Measurement Of Risk

Sensitivity analysis is one of the simplest ways of handling risk. It consists of examining the magnitude of change in the rate of return for the project, for a small change in each of its components which are uncertain. The best possible way is to select these variables whose estimated value may contain significant errors or element of uncertainty and then to calculate the effect of errors of different sizes on the present value of the project. Some of the key variables are cost, price, project life, market share etc. Sensitivity analysis takes into account a number of possible outcome estimates while evaluating an asset risk. In order to have a sense of the variability among return estimates, a possible approach is to estimate the worst(pessimistic), the expected(most likely) and the best(optimistic) returns associated with the asset. The difference between the optimistic and the pessimistic outcomes is the range, which according to the sensitivity analysis is the basic measure of risk. The greater the range, the more is the risk and vice versa.

Probability may be described as the measure of likelihood of an event’s occurrence. The risk associated with an asset can be assessed more accurately by the use of probability distribution than sensitivity analysis. For example, if the expectation is that a given outcome or return will occur six out of ten times, it can be said to have sixty percent chance of happening; if it is certain to happen, the probability of happening is 100%. An outcome which has a probability of zero will never occur. So, on the basis of the probability distributed or assigned to the rate of return, the expected value of the return can be computed. The expected rate of return is the weighted average of all possible returns multiplied by their respective probabilities and those probabilities of the various outcomes are used as weights. The expected return(R),

Let us calculate the expected return of two assets X & Y, whose probability of generating pessimistic returns of 13% and 7% is 30%, most likely returns of 15% and 14% is 30% and optimistic returns of 17% and 21% is 40%, respectively.

The most common statistical measure of risk of an asset is the standard deviation from the mean or expected value of return. It represents the square root of the average squared deviations of the individual returns from the expected returns. The standard deviation can be represented as thus:

It is a measure of relative dispersion or a measure of risk per unit of expected return. It converts standard deviation of expected values into relative units and thus facilitates comparison of risks associated with assets having different expected values. It is calculated by dividing the standard deviation of an asset by its expected value.