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«Volume Title: The Changing Roles of Debt and Equity in Financing U.S. Capital Formation Volume Author/Editor: Benjamin M. Friedman, ed. Volume ...»

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This PDF is a selection from an out-of-print volume from the National

Bureau of Economic Research

Volume Title: The Changing Roles of Debt and Equity in Financing U.S.

Capital Formation

Volume Author/Editor: Benjamin M. Friedman, ed.

Volume Publisher: University of Chicago Press

Volume ISBN: 0-226-26342-8

Volume URL: http://www.nber.org/books/frie82-1

Publication Date: 1982

Chapter Title: Risk and Return: A New Look

Chapter Author: Burton G. Malkiel

Chapter URL: http://www.nber.org/chapters/c11393 Chapter pages in book: (p. 27 - 46)

Risk and Return:

A New Look Burton G. Malkiel One of the best-documented propositions in the field of finance is that, on average, investors have received higher rates of return on investment securities for bearing greater risk. This chapter looks at the historical evidence regarding risk and return, explains the fundamentals of port- folio and asset-pricing theory, and then goes on to take a new look at the relationship between risk and return using some unexplored risk mea- sures that seem to capture quite closely the actual risks being valued in the market.

2.1 Some Historical Evidence Risk is a most slippery and elusive concept. It is hard for investors—let alone economists—to agree on a precise definition. The dictionary de- fines risk as the possibility of suffering harm or loss. If I buy one-year Treasury bills to yield, say, 10 percent and hold them until they mature, I am virtually certain of earning a 10 percent monetary return before income taxes. The possibility of loss is so small as to be considered nonexistent. But if I hold common stock in my local power and light company for one year on the basis of an anticipated 12.5 percent dividend return, the possibility of loss increases. The dividend of the company might be cut and, more important, the market price at the end of the year Burton G. Malkiel is Professor of Economics and William S. Beinecke Professor of Management Studies at Yale University, and Dean of the Yale School of Organization and Management.

The research reported in this chapter has been supported by the National Bureau of Economic Research, the Institute for Quantitative Research in Finance, the John Weinberg Foundation, and the Princeton Financial Research Center. As indicated in note 3, the empirical tests reported at the end of the chapter are taken from a joint study with John G.

Cragg of NBER and the University of British Columbia.

27 28 Burton G. Malkiel could be much lower, so that I might suffer a serious net loss. Risk is the chance that expected security returns will not materialize and, in particu- lar, that the securities I hold will fall in price.

Once academics had accepted the idea that risk for investors is related to the chance of disappointment in achieving expected security returns, a natural measure suggested itself—the probable variability or dispersion of future returns. Thus, financial risk has generally been defined as the variance or standard deviation of returns.1 Empirical studies of broad classes of securities confirm the general relationship between risk and return. The most thorough recent study has been done by Ibbotson and Sinquefield (1979). Their data covered the period 1926 through 1978. The results are shown in Table 2.1.

A quick glance shows that, over long periods of time, common stocks have, on average, provided relatively generous total rates of return.

These returns, including dividends and capital gains, have exceeded by a substantial margin the returns from long-term corporate bonds and U.S.

Treasury bills. The stock returns have also tended to be well in excess of the inflation rate as measured by the annual rate of increase in consumer prices. The data show, however, that common stock returns are highly variable as measured by the standard deviation and the range of annual returns shown in the last three columns of the table. Returns from equities have ranged from a gain of over 50 percent (in 1933) to a loss of almost the same magnitude (in 1931). Clearly, the extra returns that have been available to investors from stocks have come at the expense of assuming considerably higher risk.

The patterns evident in Ibbotson and Sinquefield's chart also appear when the returns and risks of individual stock portfolios are compared.

Indeed, most of the differences that exist in the returns from different mutual funds can be explained by differences in the risk they have assumed. However, there are ways in which investors can reduce the risks they take. This brings us to the subject of modern portfolio theory.

2.2 Reducing Risk: Modern Portfolio Theory Portfolio theory begins with the premise that all investors are risk averse. They want high returns and guaranteed outcomes. The theory tells investors how to combine stocks in their portfolios to give them the least risk possible, consistent with the return they seek. It also gives a rigorous mathematical justification for the time-honored investment

1. Variance is defined as the average squared deviation of the (periodic) investment returns from their average. The square root of the variance is the standard deviation and is also often used to measure variability and, thus, risk. While it is true that only downward surprises constitute risk, as long as the distribution of returns is symmetric, a variance measure will serve as a good proxy for the chance of disappointment.





o • 3 00 i-H

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maxim that diversification is a sensible strategy for individuals who like to reduce their risks. The basic idea was that a portfolio of risky (volatile) stocks can be put together in such a way as to be less risky than any one of the individual stocks in it. A simple illustration will make the whole game clear.

Let us suppose we have an island economy with only two businesses.

The first is a large resort with beaches, tennis courts, a golf course, and the like. The second is a manufacturer of umbrellas. Weather affects the fortunes of both. During sunny seasons the resort does a booming business and umbrella sales plummet. During rainy seasons the resort owner does very poorly, while the umbrella manufacturer enjoys high sales and large profits. Table 2.2 shows some hypothetical earnings for the two businesses during the different seasons. I assume that all earnings are paid out as dividends, so these are also the returns paid out to investors.

Suppose that, on average, one-half the seasons are sunny and one-half are rainy (i.e., the probability of a sunny or rainy season is one-half). An investor who bought stock in the umbrella manufacturer would find that half the time he earned a 50 percent return and half the time he lost 25 percent of his investment. On average, he would earn a return of 12.5 percent. This is what we call the investor's expected return. Similarly, investment in the resort would produce the same results. Investing in either one of these businesses would be fairly risky, however, because the results are quite variable, and there could be several sunny or rainy seasons in a row.

Suppose, however, that instead of buying only one security an investor with two dollars diversified and put half his money in the umbrella manufacturer's and half in the resort owner's business. In sunny seasons, a one-dollar investment in the resort would produce a fifty-cent return, while a one-dollar investment in the umbrella manufacturer would lose twenty-five cents. The investor's total return would be twenty-five cents, which is 12.5 percent of his total investment of two dollars.

Note that during rainy seasons exactly the same thing happens—only the names are changed. Investment in the umbrella manufacturer produces a good 50 percent return while the investment in the resort loses 25 percent. Again, however, the diversized investor makes a 12.5 percent return on his total investment.

This simple illustration points out the basic advantage of diversification. Whatever happens to the weather, and thus to the island economy, by diversifying investments over both of the firms an investor is sure of

–  –  –

making a 12.5 percent return each year. The trick that made the game work was that while both companies were risky (returns were variable from year to year), the companies were affected differently by weather conditions. As long as there is some lack of parallelism in the fortunes of the individual companies in the economy, diversification will always reduce risk. In the present case, where there is a perfect negative relationship between the companies' fortunes (one always does well when the other does poorly), diversification can totally eliminate risk.

Of course, there is always a rub, and the rub in this case is that the fortunes of most companies move pretty much in tandem. When there is a recession and people are unemployed, they may buy neither summer vacations nor umbrellas. Therefore, one should not expect in practice to get the neat total risk elimination just shown. Nevertheless, since company fortunes do not always move completely in parallel, investment in a diversified portfolio of stocks is likely to be less risky than investment in one or two single securities. While a portfolio of General Motors and its major steel and tire supplier would not reduce risk much, if at all, a portfolio of GM and a defense contractor in a depressed area might reduce risk substantially.

The example may seem a bit strained, and most investors will realize that when the market gets clobbered just about all stocks go down. Still, at least at certain times, some stocks do move against the market. Gold stocks are often given as an example of securities that do not typically move in the same direction as the general market. Similarly, international diversification can reduce risk. The point to realize in setting up a portfolio is that true diversification of a portfolio depends on having stocks that are not all dependent on the same economic variables (total spending in the economy, inflation rates, etc.). Wise investors will diversify their portfolios not by names or industries but by the determinants that influence the fluctuations of various securities.

2.3 Modeling Risk: The Capital-Asset Pricing Model (CAPM) Portfolio theory has important implications for how stocks are actually valued. If investors seek to reduce risk in anything like the manner described by portfolio theorists, the stock market will tend to reflect these risk-reducing activities. This brings us to what is called the "Capital-Asset Pricing Model."

I have mentioned that the reason diversification cannot usually produce the miracle of risk elimination is that usually stocks tend to move up and down together. Still, diversification is worthwhile—it can eliminate some risks. What the CAPM did was to focus directly on what part of a security's risk could be eliminated by diversification and what part could not.

32 Burton G. Malkiel The theory begins by classifying the sources of the variability of an individual stock. Part of total risk or variability may be called the security's systematic risk, arising from the basic variability of stock prices in general and the tendency for all stocks to go along with the general market, at least to some extent. The remaining variability in a stock's returns is called unsystematic risk and results from factors peculiar to that particular company, for example, a strike, the discovery of a new product, and so on.

Systematic risk, also called market risk, captures the reaction of individual stocks (or portfolios) to general market swings. Some stocks and portfolios tend to be very sensitive to market movements. Others are more stable. This relative volatility or sensitivity to market moves can be estimated on the basis of the past record, and is popularly known as the beta calculation. This calculation is essentially a comparison between the movements of an individual stock (or portfolio) and the movements of the market as a whole. It is a numerical description of systematic risk.

The calculation begins by assigning a beta of 1 to a broad market index, such as the NYSE index or the S&P 500. If a stock has a beta of 2, then on average it swings twice as far as the market. If the market goes up 10 percent, the stock rises 20 percent. If a stock has a beta of 0.5, it tends to be more stable than the market (it will go up or down 5 percent when the market rises or declines 10 percent). Professionals often call high-beta stocks aggressive investments and label low-beta stocks as defensive.

Now the important thing to realize is that systematic risk cannot be eliminated by diversification. It is precisely because all stocks move more or less in tandem (a large share of their variability is systematic) that even diversified stock portfolios are risky. Indeed, if I diversified extremely broadly by buying a share in the S&P index (which by definition has a beta of 1), I would still have quite variable (risky) returns because the market as a whole fluctuates widely.

Unsystematic risk is the variability in stock prices (and, therefore, in returns from stocks) that results from factors peculiar to an individual company. Receipt of a large new contract, discovery of mineral resources on the company's property, labor difficulties, the revelation that the corporation's treasurer has had his hand in the company till—all can make a stock's price move independently of the market. The risk associated with such variability is precisely the kind that diversification can reduce. The whole point of portfolio theory was that, to the extent that stocks do not move in tandem all the time, variations in the rehirns from any one security will tend to be washed away or smoothed out by complementary variation in the returns from other securities.

Figure 2.1 illustrates the important relationship between diversification and total risk.

Suppose we randomly selected securities for our portfolio that tended on average to be just as volatile as the market. (The average betas for the securities in our portfolio will always be equal to 1.) 33 Risk and Return

–  –  –

Figure 2.1 shows that as we add more securities, the total risk of our portfolio declines, especially at the start.



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