Page 310 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 12: Models

We repeated this calculation by substituting a historical beta (calculated using trailing Notes
daily returns) for the predicted beta; we used trailing periods of 60, 120, 180, 240, 300, and
360 business days to calculate six different values of trailing historical betas. We then
repeated all of these calculations using 60 business days’ returns for the calculation of the
realized beta.
2. Interpreting the Results: A perfect predictor would have regression results of a = 0, b = 1,
correlation = 1, and MAE = 0. While these results are far from perfect, it is important to
remember that they are for individual securities; predictions for portfolios can be expected
to be far more reliable.

It is more useful to look at the results on a comparative basis. For each line, the shaded
values of b, correlation, and MAE are the closest to ideal. We can see that all of the shaded
numbers are associated with either the daily historical beta or the average of the predicted
and historical beta. While we cannot conclude from this that daily historical betas are
significantly better predictors of realized beta than Barra-predicted betas, it certainly
raises the question of whether the Barra-betas (or any other multi-factor betas) are the best
predictors.

! There are a few other interesting results worth noting:
Caution

(a) The “b” in the regression results for the predicted betas are greater than 1. This is not
necessarily good or bad, but simply indicates that the predicted betas have less
dispersion than the realized betas. This makes intuitive sense, since the predicted
betas are based on longer-term factor relationships.
(b) The “b” in the regression results for the historical betas increases as the length of the
trailing period increases. This indicates that the dispersion of historical betas decreases
as the trailing period increases, which also makes intuitive sense.

(c) All of the prediction results are better for the 60-day realized betas than for the 20-
day realized betas.
(d) The historical beta appears to have the largest relative advantage for trailing periods
of 240-300 days (for both the 20-day and the 60-day realized betas).
3. Implications: As mentioned previously, we should not rush to draw any hard conclusions
from these results. A brief study such as this has its limitations, not the least of which is the
fact that it uses less than four years worth of data. However, the evidence presented above
supports the following claim: In recent years, a simple daily historical beta has been at least as
good a predictor of short-term security betas as the predicted betas generated by a sophisticated
multi-factor equity model.

Since beta is such a primary feature of any equity factor model, this has implications for
our investment process. It raises the question of how much we should rely on the numbers
generated by multi-factor models for our risk controls. While these numbers are useful
and should not be ignored, we can no longer claim that they are the best numbers available
for this purpose. For risk-control purposes, the daily historical beta appears to be at least
as important a measure as the multi-factor predicted beta.

LOVELY PROFESSIONAL UNIVERSITY 305