industrial production EI % change in expected inflation UI % change in unanticipated inflation CG excess return of long-term corporate bonds over long-term government bonds GB excess return of long-term government bonds over T-bills   This list gives rise to the following five-factor model of excess security returns during holding period, t, as a function of the macroeconomic indicators: Rit i i IP IPt iEIEIt iUIUIt iCGCGt iGBGBt eit (10.15) Equation 10.15 is a multidimensional security characteristic line with five factors. As before, to estimate the betas of a given stock we can use regression analysis. Here, how- ever, because there is more than one factor, we estimate a multiple regression of the excess returns of the stock in each period on the five macroeconomic factors. The residual vari- ance of the regression estimates the firm-specific risk. The approach taken in equation 10.15 requires that we specify which macroeconomic variables are relevant risk factors. Two principles guide us when we specify a reasonable list of factors. First, we want to limit ourselves to macroeconomic factors with consider- able ability to explain security returns. If our model calls for hundreds of explanatory vari- ables, it does little to simplify our description of security returns. Second, we wish to choose factors that seem likely to be important risk factors, that is, factors that concern in- vestors sufficiently that they will demand meaningful risk premiums to bear exposure to those sources of risk. We will see in the next chapter, on the so-called arbitrage pricing theory, that a multifactor security market line arises naturally from the multifactor speci- fication of risk. An alternative approach to specifying macroeconomic factors as candidates for relevant sources of systematic risk uses firm characteristics that seem on empirical grounds to rep- resent exposure to systematic risk. One such multifactor model was proposed by Fama and French.16   Rit i iMRMt i SMBSMBt iHMLHMLt eit (10.16)   where   SMB small minus big: the return of a portfolio of small stocks in excess of the return on a portfolio of large stocks HML high minus low: the return of a portfolio of stocks with high ratios of book value to market value in excess of the return on a portfolio of stocks with low book-to-market ratios   Note that in this model the market index does play a role and is expected to capture sys- tematic risk originating from macroeconomic factors. These two firm-characteristic variables are chosen because of longstanding observations that corporate capitalization (firm size) and book-to-market ratio seem to be predictive of average stock returns, and therefore risk premiums.