Return on Investment:
Economic Condition Probability A B C
Boom 0.5 25.0% 40.0% 5.0%
Principles of Finance 6e Chapter 11
Besley/Brigham
11-9
b.
2
A
= 0.5(25% – 18%)2 + 0.4(15% – 18%)2 + 0.1(-5% – 18%)2 = 81
11-24 a. ($1 million)(0.5) + ($0)(0.5) = $0.5 million.
d. (1) ($1,150,000)(0.5) + ($0)(0.5) = $575,000, or an expected profit of $75,000.
(2) $75,000/$500,000 = 15%.
11-25 a.
M
r
ˆ
= 0.1(10%) + 0.2(12%) + 0.4(13%) + 0.2(16%) + 0.1(17%) = 13.5%.
b. To determine the fund’s beta, βF, the weight for the amount invested in each stock needs to be
computed.
Chapter 11 Principles of Finance 6e
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11–10
Therefore, the SML equation is
d. Use βF = 1.8 in the SML determined in Part b:
11-26 a. Returns
Year Stock A Stock B 50/50 Portfolio
2011 –10.00% –3.00% -6.50% = 0.5(-10.00%) + 0.5(-3.00%)
2012 18.50 21.29 19.90 = 0.5(18.50%) + 0.5(21.29%)
A
5
b. The standard deviation of returns is estimated as follows:
n
2
t
t1
(r –r)
Estimated σ s
n1
=
== −
&&
19.01%361.48
4
1,445.92
===
The standard deviation of returns for Stock B and the portfolio are similarly determined, and
they are as follows:
Stock A Stock B Portfolio AB
Principles of Finance 6e Chapter 11
Besley/Brigham
11–11
c. Because the risk from diversification is small—the standard deviation falls only from 19.0
11–27 The answers to a, b, c, and d are given below:
50/50
A
r
&&
B
r
&&
Portfolio
2011 –18.0% -14.5% –16.25%
The computations for the average return, standard deviation, and coefficient of variation for
Stock A are:
A
r
&&
A
r
A
r
&&
–
A
r
(
A
r
&&
–
A
r
)2
–18.0% 11.3% –29.3% 858.49
33.0 11.3 21.7 470.89
11-28 Integrative Problem