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Unformatted text preview: Answers and Solutions: 2 - 1 Chapter 2 Risk and Return: Part I ANSWERS TO BEGINNING-OF-CHAPTER QUESTIONS Answers 2-1 Stand-alone risk is the risk faced by an investor who holds just one asset, versus the risk inherent in a diversified portfolio. Stand-alone risk is measured by the standard deviation (SD) of expected returns or the coefficient of variation (CV) of returns = SD/expected return. A portfolios risk is measured by the SD of its returns, and the risk of the individual stocks in the portfolio is measured by their beta coefficients. Note that unless returns on all stocks in a portfolio are perfectly positively correlated, the portfolios SD will be less than the average of the SDs of the individual stocks. Diversification reduces risk. In theory, investors should be concerned only with portfolio risk, but in practice many investors are not well diversified, hence are concerned with stand-alone risk. Managers or other employees who have large stockholdings in their companies are an example. They get stock (or options) as incentive compensation or else because they founded the company, and they are often constrained from selling to diversify. Note too that years ago brokerage costs and administrative hassle kept people from diversifying, but today mutual funds enable small investors to diversify efficiently. Also, the Enron and WorldCom debacles and their devastating effects on 401k plans heavily in those stocks illustrated the importance of diversification. Answers and Solutions: 2 - 2 2-2 Diversification can eliminate unsystematic risk , but market risk will remain. See Figure 2-8 for a picture of what happens as stocks are added to a portfolio. The graph shows that the risk of the portfolio as measured by its SD declines as more and more stocks are added. This is the situation if randomly selected stocks are added, but if stocks in the same industry are added, the benefits of diversification will be lessened. Conventional wisdom says that 40 to 50 stocks from a number of different industries is sufficient to eliminate most unsystematic risk, but in recent years the markets have become increasingly volatile, so now it takes somewhat more, perhaps 60 or 70. Of course, the more stocks, the closer the portfolio will be to having zero unsystematic risk. Again, this assumes that stocks are randomly selected. Note, however, that the more stocks the portfolio contains, the greater the administrative costs. Mutual funds can help here. Different diversified portfolios can have different amounts of risk. First, if the portfolio concentrates on a given industry or sector (as sector mutual funds do), then the portfolio will not be well diversified even if it contains 100 stocks. Second, the betas of the individual stocks affect the risk of the portfolio. If the stock with the highest beta in each industry is selected, then the portfolio may not have much unsystematic risk, but it will have a high beta and thus have a lot of market risk. (Note:...
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- Spring '11