Using Probability Distribution to Measure Risk

Using Probability Distribution to Measure Risk                             

Probability Distribution: It is a set of possible values that a random variable can assume and their associated probabilities of occurrence. For risky securities, the actual rate of return can be viewed as a random variable subject to a probability distribution. The probability distribution can be described in terms of two parameters. 1)    The expected return 2)    The standard deviation E xpected Return It is the weighted average of possible returns, with the weights being the probabilities of occurrence. So the expected return, R is: R = t=1∑ n(Ri)(Pi) Where Ri = the return for the ith possibility Pi = the probability of the return occurring N= the total number of possibilities S tandard Deviation It is a statistical measure of the variability of a distribution around its mean and it is the square root of the variance. We must keep in mind that, “The greater the standard deviation of returns, the greater the variability of returns and greater the risk of the investment”. The standard deviation can be expressed mathematically as σ = √ [t=1∑n( Ri - R‾)(Pi)] Where, Ri = Possible Return R‾= Expected Return Pi = Probability of Return occurring C oefficient of Variation It is the ratio of the standard deviation of a distribution to the mean of that distribution and it is the measure of relevant risk, i.e. a measure of risk per unit of expected return. Coefficient of Variation (CV) = σ/R‾ Where, σ = Standard deviation R‾= Expected Return “The larger the CV, the larger the relative risk of the investment”.