Diversification And Portfolio Risk

Suppose your portfolio is composed of only one stock, Compaq Computer Corporation. What would be the sources of risk to this "portfolio"? You might think of two broad sources of uncertainty. First, there is the risk that comes from conditions in the general economy, such as the business cycle, inflation, interest rates, and exchange rates. None of these macroeconomic factors can be predicted with certainty, and all affect the rate of return on Compaq stock. In addition to these macroeconomic factors there are firm-specific influences, such as Compaq's success in research and development, and personnel changes. These factors affect Compaq without noticeably affecting other firms in the economy.

Now consider a naive diversification strategy, in which you include additional securities in your portfolio. For example, place half your funds in Exxon and half in Compaq. What should happen to portfolio risk? To the extent that the firm-specific influences on the two stocks differ, diversification should reduce portfolio risk. For example, when oil prices fall, hurting Exxon, computer prices might rise, helping Compaq. The two effects are offsetting and stabilize portfolio return.

But why end diversification at only two stocks? If we diversify into many more securities, we continue to spread out our exposure to firm-specific factors, and portfolio volatility should continue to fall. Ultimately, however, even with a large number of stocks we cannot avoid risk altogether, since virtually all securities are affected by the common macroeconomic factors. For example, if all stocks are affected by the business cycle, we cannot avoid exposure to business cycle risk no matter how many stocks we hold.

When all risk is firm-specific, as in Figure 8.1A, diversification can reduce risk to arbitrarily low levels. The reason is that with all risk sources independent, the exposure to any particular source of risk is reduced to a negligible level. The reduction of risk to very low levels in the case of independent risk sources is sometimes called the insurance principle, because of the notion that an insurance company depends on the risk reduction achieved through diversification when it writes many policies insuring against many independent sources of risk, each policy being a small part of the company's overall portfolio. (See Appendix B to this chapter for a discussion of the insurance principle.)

When common sources of risk affect all firms, however, even extensive diversification cannot eliminate risk. In Figure 8.1B, portfolio standard deviation falls as the number of securities increases, but it cannot be reduced to zero.1 The risk that remains even after extensive diversification is called market risk, risk that is attributable to marketwide risk sources. Such risk is also called systematic risk, or nondiversifiable risk. In contrast, the risk that can be eliminated by diversification is called unique risk, firm-specific risk, nonsystematic risk, or diversifiable risk.

This analysis is borne out by empirical studies. Figure 8.2 shows the effect of portfolio diversification, using data on NYSE stocks.2 The figure shows the average standard deviation of equally weighted portfolios constructed by selecting stocks at random as a function of the number of stocks in the portfolio. On average, portfolio risk does fall with diversification, but the power of diversification to reduce risk is limited by systematic or common sources of risk.

1 The interested reader can find a more rigorous demonstration of these points in Appendix A. That discussion, however, relies on tools developed later in this chapter

2 Meir Statman, "How Many Stocks Make a Diversified Portfolio," Journal of Financial and Quantitative Analysis 22 (September 1987).

CHAPTER 8 Optimal Risky Portfolios

Figure 8.1 Portfolio risk as a function of the number of stocks in the portfolio.

■ Unique risk

Market risk

Figure 8.2 Portfolio diversification. The average standard deviation of returns of portfolios composed of only one stock was 49.2%. The average portfolio risk fell rapidly as the number of stocks included in the portfolio increased. In the limit, portfolio risk could be reduced to only 19.2%.

Figure 8.2 Portfolio diversification. The average standard deviation of returns of portfolios composed of only one stock was 49.2%. The average portfolio risk fell rapidly as the number of stocks included in the portfolio increased. In the limit, portfolio risk could be reduced to only 19.2%.

Source: Meir Statman, "How Many Stocks Make a Diversified Portfolio," Journal of Financial and Quantitative Analysis 22 (September 1987).
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  • SANNI
    Can exposure to business risk be reduced by portfolio diversification?
    7 years ago

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