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cost of capital for an average-risk

How can one estimate the opportunity cost of capital for an average-risk project?

Over the past 73 years the return on the Standard & Poor s Composite Index of common stocks has averaged almost 9.4 percent a year higher than the return on safe Treasury bills. This is the risk premium that investors have received for taking on the risk of investing in stocks. Long- term bonds have offered a higher return than Treasury bills but less than stocks. If the risk premium in the past is a guide to the future, we can estimate the expected return on the market today by adding that 9.4 percent expected risk premium to today s interest rate on Treasury bills. This would be the opportunity cost of capital for an averagerisk project, that is, one with the same risk as a typical share of common stock.

How is the standard deviation of returns for individual common stocks or for a stock portfolio calculated?

The spread of outcomes on different investments is commonly measured by the variance or standard deviation of the possible outcomes. The variance is the average of the squared deviations around the average outcome, and the standard deviation is the square root of the variance. The standard deviation of the returns on a market portfolio of common stocks has averaged about 20 percent a year.

Why does diversification reduce risk?

The standard deviation of returns is generally higher on individual stocks than it is on the market. Because individual stocks do not move in exact lockstep, much of their risk can be diversified away. By spreading your portfolio across many investments you smooth out the risk of your overall position. The risk that can be eliminated through diversification is known as unique risk.

What is the difference between unique risk, which can be diversified away, and market risk, which cannot?

Even if you hold a well-diversified portfolio, you will not eliminate all risk. You will still be exposed to macroeconomic changes that affect most stocks and the overall stock market. These macro risks combine to create market risk that is, the risk that the market as a whole will slump.

Stocks are not all equally risky. But what do we mean by a high-risk stock ? We don t mean a stock that is risky if held in isolation; we mean a stock that makes an above-average contribution to the risk of a diversified portfolio. In other words, investors don t need to worry much about the risk that they can diversify away; they do need to worry about risk that can t be diversified. This depends on the stock s sensitivity to macroeconomic conditions.

Rate of Return. A stock is selling today for $40 per share. At the end of the year, it pays a dividend of $2 per share and sells for $44. What is the total rate of return on the stock? What are the dividend yield and capital gains yield?

2. Rate of Return. Return to problem 1. Suppose the year-end stock price after the dividend is paid is $36. What are the dividend yield and capital gains yield in this case? Why is the dividend yield unaffected?

3. Real versus Nominal Returns. You purchase 100 shares of stock for $40 a share. The stock pays a $2 per share dividend at year-end. What is the rate of return on your investment for these end-of-year stock prices? What is your real (inflation-adjusted) rate of return? Assume an inflation rate of 5 percent.

a. $38

b. $40

c. $42

4. Real versus Nominal Returns. The Costaguanan stock market provided a rate of return of 95 percent. The inflation rate in Costaguana during the year was 80 percent. In the United States, in contrast, the stock market return was only 14 percent, but the inflation rate was only 3 percent. Which country s stock market provided the higher real rate of return? 5. Real versus Nominal Returns. The inflation rate in the United States between 1950 and 1998 averaged 4.4 percent. What was the average real rate of return on Treasury bills, Treasury bonds, and common stocks in that period? Use the data in Self-Test 2.

6. Real versus Nominal Returns. Do you think it is possible for risk-free Treasury bills to offer a negative nominal interest rate? Might they offer a negative real expected rate of return?

7. Market Indexes. The accompanying table shows the complete history of stock prices on the Polish stock exchange for 9 weeks in 1991. At that time only five stocks were traded. Construct two stock market indexes, one using weights as calculated in the Dow Jones Industrial Average, the other using weights as calculated in the Standard & Poor s Composite Index.