Corporate Finance

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Corporate Finance

Exhibit 4.2 Beta estimates for different return intervals

Company Weekly Monthly Quarterly

Ashok Leyland 0.77 0.80 1.02
Bajaj Auto 0.85 0.86 1.18
TELCO 1.0 0.96 1.11
SBI 1.3 2.04 2.72
ACC 1.23 1.31 1.18
Colgate Palmolive 0.68 0.54 0.35
Reliance 1.38 1.60 1.67

In the case of SBI, the beta estimate jumps from 1.30 to 2.72 when weekly returns are replaced by
quarterly returns. Obviously, this affects the cost of equity estimate. One could conveniently choose that
interval which gives the lowest estimate. This leads to erroneous investment decision as we shall see later.
The beta estimates come with statistical noise. The quality of regression can be determined by some
simple statistical parameters like standard error and R^2. If the beta estimate is 0.8 and the standard error of
beta is 0.30, we could be more than 99 percent confident that the true beta lies in the range of –0.10 and 1.7
(i.e., +/–3σ limit). R^2 provides an estimate of the proportion of risk (variance) of the stock that can be traced
to the systematic factors. The balance (1 – R^2 ) is the unsystematic risk.

An Illustration

The weekly returns of Reliance Industries Limited (RIL) were regressed against Sensex returns for the
period 1994–97. The results of the regression are:

α = 0.3197

β= 1.54

Standard error of beta = 0.177

2 σ limit = 1.54 +/– (2 × 0.177)

So, we can be 95 percent confident that the true beta lies in the range of 1.186–1.894.
The R^2 of the regression is 0.44. That is, 44 percent of total risk is systematic and the rest is unsystematic.
The beta of 1.54 suggests that RIL stock is riskier than average stock. This estimate may be compared
with publicly available estimates such as the one provided by Dalal Street Journal. They may not match due
to estimation issues outlined earlier. There are two more pitfalls in India. First, the data may not be available
on all days (may be due to lack of trading). This leads to non-trading bias. Second, prices may be rigged up
in some cases. The resulting estimate of beta will be biased.
The holding period return is the sum of capital gains yield and dividend yield. Dividends are paid semi-
annually or annually. To calculate returns, dividends are added to the capital gain/loss in the month in which
the stock goes ex-dividend. That is, dividends are not added in all the months but only in that month in which
dividends are announced.

Estimation of Market Return and Market Premium

Market return is the average of past realized return on market index. Weekly or monthly intervals are chosen
and the average return is calculated for the period. The average could be arithmetic mean or geometric mean.