The market return on any day is similarly defined as:
Today’s index – Yesterday’s index
Today’s market return = ------------------------------------------
Yesterday’s indexAgain, weekly and monthly index returns, etc. can be consistently defined.
Once we have computed the security and market returns for a sufficiently long period to
get a large number (50 or more) of pairs of returns, we can use the linear regression
technique to estimate the beta.
As investors we need not worry too much about the details of the linear regression
technique by which the beta is estimated. But there are a few things about Beta
estimation that we must be careful about:
- Daily, weekly or monthly returns We (the authors) prefer daily returns
because it gives us more number of returns and therefore improves the
accuracy of the beta estimate. In some cases, however, we may use
weekly or monthly returns because these may be easier to collect. - Period of analysis In general, using a longer period gives us more date to
estimate the beta correctly. But if we believe that beta has changed in the
recent past because of any changes in the riskiness of the company, we
may wish to use a shorter period. We, the authors, have found that using
daily returns for 18-24 months is usually a good compromise between
these conflicting requirements. - Exceptional price movements Occasionally, we find that on some specific
days, the share price has recorded an exceptional rise or fall of a kind
which we do not expect to recur in future. We may sometimes find it
advantageous to eliminate the returns of these days before estimating the
beta.
Some of the factors discussed above do, at times, require some degree of judgment and
statistical analysis. For this reason, in many developed countries, there are specialized
agencies which perform all this analysis and publish their beta estimates for various
stocks at regular intervals. In India, we do not yet have these agencies. In the meantime,
we will have to do this analysis ourselves to estimate the betas that we need.
EXAMPLE 2
Let us consider the daily prices of the ITC share and the daily Bombay National Index for
the period January 1989 – October 1990 (BSE data), based on the trading days. Columns