• Assume that you recently graduated with a major in finance and that you just landed a job as a financial planner with Barney Smith Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds are to be invested in a new business that the client plans to start at the end of 1 year, you have been instructed to plan for a 1-year holding period. Further, your boss has restricted you to the investment alternatives shown in the table below. (Disregard for now the items at the bottom of the data; you will fill in the blanks later.) Barney Smith’s economic forecasting staff has developed probability estimates for the state of the economy, and its security analysts have developed a sophisticated computer program that was used to estimate the rate of return on each alternative under each state of the economy. Alta Industries is an electronics firm; Repo Men Inc. collects past-due debts; and American Foam manufactures mattresses and various other foam products. Barney Smith also maintains an “index fund” that owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund and thus obtain average stock market results. Given the situation as described, answer the following questions. a. What are investment returns? What is the return on an investment that costs $1,000 and is sold after 1 year for $1,100? Estimated Returns on Alternative Investments State of the Economy Probability T-Bills Alta Industries Repo Men American Foam Market Portfolio 2-Stock Portfolio Recession 0.1 8.0% −22.0% 28.0% 10.0%a −13.0% 3.0% Below average 0.2 8.0 −2.0 14.7 −10.0 1.0 Average 0.4 8.0 20.0 0.0 7.0 15.0 10.0 Above average 0.2 8.0 35.0 −10.0 45.0 29.0 Boom 0.1 8.0 50.0 −20.0 30.0 43.0 15.0 r ^ 8.0% 1.7% 13.8% 15.0% σ 0.0% 13.4% 18.8% 15.3% CV 7.9 1.4 1.0 b −0.86 0.68 a Note that the estimated returns of American Foam do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer mattresses than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a more expensive inner spring mattress may purchase, instead, a cheaper foam mattress. Under these circumstances, we would expect American Foam’s stock price to be higher if there is a recession than if the economy was just below average. Chapter 6: Risk, Return, and the Capital Asset Pricing Model 263 b. (1) Why is the T-bill’s return independent of the state of the economy? Do T-bills promise a completely risk-free return? (2) Why are Alta Industries’s returns expected to move with the economy whereas Repo Men’s are expected to move counter to the economy? c. Calculate the expected rate of return on each alternative and fill in the blanks in the row for ^r in the table. d. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because your client, like virtually everyone, is risk averse, the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. (1) Calculate this value for each alternative, and fill in the blank in the row for σ in the table. (2) What type of risk is measured by the standard deviation? (3) Draw a graph that shows roughly the shape of the probability distributions for Alta Industries, American Foam, and T-bills. e. Suppose you suddenly remembered that the coefficient of variation (CV) is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVs, and fill in the blanks in the row for CV in the table. Does the CV produce the same risk rankings as the standard deviation? f. Suppose you created a two-stock portfolio by investing $50,000 in Alta Industries and $50,000 in Repo Men. (1) Calculate the expected return (^r p), the standard deviation (σp), and the coefficient of variation (CVp) for this portfolio and fill in the appropriate blanks in the table. (2) How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation? g. Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio’s risk and its expected return? What is the implication for investors? Draw a graph of the two portfolios to illustrate your answer. h. (1) Should portfolio effects influence how investors think about the risk of individual stocks? (2) If you decided to hold a one-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying? i. How is market risk measured for individual securities? How are beta coefficients calculated? j. Suppose you have the following historical returns for the stock market and for the company P. Q. Unlimited. Explain how to calculate beta, and use the historical stock returns to calculate the beta for PQU. Interpret your results. Year Market PQU 1 25.7% 40.0% 2 8.0 −15.0 3 −11.0 −15.0 4 15.0 35.0 5 32.5 10.0 6 13.7 30.0 7 40.0 42.0 8 10.0 −10.0 9 −10.8 −25.0 10 −13.1 25.0 264 Part 3: Stocks and Options k. The expected rates of return and the beta coefficients of the alternatives, as supplied by Barney Smith’s computer program, are as follows: (1) Do the expected returns appear to be related to each alternative’s market risk? (2) Is it possible to choose among the alternatives on the basis of the information developed thus far? l. (1) Write out the Security Market Line (SML) equation, use it to calculate the required rate of return on each alternative, and then graph the relationship between the expected and required rates of return. (2) How do the expected rates of return compare with the required rates of return? (3) Does it make sense that Repo Men has an expected return that is less than the T-bill rate? (4) What would be the market risk and the required return of a 50-50 portfolio of Alta Industries and Repo Men? Of Alta Industries and American Foam? m. (1) Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 8% T-bill rate. What effect would higher inflation have on the SML and on the returns required on high- and low-risk securities? (2) Suppose instead that investors’ risk aversion increased enough to cause the market risk premium to increase by 3 percentage points. (Assume inflation remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities?