Calculations:
None necessary
Answer:
Problem 7-1
Which of the following factors reflect pure market risk for a given corporation? (Select all that apply.)
Increased short-term interest rates.
Fire in the corporate warehouse.
Increased insurance costs.
Death of the CEO.
Increased labor costs.
Answer:
Problem 7-2
When adding real estate to an asset allocation program that currently includes only stocks, bonds, and cash, which of the properties of real
estate returns affect portfolio risk?(Select all that apply.)
Standard deviation.
Expected return.
Correlation with returns of the other asset classes.
Problem 7-3
Which of the following statements about the minimum variance portfolio of all risky securities are valid? (Assume short sales are allowed.)
Its variance must be lower than those of all other securities or portfolios.
Its expected return can be lower than the risk-free rate.
It may be the optimal risky portfolio.
It must include all individual securities.
Stock Bond
Expected Return 0.22 0.12 Expected Value 0.1237
Std Deviation 0.38 0.16 Std Deviation 14.82
Correlation 0.1
Minimum variance stock 0.1324
Minimum variance bond 0.8763
Covariance matrix Stock Bond
Stock 1444 60.8
Bond 60.8 256
Answers:
(Do not round intermediate calculations. Round your
Expected Return Std Deviation Covariance Matrix
Stock Fund 0.2 0.3 Stock Bonds
Proportion in SF Proportion in BF Expected Return Std Deviation Minimum variance stock 0.1739
Minimum variance bond 0.8261
0 1 0.12 0.15
0.1739 0.8261 0.1339 0.1392
Problem 7-5
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the
third is a T-bill money market fund that yields a rate of 8%. The probability distribution of the risky funds is as follows:
Expected Return Standard Deviation
Tabulate the investment opportunity set of the two risky funds. (Round your answers to 2 decimal places. Omit the “%” sign in your response.)
Proportion in Stock Fund Proportion in Bond Fund Expected Return Standard Deviation
0.00% 100.00% % %
Bond Fund 0.12 0.15 Stock 0.09 0.0045
Risk Free Rate 0.08
Stock Bond
Expected Return 0.17 0.13
Std Deviation 0.38 0.18
Correlation 0.12
Answers: Expected Value 0.136034
Std Deviation 0.169561
Ws30.66% Portfolio invested in stock
WB69.34% Portfolio invested in bonds
Problem 7-7
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the
third is a T-bill money market fund that yields a rate of 8%. The probability distribution of the risky funds is as follows:
Expected Return Standard Deviation
Stock fund (S) 20% 30%
Bond fund (B) 12 15
Stock Bond
Expected Return 0.24 0.12
Std Deviation 0.3 0.19
Correlation 0.13
Minimum variance stock 0.2578
Minimum variance bond 0.7422
Expected Value 0.1844
Std Deviation 0.1933
WS0.5368
WB0.4632
Problem 7-8
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and
the third is a T-bill money market fund that yields a rate of 8%. The probability distribution of the risky funds is as follows:
Expected Return Standard Deviation
Stock fund (S) 20% 30%
Bond fund (B)12 15
Stock Bond
Expected Return 0.19 0.12
Std Deviation 0.32 0.15
Correlation 0.11
Risk Free Rate 0.05
Covariance matrix Stock Bond
WS0.3019
WB0.6981 Portfolio ER E(rc) = 0.14
rf = 0.05
ER 0.1411
E(rp) = 0.1411
Problem 7-9
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and co
rporate bond fund,
and the third is a T-bill money market fund that yields a rate of 8%. The probability distribution of the risky funds is as follows:
Expected Return Standard Deviation Stock fund
(S) 20% 30% Bond fund (B)
12 15
The correlation between the fund returns is 0.10.
You require that your portfolio yield an expected return of 14%, and that it be efficient, on the best feasible CAL.
Standard deviation %
b. What is the proportion invested in the T-bill fund and each of the two risky funds? (Round your answers to 2 decimal places. Omit the “%” sign
Stock A Stock B
Expected Return 0.12 0.19
Std Deviation 0.04 0.12
Correlation -1
wA0.75
wB0.25
Answer: E(r) 0.1375
Problem 7-12
Suppose that there are many stocks in the security market and that the characteristics of stocks Aand B are given as follows:
Stock Expected Return Standard Deviation
A 10% 5%
B 15 10
σP= Absolute value [wAσA–wBσB]
0 = .05 × wA− [.10 × (1 –wA)] => wA= 0.6667
The expected rate of return for this risk-free
Calculations:
None necessary
value:
10.00 points
Problem 7-13
Assume that expected returns and standard deviations for all securities (including the risk-free rate for
borrowing and lending) are known. In this case all investors will have the same optimal risky portfolio.
Calculations:
None necessary
Problem 7-14
The standard deviation of the portfolio is always equal to the weighted average of the standard deviations of the assets in the portfolio.
True
False
Inputs:
Probability Rate of Return
Problem 7-15
Suppose you have a project that has a 0.7 chance of doubling your investment in a year and a 0.3 chance of halving your investment in a year. What is the
standard deviation of the rate of return on this investment?(Do not round your intermediate calculations. Round your answer to 2 decimal places. Omit
the “%” sign in your response.)
Problem 7-16
Suppose that you have $1 million and the following two opportunities from which to construct a portfolio:
a.Risk-free asset earning 12% per year.
b.Risky asset with expected return of 30% per year and standard deviation of 40%.
If you construct a portfolio with a standard deviation of 30%, what is its expected rate of return? (Do not round your intermediate calculations. Round your
answer to 1 decimal place. Omit the “%” sign in your response.)
Risk Premium SD
S&P 0.08 0.14
Answers:
S&P Portfolio Hedge Fund Portfolio
Problem 7-22
Greta, an elderly investor, has a degree of risk aversion of A= 3 when applied to return on wealth over a 3-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund,
as well as a number of 3-year strategies. (All rates are annual, continuously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a SD of 20%. The hedge fund risk
premium is estimated at 10% with a SD of 35%. The return on each of these portfolios in any year is uncorrelated with its ret urn or the return of any other portfolio in any other year.
The hedge fund management claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta believes this is far
from certain.
Compute the estimated 3-year risk premiums, SDs, and Sharpe ratios for the two portfolios. (Do not round your intermediate calculations. Round “sharpe ratios” into 4 decimal
places. Omit the “%” sign in your response.)
S&P Portfolio Hedge Fund Portfolio
Risk Premium SD
S&P 0.1 0.24
Hedge Fund 0.08 0.38
σP0.3533
Answers:
Sharpe ratio of Portfolio 0.888671
a1. Optimal Asset Allocation
% invested in risky portfolio 0.8383
S&P 0.7616
Hedge 0.2384
Problem 7-23
Greta, an elderly investor, has a degree of risk aversion ofA= 3 when applied to return on wealth over a 3-year horizon. She is pondering two portfolios, the S&P 500 and
a hedge fund, as well as a number of 3-year strategies. (All rates are annual, continuously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a SD
of 20%. The hedge fund risk premium is estimated at 10% with a SD of 35%. The return on each of these portfolios in any year is uncorrelated with its return or the return
of any other portfolio in any other year. The hedge fund management claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in
the same year is zero, but Greta believes this is far from certain.
a-1.Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation? (Do not round intermediate
calculations. Round your answers to 4 decimal places.)
S&P
Inputs:
Problem 7-24
Greta, an elderly investor, has a degree of risk aversion of A= 3 when applied to return on wealth over a 3-year horizon. She is pondering two portfolios, the S&P 500
and a hedge fund, as well as a number of 3-year strategies. (All rates are annual, continuously compounded.) The S&P 500 risk premium is estimated at 5% per year,
with a SD of 20%. The hedge fund risk premium is estimated at 10% with a SD of 35%. The return on each of these portfolios in any year is uncorrelated with its return
Inputs:
Risk aversion 5
S&P RP 0.05
Problem 7-25
Greta, an elderly investor, has a degree of risk aversion ofA= 3 when applied to return on wealth over a 3-year horizon. She is pondering two
portfolios, the S&P 500 and a hedge fund, as well as a number of 3-year strategies. (All rates are annual, continuously compounded.) The S&P 500 risk
premium is estimated at 5% per year, with a SD of 20%. The hedge fund risk premium is estimated at 10% with a SD of 35%. The ret
urn on each of these
S&P SD 0.2
Hedge Fund RP 0.12
Hedge Fund SD 0.4
S&P 3yr SD 0.447214
Hedge Fund 3yr SD 0.894427
3yr Covariance 0.12
Inputs:
Risk aversion 5
S&P RP 0.09
S&P SD 0.17
Hedge Fund RP 0.09
Hedge Fund SD 0.34
S&P 3yr SD 0.380132
Problem 7-26
Greta, an elderly investor, has a degree of risk aversion of A= 3 when applied to return on wealth over a 3-year horizon. She is
pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 3-year strategies. (All rates are annual,
continuously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a SD of 20%. The hedge fund risk premium
is estimated at 10% with a SD of 35%. The return on each of these portfolios in any year is uncorrelated with its return or the
return
of any other portfolio in any other year. The hedge fund management claims the correlation coefficient between the annual return
s
on the S&P 500 and the hedge fund in the same year is zero, but Greta believes this is far from certain.