Corporate Finance

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Corporate Finance

MEASURING RISK

Investors buy shares in anticipation of a particular return but the fluctuation in stock prices results in fluctu-
ating returns. Therefore, shares are considered risky. As the returns from government securities like Treasury
bills do not deviate from their expected returns, they are considered risk-free. Financial theory defines risk
as the possibility that actual returns will deviate from expected returns. The degree of potential fluctuations
determines the degree of risk. More specifically, the risk in holding a security is the variance in expected
returns. The variance in returns measures the disparity between actual and expected returns. Modern finance
theory hypothesizes that investors choose securities on the basis of expected return and standard deviation
(square root of variance). So given a choice between two investments with the same expected return, the
investor would choose the one with lower standard deviation (two such investments are shown in Exhibit 3.4).
Investment B is preferable as its variance is lower.

Exhibit 3.4 Expected returns of two investments

Investment B

Investment A

Expected return (in percent)

The mean and standard deviation of returns of some Sensex stocks are presented in Exhibit 3.5. The past
realized return is taken as a proxy for future expected returns. Obviously, the forecast will almost never be
accurate. So we need a measure of upside potential and downside risk. The variance of returns is supposed
to measure how uncertain our forecast is. It is the breadth of the distribution of returns. In short, an investor
is supposed to think of future returns as a probability distribution. The variance of such a distribution is the
measure of risk. But how do we get the variance of future returns? Look at the past.
Another measure of variability is the square root of the variance—the standard deviation. Note that the dis-
tribution of returns (Exhibit 3.3) is normal, i.e., the upside potential and downside risk are of the same magnitude.
Returns from securities, in real life situations, may not be normal. To make life easy we assume normality.

Exhibit 3.5 Mean and standard deviation of returns

Mean (monthly) Standard

return deviation

ACC 0.00361 0.13159
BSES –0.00051 0.08815
Bajaj Auto –0.00599 0.08600
BHEL –0.00426 0.1327
Castrol –0.00197 0.0875
Cipla 0.02508 0.11182