In order to measure risk in investment analysis, we may express estimates of the results of a project as probability distributions by giving a list of the possible cash flows with an estimate of the relative likelihood (probability) of the occurrence of each one. This leads to a characterization of the results of a project in two measures:
- The expected value: the weighted average of the present values of the various possible outcomes, using probabilities as weight; and,
- A measure of the dispersion of possible outcomes (the risk of the project), conveniently summarized in a statistical quantity, the variance or standard deviation.
