# Foundations of Finance – Class 3 & 4 – Portfolio Theory: BKM Ch.6, 7 and 8

 Chapter 61. Which of the following choices best completes the following statement? Explain. An investor with a higher degree of risk aversion, compared to one with a lower degree, will prefer investment portfoliosa. with higher risk premiums.b. that are riskier (with higher standard deviations).c. with lower Sharpe ratios.d. with higher Sharpe ratios.e. None of the above is true. e Chapter 63. What do you think would happen to the expected return on stocks if investors perceived higher volatility in the equity market? Relate your answer to Equation 6.7. Assuming no change in risk tolerance, that is, an unchanged risk aversion coefficient (A),then higher perceived volatility increases the denominator of the equation for the optimal investment in the risky portfolio (Equation 6.12). The proportion invested in therisky portfolio will therefore decrease. Chapter 610. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as follows:W bills W index0 1.00.2 0.80.4 0.60.6 0.40.8 0.21.0 0 Chapter 613. You manage a risky portfolio with expected rateof return of 18% and standard deviation of 28%. The T-bill rate is 8%.Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected value and standard deviation of the rate of return on his portfolio? Chapter 7The 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: Expected Return Standard DeviationStock fund (S) 20% 30%Bond fund (B) 12 155. Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportionsfor the stock fund of zero to 100% in increments of 20%. Chapter 7The 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: Expected Return Standard DeviationStock fund (S) 20% 30%Bond fund (B) 12 156. 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? Chapter 7The 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: Expected Return Standard DeviationStock fund (S) 20% 30%Bond fund (B) 12 158. What is the Sharpe ratio of the best feasible CAL? Chapter 7The 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: Expected Return Standard DeviationStock fund (S) 20% 30%Bond fund (B) 12 159. You require that your portfolio yield an expected return of 14%, and that it be efficient, on the best feasible CAL. Chapter 7The 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: Expected Return Standard DeviationStock fund (S) 20% 30%Bond fund (B) 12 1510. If you were to use only the two risky funds, and still require an expected return of 14%, what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimized portfolio in Problem 9. What do you conclude? Chapter 711. Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold offers an expected return of 10% with a standard deviation of 30%.a. In light of the apparent inferiority of gold with respect to both mean return and volatility, would anyone hold gold? If so, demonstrate graphically why one would do so.b. Given the data above, reanswer ( a ) with the additional assumption that the correlation coefficient between gold and stocks equals 1. Draw a graph illustrating why one would or would not hold gold in one’s portfolio. Could this set of assumptions for expected returns, standard deviations, and correlation represent an equilibrium for the security market? Chapter 712. Suppose that there are many stocks in the security market and that the characteristics of stocksA and B are given as follows:Stock Expected Return Standard DeviationA 10% 5%B 15 10Correlation = -1Suppose that it is possible to borrow at the risk-free rate, rf. What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from stocks A and B.) Chapter 86. The following are estimates for two stocks.Stock Exptd Return Beta Firm-Specific Std Dev A 13% 0.8 30% B 18 1.2 40The market index has a standard deviation of 22% and the risk-free rate is 8%.a. What are the standard deviations of stocks A and B?b. Suppose that we were to construct a portfolio with proportions:Stock A: .30Stock B: .45T-bills: .25Compute the expected return, standard deviation, beta, and non-systematic standard deviation of the portfolio. Chapter 8THIS PROBLEM NEEDS WORK – I WOULD USE THE BOOK AND ANSWER KEY FOR THIS ONETHIS IS THE ANSWER7.a. The two figures depict the stocks’ security characteristic lines (SCL). Stock A has higher firm-specific risk because the deviations of the observations from the SCL are larger for Stock A than for Stock B. Deviations are measured by the vertical distance of each observation from the SCL.b. Beta is the slope of the SCL, which is the measure of systematic risk. The SCL for Stock B is steeper; hence Stock B’s systematic risk is greater.c. the ratio of the explainedce of the stock’s return to total variance, and the total variance is the sum ofβ 2 σ 22 = i M 2 2 2βi σ M + σ(eithe explained variance plus the unexplained variance (the stock’s residual variance):Since the explained variance for Stock B is greater than for Stock A (the explainedvariance is2 2, which is greater since its beta is higher), and its residualB Mvariance 2(eB ) is smaller, its R2 is higher than Stock A’s.d. Alpha is the intercept of the SCL with the expected return axis. Stock A has a small positive alpha whereas Stock B has a negative alpha; hence, Stock A’s alpha is larger.e. The correlation coefficient is simply the square root of R2, so Stock B’s correlation the market is higher. 7. Chapter 88. Consider the two (excess return) index model regression results for A and B:R A = 1% + 1.2 R MR -square = 0.576Residual standard deviation = 10.3%R B = -2% + .8 R MR -square = 0.436Residual standard deviation = 9.1%a. Which stock has more firm-specific risk?b. Which has greater market risk?c. For which stock does market movement explain a greater fraction of return variability?d. If r f were constant at 6% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A ? Chapter 89. Use the following data for Problems 9 through 14. Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + 0.7RM + eARB = -2% + 1.2RM + eBsM = 20%; R-squareA = .20; R-squareB = 0.129. What is the standard deviation of each stock? Chapter 810. Use the following data for Problems 9 through 14. Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + 0.7RM + eARB = -2% + 1.2RM + eBsM = 20%; R-squareA = .20; R-squareB = 0.1210. Break down the variance of each stock to the systematic and firm-specific components. Chapter 811. Use the following data for Problems 9 through 14. Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + 0.7RM + eARB = -2% + 1.2RM + eBsM = 20%; R-squareA = .20; R-squareB = 0.1211. What are the covariance and correlation coefficient between the two stocks? Chapter 812. Use the following data for Problems 9 through 14. Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + 0.7RM + eARB = -2% + 1.2RM + eBsM = 20%; R-squareA = .20; R-squareB = 0.1212. What is the covariance between each stock and the market index? Chapter 813. Use the following data for Problems 9 through 14. Suppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + 0.7RM + eARB = -2% + 1.2RM + eBsM = 20%; R-squareA = .20; R-squareB = 0.1213. For portfolio P with investment proportions of .60 in A and .40 in B, rework Problems 9, 10, and 12.
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