index model regression measures the fraction of the varia- tion in a securitys return that can be attributed to variation in the market return. The values in the table range from 0.00 to 0.61, with an average value of .16, indicating that the index model explains only a small fraction of the variance of stock returns. Although this sample is small, it turns out that such results are typical. How can we improve on the single-index model but still maintain the useful dichotomy between systematic and diversifiable risk? To illustrate the approach, lets start with a two-factor model. Suppose the two most im- portant macroeconomic sources of risk are uncertainties surrounding the state of the busi- ness cycle, which we will measure by gross domestic product, GDP, and interest rates, denoted IR. The return on any stock will respond to both sources of macro risk as well as to its own firm-specific risks. We therefore can generalize the single-index model into a two- factor model describing the excess rate of return on a stock in some time period as follows:   Rt GDPGDPt IRIRt et   The two macro factors on the right-hand side of the equation comprise the systematic fac- tors in the economy; thus they play the role of the market index in the single-index model. As before, et reflects firm-specific influences. Now consider two firms, one a regulated utility, the other an airline. Because its profits are controlled by regulators, the utility is likely to have a low sensitivity to GDP risk, that is, a "low GDP beta." But it may have a relatively high sensitivity to interest rates: When rates rise, its stock price will fall; this will be reflected in a large (negative) interest rate beta. Conversely, the performance of the airline is very sensitive to economic activity, but it is not very sensitive to interest rates. It will have a high GDP beta and a small interest rate beta. Suppose that on a particular day, a news item suggests that the economy will expand. GDP is expected to increase, but so are interest rates. Is the "macro news" on this day good or bad? For the utility this is bad news, since its dominant sensitivity is to rates. But for the airline, which responds more to GDP, this is good news. Clearly a one-factor or single-in- dex model cannot capture such differential responses to varying sources of macroeconomic uncertainty. Of course the market return reflects macro factors as well as the average sensitivity of firms to those factors. When we estimate a single-index regression, therefore, we implicitly impose an (incorrect) assumption that each stock has the same relative sensitivity to each risk factor. If stocks actually differ in their betas relative to the various macroeconomic fac- tors, then lumping all systematic sources of risk into one variable such as the return on the market index will ignore the nuances that better explain individual-stock returns. Of course, once you see why a two-factor model can better explain stock returns, it is easy to see that models with even more factors-multifactor models-can provide even better de- scriptions of returns.13 Another reason that multifactor models can improve on the descriptive power of the in- dex model is that betas seem to vary over the business cycle. In fact, the preceding section on predicting betas pointed out that some of the variables that are used to predict beta are re- lated to the business cycle (e.g., earnings growth). Therefore, it