How the probability theory be utilized in analyzing risk of investment projects?

Answer 1

Generally, in an investment analysis, one is interested in determining if the risk is justified by the expected return and if the expected return is competitive to other uses of funds. Several approaches are used in risk analyses, which range from very simple approaches to more complex ones. First there is a simple qualitative approach, where one lists elements that could reduce profit (lower product price, higher costs, higher investments, delays from suppliers) and calculates expected decline in revenue. This is called the worse case scenario. Probability theory really doesn't play a role in this approach. Second, one can associate probabilities to factors (i.e. low, medium and high product price could be associated with 25, 50 and 25% probabilities) and a decision tree (risk analysis diagram) is constructed to provide the full range of combinations of events/factors, their probability of occurrence and outcome. These can be ranged and statistics, such as the mean or median outcome, and the high and low outcomes, can be identified. The third option is to associate factors with a distribution, and run Monte-Carlo simulation. Common distributions used are the uniform, triangular and normal distribution. Many programs exist to run Monte-Carlo models and summarize results. I've included a related link on the use of simulation in finance.