The effects of different sources of stock return can overlap. In Exhibit 7.1, the lines represent connections documented by academic studies; they may appear like a ball of yarn after the cat got to it. To unravel the connections between predictor variables and return, it is necessary to examine all the variables simultaneously.

For instance, the low P/E effect is widely recognized, as is the small-size effect. But stocks with low P/Es also tend to be of small size. Are P/E and size merely two ways of looking at the same effect? Or does each variable matter? Perhaps the excess returns to small-cap stocks are merely a January effect, reflecting the tendency of taxable investors to sell depressed stocks at year-end. Answering these questions requires disentangling return effects via multivariate regression.5

Common methods of measuring return effects (such as quintiling or univariate, single-variable, regression) are naive because they assume, naively, that prices are responding only to the single variable under consideration, low P/E, say. But a number of related variables may be affecting returns. As we have noted, small-cap stocks and banking and utility industry stocks tend to have low P/Es. A univariate regression of return on low P/E will capture, along with the effect of P/E, a great deal of noise related to firm size, industry affiliation, and other variables.

EXHIBIT 7.1 Return Effects Form a Tangled Web

Simultaneous analysis of all relevant variables via ...

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