142Part TWO Portfolio TheoryFor Problems 12-16, assume that you manage a risky portfolio with an expected rate ofreturn of 17% and a standard deviation of 27%. The T-bill rate is 7%.12. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-billmarket fund. (LO 5-3)a. What are the expected return and standard deviation of your client's portfolio?b. Suppose your risky portfolio includes the following investments in the givenproportions:money27%Stock AStock B33Stock C40your client's overall portfolio.I

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Chapter8: Analysis Of Risk And Return

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142
Part TWO Portfolio Theory
For Problems 12-16, assume that you manage a risky portfolio with an expected rate of
return of 17% and a standard deviation of 27%. The T-bill rate is 7%.
12. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill
market fund. (LO 5-3)
a. What are the expected return and standard deviation of your client's portfolio?
b. Suppose your risky portfolio includes the following investments in the given
proportions:
money
27%
Stock A
Stock B
33
Stock C
40
your client's overall portfolio.
I

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Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The covariance between the two is 0.084. 1. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio? 2. In addition to the funds A and B in the previous question, now you decide to include fund C to your portfolio. Its expected return is 10, its variance 0.0625, its correlation with A is 0.1050 and its correlation with B is 0.07. You want to achieve an expected return of 16% on your portfolio, with the minimum possible risk (measured by the standard deviation). Derive analytically (that is, without the help of solver, but trough calculus) the weights of such desired portfolio, and its standard deviation.
3.1 Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The covariance between the two is 0.084. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio?
Suppose you have the following investments: Security Amount Invested Expected Return Beta A $2,000 5% .80 B $4,000 10% .95 C $6,000 15% 1.10 D $8,000 18% 1.40 What is the beta of the portfolio? Select one: a. 1.16 b. 0.59 c. 1.34 d. 1.20
Question 7 The following figures show the optimal portfolio choice for two investors with different levels of risk-aversion graphically. Which statement is correct? E[R] 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 Figure 1 0.2 0.25 0.3 0.35 0.4 0.45 o(R) [a]H 0.3 0.25 0.2 0.15 0.1 0.05 0 0 Figure (2) shows an investor that borrows in risk-free rate and invests in the risky asset. Figure (1) shows an investor with a conservative investment behavior. 0.05 0.1 0.15 In the optimal point of both figures, the highest indifference curve is tangent to the efficient frontier. In Figure (1), more aggressive investment decision led to a higher Sharpe ratio. Figure 2 0.2 0.25 o (R) 0.3 0.35 0.4 0.45
Question 14 If the simple CAPM is valid and all portfolios are priced correctly, which of the situations below is possible? Consider each situation independently. and assume the rísk-free rate is 2.5%. A) Portfolio Expected Return Beta A 17.5% 1.5 Market 12.5% 1.0 B) Portfolio Expected Return Standard Deviation A 8.5% 18.0% Market 10.0% 24.0% Portfolio Expected Return 13.5% 10.0% Beta A 1.2 Market 1.0 D) Portfolio Expected Return Beta A 7.5% 0.6 Market 10.0% 1.0 Option D Option A Option C Option B
Suppose you have the following investments: Security Amount Invested Expected Return Beta A $2,000 5% .80 B $4,000 10% .95 C $6,000 15% 1.10 D $8,000 18% 1.40 What is the expected return on this portfolio? Select one: a. 15.2% b. 16.4% c. 14.2% d. 14.9%
QUESTION 4 There are only 2 assets to invest in, both being risky. AAPL has an expected return of 10% and volatility of 15%. MSFT has an expected return of 12% and volatility of 18%. Which one of the following statements is correct? On the expected return-volatility space, the set of all feasible risky portfolios is a straight line. On the expected return-volatility space, the set of all feasible risky portfolios is a curve that does not go through any of the 2 risky assets. 100% invested in MSFT is an efficient portfolio. 100% invested in AAPL is an efficient portfolio.
Question 2: If the simple CAPM is valid, which of the following situations are possible? Consider each situation separately. a) b) c) d) f) Portfolio A B Portfolio A B Expected Return 20 25 Expected Return 30 40 Portfolio Risk-free 7 Market A Portfolio Risk-free Market A Expected Return 16 14 Portfolio Risk-free 10 Market 18 A 20 Expected Return Expected Return 7 17 13 Portfolio Risk-free 4 Market A Expected Return 17 13 Beta 1.4 1.2 Standard Deviation 35 25 Standard Deviation 0 30 15 Standard Deviation 0 24 22 Beta 0 1.5 2 Standard Deviation 0 31 16
Question 1: Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. Stock A Stock B Stock C 1. Calculate the client expected return on the complete portfolio 2. Calculate the reward-to-variability ratio (Sharpe ratio): Part B A three-asset portfolio has the following characteristics: Expected Return Asset X Y Z 15% 10 6 Standard Deviation What is the expected return on this three-asset portfolio? 27% 33% 40% 22% 8 3 Weight 0.50 0.40 0.10
9. Plot the following risky portfolios on a graph: B 10 11 Portfolio A Expected return, % 8 Standard Deviation, % 13 C D E F 12.5 14 16 20 15 19 19 22 G 20 25 H 23 33 a) Which of these portfolios are efficient? Which portfolios are inefficient? b) Suppose you can also borrow and lend at an interest-rate of 10 percent. Which of the above portfolios is the best one? c) Suppose you are prepared to tolerate a standard deviation of 15 percent. What is the maximum expected return that you can achieve if you cannot borrow nor lend? d) What is your optimal strategy, if you can borrow or lend at 10 percent and are prepared to tolerate a standard deviation of 15 percent? What is the maximum expected return that you can achieve?
Question 7 Consider the following Information: Portfolio ER Risk Free Market SD 6.00 13.2 A 11.2 a. Calculate the Sharpe ratios for the market portfolio and portfolio A Sharpe Ratio=(Return on portfolio-Riskfreerate)/SD Market Portfo 0.2 Portfolio A 0.21 2.1 b. If the simple CAPM is valid, is the above situation possible? 0.00 36 25 Beta Market Beta A
Question 2: If the simple CAPM is valid, which of the following situations are possible? Consider each situation separately. a) b) c) d) e) f) Portfolio A B Portfolio A B Expected Return 20 25 Expected Return 30 40 Portfolio Risk-free 7 Market A Expected Return 16 14 Portfolio Risk-free 10 Market 18 A 20 Expected Return Portfolio Risk-free 7 Market A Expected Return 17 13 Portfolio Risk-free 4 Market A Expected Return 17 13 Beta 1.4 1.2 Standard Deviation 35 25 Standard Deviation 0 30 15 Standard Deviation 0 24 22 Beta 0 1.5 2 Standard Deviation 0 31 16

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