# sm09 - CHAPTER 9 MULTIFACTOR MODELS OF RISK AND RETURN...

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CHAPTER 9 MULTIFACTOR MODELS OF RISK AND RETURN Answers to Questions 1. Both the Capital Asset Pricing Model and the Arbitrage Pricing Model rest on the assumption that investors are reward with non-zero return for undertaking two activities: (1) committing capital (non-zero investment); and (2) taking risk. If an investor could earn a positive return for no investment and no risk, then it should be possible for all investors to do the same. This would eliminate the source of the “something for nothing” return. In either model, superior performance relative to a benchmark would be found by positive excess returns as measured by a statistically significant positive constant term, or alpha. This would be the return not explained by the variables in the model. 2. CFA Examination III (1989) 2a. The Capital Asset pricing Model (CAPM) is an equilibrium asset pricing theory showing that equilibrium rates of expected return on all risky assets are a function of their covariance with the market portfolio. The CAPM is a single-index model that defines systematic risk in relation to a broad-based market portfolio (i.e., the market index). This single factor (“beta”) is unchanging: R j = R f + B j (R m – R f ) where R j = expected return on an asset or portfolio R f = risk-free rate of return R m = expected return on the market B j = volatility of the asset or portfolio to that of the market m. Arbitrage Pricing Theory (APT) is an equilibrium asset pricing theory derived from a factor model by using diversification and arbitrage. The APT shows that the expected return on any risky asset is a linear combination of various factors. That is, the APT asserts that an asset’s riskiness and, hence, its average long-term return, is directly related to its sensitivities to certain factors. Thus, the APT is a multi-factor model which allows for as many factors as are important in the pricing of assets. However, the model itself does not define these variables. Unlike the CAPM, which recognizes only one unchanging factor, the key factors in APT can change over time. R j = R f + B j1 (RF 1 – R f ) + … + B jk (R Fk – R f ) where 9 - 1

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R j = return on an asset R f = risk-free rate of return B j = sensitivity of an asset to a particular factor R Fk = expected return on a portfolio with an average (1.0) sensitivity to a factor k j = an asset k = a factor Research suggests that several macroeconomic factors may be significant in explaining expected stock returns (i.e., these factors are systematically priced): (1) Inflation; (2) Industrial production; (3) Risk premia as measured by the spread between low and high grade bonds; (4) Yield curve, (i.e., slope of the term structure of interest rates. Other researchers have identified additional factors which may influence an asset’s
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sm09 - CHAPTER 9 MULTIFACTOR MODELS OF RISK AND RETURN...

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