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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

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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

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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

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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

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