Standard Deviation: Absolute Measure of Risk
In statistical terms, standard deviation is defined as the square root of the mean of the squared deviation, where deviation is the difference between an outcome and the expected mean value of all outcomes. Further, to calculate the value of standard deviation, we provide weights to the square of each deviation by its probability of occurrence.
Assume there are n possible levels of cash flows which are signified as CF1,. CF2 … CF,. The mean of these cash flows equals CF. The probability of any CF1 is signified as P, for example. the probability of CF4 is signified as P4 and so on. The formula to calculate the standard deviation (o) is as follows:
The greater the standard deviation of a probability distribution. the greater is the dispersion of outcomes around the expected value. Standard deviation is a measure that indicates the degree of uncertainty (or dispersion) of cash flow and is one precise measure of risk.
If two projects have the same expected value (mean), then one which has a greater o will be said to have higher degree of uncertainty or risk. Table presents the calculations of the standard deviation for Projects X and Y based on the data presented in our Table.
The standard deviation of project X is smaller than that of project Y. Therefore, it can be concluded that project X is less risky than project Y.
The conclusion regarding the superiority of project X over project Y would hold because both the projects have an equal outlay. However, if the sizes of the projects outlay differ, the decision maker should make use of the coefficient of variation to judge the riskiness of the projects.