168 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
The set of efficient portfolios is approximately those portfolios with no more than 60% invested in J&J
(this is the portfolio with the lowest possible volatility).
Weight in Johnson
& Johnson’s
Weight in
Walgreen’s
E[Rp]
SD[Rp]
0
1
9.60%
21.60%
0.05
0.95
9.47%
20.73%
0.1
0.9
9.33%
19.89%
0.15
0.85
9.20%
19.11%
0.2
0.8
9.06%
18.37%
0.25
0.75
8.93%
17.69%
0.3
0.7
8.79%
17.07%
0.35
0.65
8.66%
16.53%
0.4
0.6
8.52%
16.07%
0.45
0.55
8.39%
15.69%
0.5
0.5
8.25%
15.41%
0.55
0.45
8.12%
15.22%
0.6
0.4
7.98%
15.13%
0.65
0.35
7.85%
15.15%
0.7
0.3
7.71%
15.27%
0.75
0.25
7.58%
15.49%
0.8
0.2
7.44%
15.80%
0.85
0.15
7.31%
16.21%
0.9
0.1
7.17%
16.70%
0.95
0.05
7.04%
17.26%
1
0
6.90%
17.90%
11–27. A hedge fund has created a portfolio using just two stocks. It has shorted $36,000,000 worth of
Oracle stock and has purchased $95,000,000 of Intel stock. The correlation between Oracle’s and
Intel’s returns is 0.65. The expected returns and standard deviations of the two stocks are given in
the table below:
a. What is the expected return of the hedge fund’s portfolio?
b. What is the standard deviation of the hedge fund’s portfolio?
P
=48.79%
11–28. Consider the portfolio in Problem 27. Suppose the correlation between Intel and Oracle’s stock
increases, but nothing else changes. Would the portfolio be more or less risky with this change?
11–31. You have $8600 to invest. You decide to invest $17,000 in Google and short sell $8400 worth of
Yahoo! Google’s expected return is 14% with a volatility of 26% and Yahoo!’s expected return is
12% with a volatility of 26%. The stocks have a correlation of 0.92. What is the expected return
and volatility of the portfolio?
Chapter 11/Optimal Portfolio Choice and the Capital Asset Pricing Model 175
Weight in venture fund
Expected Return
Volatility
Sharpe Ratio
0.48
0.1584
0.42932971
0.275778725
0.49
0.1592
0.435789227
0.273526725
0.5
0.16
0.44229515
0.271312041
Part b
0.51
0.1608
0.448845463
0.269134947
0.52
0.1616
0.45543825
0.26699558
0.53
0.1624
0.462071694
0.264893958
0.54
0.1632
0.468744067
0.262829994
0.55
0.164
0.475453731
0.260803506
0.56
0.1648
0.482199129
0.258814238
0.57
0.1656
0.488978783
0.256861861
0.58
0.1664
0.495791287
0.254945989
0.59
0.1672
0.502635305
0.253066187
0.6
0.168
0.509509568
0.251221975
0.61
0.1688
0.516412868
0.24941284
0.62
0.1696
0.523344055
0.247638239
0.63
0.1704
0.530302037
0.245897604
0.64
0.1712
0.537285771
0.244190349
0.65
0.172
0.544294268
0.242515874
0.66
0.1728
0.551326582
0.240873566
0.67
0.1736
0.558381814
0.239262807
0.68
0.1744
0.565459106
0.237682971
0.69
0.1752
0.572557639
0.236133431
11–44. When the CAPM correctly prices risk, the market portfolio is an efficient portfolio. Explain why.
11–45. A big pharmaceutical company, DRIg, has just announced a potential cure for cancer. The stock
price increased from $5 to $100 in one day. A friend calls to tell you that he owns DRIg. You
proudly reply that you do too. Since you have been friends for some time, you know that he holds
the market, as do you, and so you both are invested in this stock. Both of you care only about
expected return and volatility. The risk-free rate is 3%, quoted as an APR based on a 365-day
year. DRIg made up 0.2% of the market portfolio before the news announcement.
a. On the announcement, your overall wealth went up by 1% (assume all other price changes
canceled out so that without DRIg, the market return would have been zero). How is your
wealth invested?
b. Your friend’s wealth went up by 2%. How is he invested?
11–46. Your investment portfolio consists of $18,000 invested in only one stock—Microsoft. Suppose the
risk-free rate is 6%, Microsoft stock has an expected return of 13% and a volatility of 44%, and
176 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
the market portfolio has an expected return of 12% and a volatility of 19%. Under the CAPM
assumptions,
a. What alternative investment has the lowest possible volatility while having the same expected
return as Microsoft? What is the volatility of this investment?
b. What investment has the highest possible expected return while having the same volatility as
Microsoft? What is the expected return of this investment?
11–47. Suppose you group all the stocks in the world into two mutually exclusive portfolios (each stock is
in only one portfolio): growth stocks and value stocks. Suppose the two portfolios have equal size
(in terms of total value), a correlation of 0.5, and the following characteristics:
The risk-free rate is 3%.
a. What is the expected return and volatility of the market portfolio (which is a 50–50
combination of the two portfolios)?
b. Does the CAPM hold in this economy? (Hint: Is the market portfolio efficient?)
