In this section, we take a somewhat different approach to measuring the same basic phenomenon. In the most general terms, our central hypothesis is that stocks which are small and which have low residual analyst coverage should display more positively autocorrelated returns at medium horizons. A simple (perhaps naive) way to test this would be to estimate a serial correlation coefficient for each stock, and then regress this serial correlation coefficient on measures of the stock’s analyst coverage and size.
This is what we attempt to do now. More precisely, at the beginning of each year t, we collect all stocks which have a market capitalization greater than the 20th percentile NYSE/AMEX breakpoint, and for which we have complete return data through year t+5. We then estimate for each stock i the serial correlation of its six-month excess returns (relative to T-bills), using 49 overlapping observations over the five-year period from t to t + 5, and call this variable RHOit. Next, we perform a cross-sectional regression, running RHOit against log(l+ANALYSTS*) and log(SIZElt), as well as a NASDAQ dummy variable.
We should note one caveat associated with this method. For any stock i, our measure of serial correlation RHOit is affected not only by the correlation of its firm-specific information, but also by its loading on any common factors. To see this, suppose the returns on stock i, r(t, are given by a one-factor model (suppressing constants):
where mt is the common factor, b: is the loading on this factor, and elt represents firm-specific information. Even if we assume for simplicity that the common factor is serially uncorrelated, (cov(mt, mt_,) = 0) a regression of rit on rit_, produces the following theoretical coefficient p’:
This suggests that, all else equal, our constructed left-hand side variable RH01t will be lower for stocks with higher factor loadings—i.e., higher betas. This is potentially a matter of concern because as we have seen in Table 2, there is a positive cross-sectional correlation between beta and analyst coverage. Thus one might mistakenly conclude that high coverage is reducing RHOit by reducing the serial correlation of firm-specific information, when in fact it is proxying for a beta effect. In order to address this issue, we have rerun the regressions that we present below, adding firm betas to the right-hand side. As it turns out. none of our results is materially altered.
Before turning to these results, it is useful to discuss how this general approach compares to what we have done above. The main difference is that it imposes more parametric structure, some of which may be unwarranted. For example, the regression approach we are now proposing does not allow for asymmetries across winners and losers; yet we have seen that such asymmetries are pronounced in the data. In addition, the regression approach only makes sense if residual analyst coverage is a firm-level attribute that is “quasi-fixed “–i.e., that does not vary much over five-year periods of time. If there is significant high-frequency variation in residual coverage, this is again something that the less structured method of the previous section will be better equipped to handle.