BKM CHAPTER 7
1. Which of the following factors reflect pure market risk for a given corporation?
a. Increased short-term interest rates
b. Fire in the corporate warehouse
c. Increased insurance costs
d. Death of the CEO, e. Increased labor costs)
(a) and (e) – The other three do not affect all participants in the economy.
2. When adding real estate to an asset allocation program that currently includes only stocks, bonds, and cash alternatives (risk-free-money market investments), which of the properties of real estate returns affect portfolio risk? Explain.
a. Standard Deviation
b. Expected Return
c. Correlation with the returns of other ...view middle of the document...
Since the standard deviation is the square root of the variance, the portfolio with the minimum standard deviation must also have the minimum variance so it is therefore the minimum risk portfolio. All three terms describe the same portfolio.
(a) is valid. This is the definition of the minimum variance (aka minimum risk or minimum standard deviation) portfolio.
(b) is not valid. The E(r) of the minimum variance portfolio must exceed the risk-free rate since the risk is still greater than zero.
(c) is not valid. It will not be the optimal risky portfolio because there exists another portfolio, that when combined with the risk-free assets, will produce a larger CAL slope. See your notes or figure 7.13 on page 215. G is the Global minimum variance portfolio and P is the optimal risky portfolio.
(d) is not valid. The minimum variance portfolio (or the optimal risky portfolio for that matter) may be formed using zero-weights for many assets.
The following data apply to Problems 4 through 10: 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:
| E(r) | σ |
Stock Fund (S) | 20% | 30% |
Bond Fund (B) | 12% | 15% |
The correlation between the funds is 0.10.
4. What are the investment proportions in the minimum-variance portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return?
The parameters of the opportunity set are:
E(rS) = 20%, E(rB) = 12%
σS = 30%, σB = 15%
ρAB = 0.10
From the standard deviations and the correlation coefficient we can generate the “covariance matrix” (note that σSB = ρSB x σS X σB):
| Bonds | Stocks |
Bonds | .0225 | .0045 |
Stocks | .0045 | .0900 |
For formula for the minimum variance weight is on page 204 in the text.
(I did not derive this in class.)
WSMin = 1 0.1739 = 0.8261
Expected Return Standard Deviation of the minimum variance portfolio are:
E(rMin) = (0.1739)(0.20) + (0.8261)(0.12) = 13.39%
= [(0.1739)2(0.30) 2 + (0.8261)2(0.15) 2 + 2(0.1739)(0.8261)(0.0045)]1/2 = 13.92%
5. Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of zero to 100% in increments of 20%.
WS | WB | E(r) | | |
0% | 100% | 12.00% | 15.00% | |
20% | 80% | 13.60% | 13.94% | |
40% | 60% | 15.20% | 15.70% | |
60% | 40% | 16.80% | 19.53% | |
80% | 20% | 18.40% | 24.48% | |
100% | 0% | 20.00% | 30.00% | |
6. Draw a tangent from the risk-free rate to the opportunity set. What does your graph show for the expected return and standard deviation of the optimal portfolio?
(Chart of everything later.)
7. Solve numerically...