# Monte Carlo Simulation

Monte Carlo simulations involve the creation of a computer-based model into which variabilities and interrelationships between random variables are entered. A spread of results is obtained when the model is run hundreds or thousands of times. This explains why this method is very useful when the number of random variables is so high that it makes the analysis using ordinary methods very complex.

In finance, we use Monte Carlo simulations to define potential risk. For example, a mutual fund manager may use the method to manage assets and liabilities. Specifically, a mutual fund manager may use the method to try and establish any downward risk – The risk that liabilities will outgrow the assets, leading to a loss.

## Monte Carlo Simulation: Project Appraisal

Monte Carlo simulation can also be used in project appraisal. To be exact, in such an instance, a project manager uses the method to establish the financial viability of the project in question. Usually, there is an initial cash outlay followed by subsequent costs during the productive life of a project. Note that, ideally, a project ought to generate profit at some point during its lifetime. The project is considered financially feasible if the present profit value outweighs the costs.

It is worth noting that both profits and costs are likely to be affected by numerous underlying variables. Such variables may include interest rate movements, exchange rate fluctuations, technological changes, and labor supply costs. Monte Carlo simulation can merge all the variables into a model that can be iterated to highlight all the possible future outcomes of a project. The outcomes are then summarized in terms of probabilities. In the end, the least likely outcome and the most likely one can then be deduced.

### Steps Involved in Project Appraisal

1. Create a model of the project and establish all the interdependencies as well as serial correlations between the variables.
2. Specify the probability for the distribution of each key variable present in the model.
3. Use random values extracted randomly from the variables’ distribution and repeatedly simulate the cash flows. Hundreds or thousands of simulations are usually performed.
4. Record and order all the outputs and establish their probability distributions.

From the results, we can determine the mean profit, the variance as well as skewness of the distribution. Nowadays, financial modeling software specifically designed to carry out such simulations can be purchased.

## Major Applications of Monte Carlo Simulations

• It is used to value projects that require significant amounts of funds and may have future financial implications for a company.
• It can be used to simulate profits or losses in the online trading of stocks.
• It is used in the simulation of the values of assets and liabilities of a pension benefit scheme.
• It can also be used to value complex securities such as American or European options.

## Limitations of Monte Carlo Simulations

• It only provides us with statistical estimates of results, not exact figures.
• It is fairly complex and can only be carried out using specially designed software that may be expensive.
• The complexity of the process may cause errors, leading to wrong results that can be potentially misleading.

### Question

Which of the following is least likely a limitation of Monte Carlo simulations?

1. Monte Carlo simulations provide exact figures, not statistical estimates of results.
2. The complexity of the process may cause errors leading to wrong results that can be potentially misleading.
3. Monte Carlo simulations are relatively complex and can only be carried out using specially designed software that may be expensive.

Solution

Monte Carlo simulations only provide us with statistical estimates of results, not exact figures.
B is incorrect. Monte Carlo simulations are relatively complex and can only be carried out using specially designed software that may be expensive.
C is incorrect. The complexity of the process may cause errors leading to wrong results that can be potentially misleading.

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