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C HAPTER 3 R ISK AND R ETURN: P ART II OVERVIEW In Chapter 2 we presented the key elements of risk and return analysis. There we saw that much of the risk inherent in a stock can be eliminated by diversification, so rational investors should hold portfolios of stocks rather than just one stock. We also introduced the Capital Asset Pricing Model (CAPM), which links risk and required rates of return, using a stock’s beta coefficient as the relevant measure of risk. In this chapter, we extend the Chapter 2 material by presenting an in-depth treatment of portfolio concepts and the CAPM. We continue the discussion of risk and return by adding a risk-free asset to the set of investment opportunities. This leads all investors to hold the same well-diversified portfolio of risky assets, and then to account for differing degrees of risk aversion by combining the risky portfolio in different proportions with the risk-free asset. Additionally, we show how betas are actually calculated, and we discuss two alternative views of the risk/return relationship, the Arbitrage Pricing Theory (APT) and the Fama-French 3-Factor Model. The riskiness of a portfolio, because it is assumed to be a single asset held in isolation, is measured by the standard deviation of its return distribution. This equation is exactly the same as the one for the standard deviation of a single asset, except that here the asset is a portfolio of assets (for example, a mutual fund). ( 29 . P r σ deviation standard Portfolio n 1 i i 2 P pi p = - = = Two key concepts in portfolio analysis are covariance and the correlation coefficient. Covariance is a measure of the general movement relationship between two variables. It combines the variance or volatility of a stock’s returns with the tendency of those returns OUTLINE
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RISK AND RETURN: EXTENSIONS 5 - 2 to move up or down at the same time other stocks move up or down. The following equation defines the covariance (Cov) between Stocks A and B: . )P - (r ) - (r = (AB) Cov = Covariance n 1 = i i B Bi A Ai If the returns move together, the terms in parentheses will both be positive or both be negative, hence the product of the two terms will be positive, while if the returns move counter to one another, the products will tend to be negative. Cov(AB) will be large and positive if two assets have large standard deviations and tend to move together; it will be large and negative for two high σ assets which move counter to one another; and it will be small if the two assets’ returns move randomly, rather than up or down with one another, or if either of the assets has a small standard deviation. The correlation coefficient also measures the degree of comovement between two variables, but its values are limited to the range from -1.0 (perfect negative correlation) to +1.0 (perfect positive correlation). The relationship between covariance and the correlation coefficient can be expressed as . Cov(AB)
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