Homework 5 Chapter 7

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Chapter 7 HW 12.Consider the following table, which gives a security analyst’s expected return on two stocks and the market index in two scenarios: (LO 7-2) a.What are the betas of the two stocks? Beta A = 2%-32%/5%-20% = 2 Beta D = 3.5% - 14% / 5% - 20% = 0.7 b. What is the expected rate of return on each stock? Expected return = [ ( 50% * 2%) + ( 50% * 32%) ] c. If the T-bill rate is 8%, draw the SML for this economy. [(50% * 5%) + (50% * 20%)] (2.5% * 10%) = 12.5% = 8% + B (12.5%-8%) Graph: d. Plot the two securities on the SML graph. What are the alphas of each? Graph: e. What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm’s stock? The rate to be used is set by the project's Beta which is 0.7 and not the firm's Beta. The optimum hurdle for Business A is 11.5 percent.

25.Suppose the yield on short-term government securities (perceived to be risk-free) is about 4%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 12%. According to the capital asset pricing model: (LO 7-2) a. What is the expected return on the market portfolio? The expected return on the market portfolio would be 12%. b. What would be the expected return on a zero-beta stock? The expected return on the zero-beta stock is 4%. c. Suppose you consider buying a share of stock at a price of $40. The stock is expected to pay a dividend of $3 next year and to sell them for $41. The stock risk has been evaluated at β = −.5. Is the stock overpriced or underpriced The fair rate of return is = 4% - 0.5 (12%-4%) = 0% Expected rate of return is =(3+41)/40-1 = 10% The stock is underpriced. 27.Consider the following data for a single-index economy. All portfolios are well diversified. Suppose another portfolio E is well diversified with a beta of 2/3 and expected return of 9%. Is there an arbitrage opportunity? If so, what is it? Treynor Ratio for A: E(R) - Risk Free / Beta 10% - 4% / 1 = 6 Treynor for E: 9% - 4% / 0.667= 7.5 The treynor ratio for portfolio E is higher. Due to that, no arbitrage opportunity exists. 29.Assume the return on a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 30%. Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 3% and one-half have an alpha of −3%. The analyst then buys $1 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1 million of an equally weighted portfolio of the negative-alpha stocks. (LO 7-4) a. What is the expected profit (in dollars), and what is the standard deviation of the analyst’s profit? 1,000,000 (0.03+ 1*Rm) - 1,000,000 (-0.03 * Rm) = 9,000 Standard Deviation: 20(1,000,000*0.3)^2 = 1800000000000 Square root of 1.8 X 10^11 = 1341640 SD b. How does your answer change if the analyst examines 50 stocks instead of 20? 100 stocks? 2,000,000 / 50 = 40,000 placed in each position.

50*(40,000*0.3)^2 = 7200000000 Square root = 84852 SD 33.Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 7%, and all stocks have independent firm-specific components with a standard deviation of 50%. Portfolios A and B are both well diversified. A expect return=Risk free rate + Beta on M1 * Risk premium 1 * Beta on M2 * Risk premium 2 40 = 7% + 1.8 * Risk Premium 1 * 2.1 * Risk Premium 2 B expected return=Risk free rate + Beta on M1 * Risk premium 1 * Beta on M2 * Risk premium 2 10 = 7% + 2.0 * Risk premium 1 * -0.5 * Risk premium 2 What is the expected return–beta relationship in this economy? Expected return beta relationship in this economy is 6.50% + 3.42% BP1 + 8.30% BP2.

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