###### Confidence Intervals

Monte Carlo simulation and historical simulation are both methods that can be used to determine the riskiness of a financial project. However, each method uses different assumptions and techniques to develop the probability distribution of possible outcomes.

Historical simulation involves the use of a historical record of returns or random variables to simulate the possible outcomes. The method assumes that past performance is an indication of future performance. Historical simulation uses actual past figures or variables that have been experienced before. Each simulation involves factoring in a specific value of a random variable and calculating the value of the project or asset.

In contrast, Monte Carlo simulation relies on modeling the distribution of risk factors using a random number generator. It involves the creation of a computer-based model that incorporates all the random variables that may affect the performance of a financial project, including any interrelationships, interdependencies, and serial correlations between them. The model is run hundreds or thousands of times to provide output that can be recorded and ordered to estimate the probability distribution of the possible outcomes.

Monte Carlo simulation comes with the advantage of incorporating a wider variety of scenarios than historical data, whose information scope is limited. In addition, Monte Carlo simulation answers the “what if” question, which is not possible under historical simulation. For example, it is possible to increase a specific variable by, say, 20%. One can then determine the overall effect of such an action on the model. However, it is more expensive relative to historical data and may require the acquisition of the services of an expert.

Historical simulation uses the actual distribution of risk factors. This means that the estimation of the actual distribution of changes in the risk factors is not required. However, past performance or changes may not be indicative of future performance. In addition, “outliers” or the events that occur infrequently may not be incorporated in the simulation. Similarly, variables or risks not occurring within the time period chosen for simulation purposes are likely to be left out.