Page 309 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes Where
R = Return on i security during t holding period
th
th
it
R = Return on a Market Index during t holding period
th
mt
= Constant term
= Market Beta or Market Sensitivity of a given stock
mt

Notes Since the regression coefficient (Beta) indicates the manner in which a security’s
return changes systematically with the changes in market, this linear line is also called
Characteristic Line. The slope of the line is called Beta. It gained lot of popularity in security
analysis as a measure of relative market risk. Beta is ‘one’ for such a stock, which is said to
have the risk exactly equal to that of the market. On the other hand, the stock with Beta
greater than one indicates the aggressiveness of the stock in the market and less than one
indicates the slow response in the price of that stock.
1. Beta Predicting: Beta, as commonly defined, represents how sensitive the return of an
equity portfolio (or security) is to the return of the overall market. It can be measured by
regressing the historical returns of a portfolio (or security) against the historical returns of
an index; the resulting slope of this regression line would be the historical beta. This can
be useful for attributing relative performance to various sources or for explaining active
risk over a certain period of time.
Portfolio managers are also very interested in what the beta of a portfolio (or security)
will be in the future, or what the realized beta will be. As one might expect, predicting the
value of beta can be a complicated process. In the past, when returns were typically
available no more frequently than monthly, historical betas were not very reliable
predictors of realized betas; achieving statistical significance usually meant using returns
from past periods that were no longer relevant. In the 1970s, Barra pioneered the use of
multi-factor equity models to calculate, among other things, predicted betas that were
based on statistically significant historical relationships between equity returns and a
number of risk factors. Other vendors followed this lead with their own multi-factor
models, with the belief that predicted betas calculated in this manner would be better
predictors of realized betas than historical betas were.
Back to Basics

Since daily returns are now widely available, it is worth asking the question: are multi-
factor predicted betas better predictors of realized betas than historical betas, which use
daily returns? A related question, which probably should have been asked some time ago,
is: how good are these predictors? We will try to address these questions below.
Using daily security returns, going back to the end of 1998 and Barra-predicted betas for
the same time period, we performed the following calculations for each month:
(a) For each security, we calculated the beta relative to the S&P 500 using the 20 business
days’ returns starting in that month (the realized beta).
(b) For each security, we obtained the Barra-predicted beta as of the beginning of that
month.

(c) Using the data points for all these securities, we performed the regression:
Realized Beta = a + b x Predicted Beta + e

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