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Chapter 07_Hand-out 6


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CHAPTER 7 OPTIMAL RISKY PORTOFLIOS 7.1 DIVERSIFICATION AND PORTFOLIO RISK Suppose you have in your risky portfolio only one stock, say Dell Computer Corporation. What are the sources of risk affecting this “portfolio”? We can identify two broad sources of uncertainty. The first is a risk that has to do with general economic conditions 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 returns of Dell stocks eventually will provide. In addition to these macroeconomic factors you must add firm-specific influences, such as a company’s success in research and development, its management style, personnel changes and so on. These factors affect a company without noticeably affecting other firms in the economy. Now consider a naive diversification strategy, adding another security to the risky portfolio. If you invest half of your risky portfolio in Exxon Mobile, leaving the other half in Dell, what happens to portfolio risk? Because the firm- specific influences on the two stocks differ, this strategy should reduce portfolio risk. But why stop at only two stocks? Diversifying into many more securities continue to reduce exposure to firm-specific factors, so portfolio volatility should continue to fall. When all risk is firm-specific, diversification can reduce risk to arbitrarily low levels. With all risk sources independent, and with investment spread across many securities, exposure to any particular source of risk is negligible. The reduction of risk to very low levels because 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 common sources of risk affect all firms, however, even extensive diversification cannot eliminate risk. In Figure 7.1 in the textbook, portfolio standard deviation falls as the number of securities increases, but it cannot be reduced to zero. The risk that remains even after extensive diversification is called market risk , risk that is attributable to marketwide risk sources. Other names are systematic risk , or non-diversifiable risk . The risk that can be eliminated by diversification is called unique risk, firm-specific risk, nonsystematic risk, or diversifiable risk. 1
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7.2 PORTFOLIO WITH TWO RISKY ASSETS In the previous section we considered naive diversification, which uses equally- weighted portfolio of several securities. It is time now to study efficient diversification, whereby we construct risky portfolio to provide the lowest possible risk for any given level of expected return. Portfolios of
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