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 in order to come up with 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. The method 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 time to provide output that can be recorded and ordered to estimate the probability distribution of the possible outcomes.

**Monte Carlo simulation vs. Historical Simulation: Comparison of Advantages and Disadvantages**

Monte Carlo simulation comes with the advantage of incorporating a wider variety of scenarios than historical data which is limited in terms of the information it can provide. 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 services of an expert.

Historical simulation uses the actual distribution of risk factors. This means 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 rather the events that occur infrequently may not be incorporated in the simulation. Similarly, variables or risks not occurring in the time period chosen for simulation purposes are likely to be left out.

*Reading 9 LOS 9q:*

*Compare Monte Carlo simulation and historical simulation*