Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
36. Consider a T-bill with a rate of return of 5 percent and the following risky securities: Security A: E(r) = 0.15; Variance = 0.04 Security B: E(r) = 0.10; Variance = 0.0225 Security C: E(r) = 0.12; Variance = 0.01 Security D: E(r) = 0.13; Variance = 0.0625
From which set of portfolios, formed with the T-bill and any one of the 4 risky securities, would a risk-averse investor always choose his portfolio?
A. The set of portfolios formed with the T-bill and security A. B. The set of portfolios formed with the T-bill and security B. C. The set of portfolios formed with the T-bill and security C. D. The set of portfolios formed with the T-bill and security D. E. Cannot be determined.
Security C has the highest reward-to-volatility ratio.
AACSB: Analytic Bloom's: Apply
Difficulty: Challenge
Topic: Portfolio Risk Allocation
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081.
37. If you want to form a portfolio with an expected rate of return of 0.11, what percentages of your money must you invest in the T-bill and P, respectively? A. 0.25; 0.75 B. 0.19; 0.81 C. 0.65; 0.35 D. 0.50; 0.50
E. cannot be determined
E(rp) = 0.6(14%) + 0.4(10%) = 12.4%; 11% = 5x + 12.4(1 ? x); x = 0.189 (T-bills) (1 ? x) = 0.811 (risky asset).
AACSB: Analytic Bloom's: Apply
Difficulty: Intermediate
Topic: Portfolio Risk Allocation
6-41
Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
38. If you want to form a portfolio with an expected rate of return of 0.10, what percentages of your money must you invest in the T-bill, X, and Y, respectively if you keep X and Y in the same proportions to each other as in portfolio P? A. 0.25; 0.45; 0.30 B. 0.19; 0.49; 0.32 C. 0.32; 0.41; 0.27 D. 0.50; 0.30; 0.20
E. cannot be determined
10 = 5w + 12.4(1 ? w); w = 0.32 (weight of T-bills); as composition of X and Y are .6 and .4 of P, respectively, then for 0.68 weight in P, the respective weights must be 0.41 and 0.27; .6(.68) = 41%; .4(.68) = 27%
AACSB: Analytic Bloom's: Apply
Difficulty: Challenge
Topic: Portfolio Risk Allocation
39. What would be the dollar values of your positions in X and Y, respectively, if you decide to hold 40% percent of your money in the risky portfolio and 60% in T-bills? A. $240; $360 B. $360; $240 C. $100; $240 D. $240; $160
E. Cannot be determined
$400(0.6) = $240 in X; $400(0.4) = $160 in Y.
AACSB: Analytic Bloom's: Apply
Difficulty: Intermediate
Topic: Portfolio Risk Allocation
6-42
Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
40. What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a portfolio that has an expected outcome of $1,120? A. Cannot be determined B. $568; $378; $54 C. $568; $54; $378 D. $378; $54; $568 E. $108; $514; $378
($1,120 - $1,000)/$1,000 = 12%; (0.6)14% + (0.4)10% = 12.4%; 12% = w5% + 12.4%(1 ? w);w = .054; 1 ? w = .946; w = 0.054($1,000) = $54 (T-bills); 1 ? w = 1 ? 0.054 = 0.946($1,000) = $946; $946 × 0.6 = $568 in X; $946 × 0.4 = $378 in Y.
AACSB: Analytic Bloom's: Apply
Difficulty: Challenge
Topic: Portfolio Risk Allocation
41. A reward-to-volatility ratio is useful in: A. measuring the standard deviation of returns.
B. understanding how returns increase relative to risk increases. C. analyzing returns on variable rate bonds. D. assessing the effects of inflation. E. None of these is correct.
A reward-to-volatility ratio is useful in understanding how returns increase relative to risk increases.
AACSB: Analytic Bloom's: Understand Difficulty: Intermediate
Topic: Portfolio Risk Allocation
6-43
Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
42. The change from a straight to a kinked capital allocation line is a result of: A. reward-to-volatility ratio increasing. B. borrowing rate exceeding lending rate. C. an investor's risk tolerance decreasing.
D. increase in the portfolio proportion of the risk-free asset. E. a flawed theory.
The linear capital allocation line assumes that the investor may borrow and lend at the same rate (the risk-free rate), which obviously is not true. Relaxing this assumption and incorporating the higher borrowing rates into the model results in the kinked capital allocation line.
AACSB: Analytic Bloom's: Understand Difficulty: Challenge
Topic: Portfolio Risk Allocation
43. The first major step in asset allocation is: A. assessing risk tolerance.
B. analyzing financial statements. C. estimating security betas. D. identifying market anomalies.
E. determining how much money a client needs to make.
Assessing risk tolerance should be the first consideration in asset allocation.
AACSB: Analytic Bloom's: Remember Difficulty: Intermediate
Topic: Portfolio Risk Allocation
6-44
Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
44. Based on their relative degrees of risk tolerance
A. investors will hold varying amounts of the risky asset in their portfolios. B. all investors will have the same portfolio asset allocations.
C. investors will hold varying amounts of the risk-free asset in their portfolios.
D. investors will hold varying amounts of the risky asset and the risk-free asset in their portfolios.
E. investors would perform vastly different levels of security analysis.
By determining levels of risk tolerance, investors can select the optimum portfolio for their own needs; these asset allocations will vary between amounts of risk-free and risky assets based on risk tolerance.
AACSB: Analytic Bloom's: Remember Difficulty: Basic
Topic: Risk Tolerance
45. Asset allocation
A. may involve the decision as to the allocation between a risk-free asset and a risky asset only. B. may involve the decision as to the allocation among different risky assets only. C. may involve considerable security analysis.
D. may involve the decision as to the allocation between a risk-free asset and a risky asset and may involve the decision as to the allocation among different risky assets.
E. may involve the decision as to the allocation between a risk-free asset and a risky asset and may involve considerable security analysis.
Asset allocation may involve the decision as to the allocation between a risk-free asset and a risky asset and also involve the decision as to the allocation among different risky assets.
AACSB: Analytic Bloom's: Understand Difficulty: Basic
Topic: Portfolio Risk Allocation
6-45