Final Exam Practice Problems
FIN 532: Investments
Fall 2024
Risk Preference and Portfolio Choice
1. Given the following scenario analysis for stocks X and Y,
Bear Market Normal Market Bull Market
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Probability
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0.2
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0.5
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0.3
|
|
Stock X
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-20%
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18%
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50%
|
|
Stock Y
|
-15%
|
20%
|
10%
|
(a) What are the expected rates of return for Stocks X and Y?
(b) What are the standard deviations of returns on Stocks X and Y?
(c) What is the expected return and standard deviation of a portfolio with weight 0.8 in Stock X and 0.2 in Stock Y.
2. You can invest in a risky asset with an expected rate of return of 20% per year and a standard deviation of 40% per year or a risk free asset earning 5% per year or a combination of the two. The borrowing rate is 6% per year.
(a) Draw the Capital Allocation Line. Indicate the points corresponding to (1) 50% in the risk-less asset and 50% in the risky asset; and (2) -50% in the riskless asset and 150% in the risky asset.
(b) Compute the expected rate of return and standard deviation for the two portfolios in part (a).
(c) Suppose you have a target risk level of 50% per year. How would you construct a portfolio of the risky and the riskless asset to attain this target level of risk? What is the expected rate of return of the portfolio you constructed?
3. An investor is considering 3 ETFs: a stock fund, a bond fund, and T-bill fund. The T-bill fund yields a risk-free rate of 4%. The probability distribution of the risky funds are:
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Expected Ret
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Std Dev
|
|
Stock 13%
Bond 8%
Correlation = 0.3
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20%
12%
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(a) What is the mean-variance efficient mix of stocks and bonds? What is the expected return and std of the MVE?
(b) Suppose the investor has mean variance preferences with a coefficient of risk aversion of γ = 4, what would be the optimal weights in risk-free asset and the mve?
(c) In the optimal complete portfolio, what are the optimal weights in each of these three funds?
(d) Suppose that the investors has financial wealth W = $1, 000, 000 and riskless human capital with a present value of H = $500, 000. How should the investor allocate her financial wealth to each of the three funds in order to achieve the desired weights of her total wealth you calculated in part (c)?
(e) Suppose that the investor takes your advice in part (d). Over the next year, the stock fund appreciates by 20%, the bond fund appreciates by 10% and the present value of H decreases to $400,000. Explain how the investor should rebalance her portfolio?