1. You have estimated the following probability of expected future returns for Stocks
X and Y.
Stock X
&nbs p;
Stock Y
Probability
Return
Probability
Return
0.1
-10%
0.2
2%
0.2
10
0.2
7
0.4
15
0.3
12
0.2
&n bsp;
20
0.1
40
0.1
16
a.
0.2
15
What is the expected rate of return for Stock X? Stock Y?
E(RX) = .1(-10%) + .2(10%) + .4(15%) + .2(20%) + .1(40%)
= 15%
E(RY) = .2(2%) + .2(7%) + .3(12%) + .2(15%) + .1(16%)
= 10%
b.
What is the standard deviation of expected returns for Stock X? For Stock Y?
σX = [(-10-15)2.1 + (10-15)2.2 + (15-15)2.4 + (20-15)2.2 +
(40-15)2.1].5 = 11.62%
σY = [(2-10)2.2 + (7-10)2.2 + (12-10)2.3 + (15-10)2.2 +
(16-10)2.1].5 = 4.94%
c.
Which stock would you consider to be riskier? Why?
Stock X is riskier because it has a higher standard deviation of returns than Y. The
coefficient of variation of returns is also higher for X (0.77) than for Y (0.49).
2. You are considering investing in two securities, X and Y. The following data are
available for the two securities:
Security X
Security Y
Expected return
0.10
0.07
Standard deviation of returns &n bsp;
0.08
0.04
Beta
&nbs p;
1.10
0.75
a. If you invest 40 percent of your funds in Security X and 60 percent in Security Y
and if the correlation of returns between X and Y is +0.5, compute the following:
1. The expected return from the portfolio
2. The standard deviation of returns from the portfolio
(1) E(R) = .4(.10) + .6(.07) = .082 or 8.2%
(2) σp = [(.4)2(.08)2 + (.6)2(.04)2 + 2(.4)(.6)(.5)(.08)(.04)].5= .0487or 4.87%
b.
What happens to the expected return and standard deviation of returns of the
portfolio in Part a if 70 percent of your funds are invested in Security X and 30
percent of your funds are invested in Security Y?
(1) E(R) = .7(.10) + .3(.07) = .091 or 9.1%
(2) σp = [(.7)2(.08)2 + (.3)2(.04)2 + 2(.7)(.3)(.5)(.08)(.04)].5= .0629 or 6.29%
c. What happens to the expected return and standard deviation of returns of the
portfolio in Part a if the following conditions exist?
a. The correlation of returns between Securities X and Y is + 1.0
b. The correlation of returns between Securities X and Y is 0
c. The correlation of returns between Securities X and Y is -0.7
Expected returns remain the same. They do not depend on the correlation of
returns among securities.
(a) ρxy = +1;
σp = .056 or 5.6% (by substituting +1 for + 0.5 in part 6. a. (2)
above.
(b) ρxy = 0;
σp = .04 or 4%
( c ) ρxy = -.7;
σp = .023 or 2.3%
3. Given a risk free rate(rf) of 6 percent and a market risk premium (rm-rf)of 8.5
percent, calculate the required rate of return on each of the following stocks, based on the
betas given in Table 6.8:
a. American Electric Power
b. Apple
c. eBay
d. Southwest Airlines
TABLE 6.8 BETA FOR SELECTED STOCKS
COMPANY
VALUE LINE BETA
American Electric Power
1.35
Apple
1.00
EBay
1.10
Southwest Airlines
1.15
ER  R f   ( R premium )
a) American Electric Power
= 6 + 1.35(8.5)
= 17.48%
b) Apple
= 6 + 1(8.5)
= 14.5%
c) Ebay
= 6 + 1.10(8.5)
= 15.35%
d) Southwest Airlines
= 6 + 1.15(8.5)
= 15.78%
4. Security A offers an expected return of 15 percent with a standard deviation of 7
percent. Security B offers an expected return of 9 percent with a standard deviation of
percent. The correlation between the returns of A and B IF +0.6. If an investor puts onefourth of his wealth in A and three-fourths in B, what is the expected return and risk
(standard deviation) of this portfolio?
E(Rp) = .25(15%) + .75(9%) = 10.5%
σp = [(.25)2(7)2 + (.75)2(4)2 + 2(.25)(.75)(0.6)(7)(4)].5 = 4.285%
5. The real rate of interest has been estimated to be 3 percent, and the expected longterm annual inflation rate is 7 percent.
A. What is the current risk-free rate of return on 1-year Treasury bonds?
rf = 3% real return + 7% inflation premium = 10%
B.
If the yield on 10 year U.S. Treasury bonds is 12 percent, what is the maturity risk
premium between a 10 year bond and a 1- year bond?
12% - 10% = 2% maturity risk premium between a 10-year bond and a 1-year
bond.
C. If American Airlines bonds, scheduled to mature in 10 years, currently sell to yield
13 percent, what is the default risk premium on these bonds?
Default risk premium = 13% - 12% = 1%
D. If investors in the common stock of American Airlines require a 16 percent rate of
return, what is the seniority risk premium on Americans’ common stock?
American risk premium = 16% - 13% = 3%