 # Monte Carlo Simulation in CFA Level 1

Monte Carlo simulation is a statistical approach which is concerned with experiments employing random numbers. As the name suggests, the technique can be used in poker to compute probabilities for a wide array of scenarios but, more importantly for our purpose, it is used extensively in the field of finance.

Monte Carlo methods are used to handle both probabilistic and deterministic problems according to whether or not they are directly concerned with the behaviour and outcome of a random process. In the case of a probabilistic problem a simple Monte Carlo approach is to observe random numbers, chosen in such a way that they directly simulate the physical random processes of the original problem, and to infer the desired solution from the behaviour of these random numbers.

## Monte Carlo simulation applications

Monte Carlo simulation has wide application in performing risk analysis by building models of possible results by substituting a range of values (a probability distribution) for any factor that has inherent uncertainty( GDP growth, inflation rate, interest rate, asset performance…). It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete.

Monte Carlo simulation produces distributions of possible outcome values. By using probability distributions, variables can have different probabilities of different outcomes occurring.  Probability distributions are a realistic way of describing uncertainty in variables of a risk analysis.

## Monte Carlo in corporate finance

In corporate finance for example, a company may need to value a project, which may involve an initial outlay with future expected profits. If these future profits can be estimated accurately then the firm can determine whether these profits will outweigh the costs and can then decide whether to proceed with the project or not. The factors affecting the future profits could consist of many variables, including but not limited to interest rate fluctuations, currency exchange rate changes, macro-economic factors, labour costs, environmental issues or advancements in technology. Since each one of these factors can be multi-dimensional there could be a very large amount of parameters to be estimated, each having its own distribution. Therefore Monte Carlo simulation methods can be implemented.

As we will see in the derivatives section, stock options change in value depending on the price of an underlying stock, which itself can be affected by a very large number of factors. Simulation can be used to generate thousands of possible (but random) price paths in order to estimate the future value of an option. This can then allow a price to be assigned to the option at the current time point.

Yet another investment application is portfolio evaluation, which involves estimating the value of a collection of financial instruments such as stocks or bonds to determine the wealth to be gained. Monte Carlo methods can be used to simulate the correlated behaviour of the components of the portfolio over time in order to assess how the portfolio is affected by certain price level changes in order to estimate the value of the portfolio.

Monte Carlo methods provide flexibility and can handle multiple sources of uncertainty however the techniques are not always appropriate. In general such methods are likely to be preferable when there exist several sources of uncertainty such as in the above cases.

We hope you found this article on Monte Carlo simulation valuable. If you have any question about the CFA © Level 1 exam, we invite you to contact us. If you are preparing for the upcoming CFA © Level 1 exam, we invite you to purchase our CFA © Level 1 Bundle. Although you will not be required to use Monte Carlo simulation on the actual exam. It is still important that you understand the principle behind it.