McGraw-Hill

Disentangling Equity
Regularities Return
91
43. Rosenberg, Reid, and Lanstein (1985) report a tstatistic of -13.8 and
Reid’s (1982) multifactor residual reversal achieves a -15.0; our -17.8 is
slightly stronger, despite our shorter time period. Rmberg, Reid, and
h&& (RRL) report a consistency rate of 91.3 percent, while 103 out
of 108 of our monthly payoffs were negative, a for consistency of 95.4
percent. Note, however, that the RRL measure is specific return (net of
factor-return attributes), while ours and Reid’s are residual of the betaadjusted
market return. As Reid noted, the two approaches produce
reversals of similar magnitude. Note also that it is impossible to
abstract from pricing errors and bid/ask spreads by lagging price in
constructing this measure. However, RRL do some diagnostics that
indicate the measure is robust with respect to such concerns.
Furthermore, the observed second-month reversal persistence
by
construction free from any pricing concerns.
44. For an early application of cluster analysis to finance, see Farrell
(1974).
45. The explanatory power was generally much higher in months with
unusual stock returns. This stems from the increased cross-sectional
variation of returns explained by beta in such months. See the
discussion of beta in Table 2-4 for quantification of its market
sensitivity.
46. Sharpe’s model has a time-series RZ of 40 percent versus a crosssectional
R-squared of 10 percent. The former is an average across
stocks (regressed over time); the latter is an average across months
(regressed over stocks). Sharpe discusses the difference between the
two measures.
47. For example, the salient features of tax laws and their effects on
optimal trading strategies are usually relatively constant. Human
nature is even less fluid; hence observed “irrational” behavior
(inconsistent with the CAI” and EMH) need not become rational in
the future. For a discussion of human irrationality and security
markets, see Arrow (1982).
48. Whenthe number of means to be estimated jointly exceeds two,
using each historical average individually is “inadmissible.“ An
estimator is inadmissible if there is another that has smaller risk (in
terms of mean square error) independent of the true unknown
means. Stein-James estimators shrink all individual historical
averages toward the grand average. The shrinking factor for each
historical average varies inversely with its standard deviation. The
shrinking factor is thus positively correlated with the degree of
randomness or uncertainty in each measure Uames and Stein (1961)l.