Standard Deviation
An investment must be evaluated on two dimensions - rate of return and risk. An investor cannot enjoy a high return without any exposure to risk. The higher the return, the higher is the risk involved and the lower the exposure to risk, the lower would be the return. Risk is defined as the chance of injury, damage or loss. Risk in investments is the chance of the actual returns realized being much lower than the expected returns.
The risk in an investment is normally measured by the variance or standard deviation in the returns from the mean or expected return. The idea is, the higher the value of dispersion (that is, variance or standard deviation), the higher is the risk. If all possible or actual returns lie close to the mean return, then the total risk in investment is less and the investor has an assurance that at least the mean rate of return will be earned on the investment.
The variance and standard deviation of returns from the share of Godavari Petrochemicals Limited may be calculated as under:
Rates of Return
Probability of Occurrence
Deviations from Expected Rate of Return
Squares of Deviation
Probability x Squares of Devation
(X_{i})
(P_{i})
30%
0.30
10.2
104.04
31.212
18%
0.50
-1.8
3.24
1.620
9%
0.20
-10.8
116.64
23.328
Total
56.160