Chap 9 Mini Case

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Chapter 6 (11ed. Ch.)4
Risk and Return: The Basics

MINI CASE

Assume that you recently graduated with a major in finance, and 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 business at the end of one year, you have been instructed to plan for a one-year holding period. Further, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes. (Disregard for now the items at the bottom of the data; you will fill in the blanks later.)

Returns On Alternative Investments
Estimated Rate Of Return

State of the T-AltaRepoAm.Market2-stock

economy prob.Bills Inds Men Foamportfolioportfolio Recession0.1 8.0%-22.0%28.0%10.0%*-13.0%3.0%
Below avg0.28.0-2.014.7-10.01.0
Average0.48.020.00.07.015.010.0
Above avg0.28.035.0-10.045.029.0
Boom0.18.050.0-20.030.043.015.0
r-hat ([pic])1.7%13.8%15.0%
Std dev (σ)0.013.418.815.3

Coef of var (cv)7.91.41.0

beta (b)-0.860.68

*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 was 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.

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 which 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 collects past-due debts; and American Foam manufactures mattresses and other foam products. Barney Smith also maintains an “index fund” which 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 one year for $1,100?

Answer:Investment return measures the financial results of an investment. They may be expressed in either dollar terms or percentage terms. The dollar return is $1,100 - $1,000 = $100. The percentage return is $100/$1,000 = 0.10 = 10%.

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?

Answer:The 8 percent t-bill return does not depend on the state of the economy because the treasury must (and will) redeem the bills at par regardless of the state of the economy. The t-bills are risk-free in the default risk sense because the 8 percent return will be realized in all possible economic states. However, remember that this return is composed of the real risk-free rate, say 3 percent, plus an inflation premium, say 5 percent. Since there is uncertainty about inflation, it is unlikely that the realized real rate of return would equal the expected 3 percent. For example, if inflation averaged 6 percent over the year, then the realized real return would only be 8% - 6% = 2%, not the expected 3%. Thus, in terms of purchasing power, t-bills are not riskless. Also, if you invested in a portfolio of T-bills, and rates then declined, your nominal income would fall;...
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