Investments, tenth edition

10 

 Arbitrage Pricing Theory 

and Multifactor Models of 

Risk and Return 

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  Arbitrage Pricing Theory and Multifactor Models of Risk and Return 

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  The index model introduced in Chapter 8 gave us a way of decomposing stock variability 

into market or systematic risk, due largely to macroeconomic events, versus firm-specific 

or idiosyncratic effects that can be diversified in large portfolios. In the single-index model, 

the return on a broad market-index portfolio summarized the impact of the macro factor. 

In Chapter 9 we introduced the possibility that asset-risk premiums may also depend on 

correlations with extra-market risk factors, such as inflation, or changes in the parameters 

describing future investment opportunities: interest rates, volatility, market-risk premiums, 

and betas. For example, returns on an asset whose return increases when inflation increases 

can be used to hedge uncertainty in the future inflation rate. Its risk premium may fall as a 

result of investors’ extra demand for this asset. 

 Risk premiums of individual securities should reflect their sensitivities to changes in 

extra-market risk factors just as their betas on the market index determine their risk premi-

ums in the simple CAPM. When securities can be used to hedge these factors, the resulting 

hedging demands will make the SML multifactor, with each risk source that can be hedged 

adding an additional factor to the SML. Risk factors can be represented either by returns 

on these hedge portfolios (just as the index portfolio represents the market factor), or more 

directly by changes in the risk factors themselves, for example, changes in interest rates 

or inflation.