All about the Monte Carlo Simulation

Written by Vidya Kumar

September 18, 2015

Executive Summary: The Monte Carlo Simulation is a technique of risk analysis which uses probability distribution to define the outcome of a decision. Used in various fields, the Monte Carlo Simulation is also used in financial planning – more specifically in retirement planning. Although this technique has come under criticism after the financial crisis of 2008, financial pundits claim that using the Monte Carlo Simulation is a better indicator of real life market uncertainties, compared to traditional techniques. 

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We had written about the Asset Allocation Theory and the Efficient Frontier Theory  in the past. This week, in the third of our research based stories, we try and simplify the concept of Monte Carlo Simulation and how this is used in financial planning. The Monte Carlo Simulation deals with risk analysis and is a predictive model to signify the risk associated with a decision. It is used in various fields including finance, research, project management, manufacturing, transport and engineering. So what exactly is the Monte Carlo method?

Named after the city in Monaco, which is famous for casinos associated with risk, the Monte Carlo Simulation is a mathematical computerized technique. This allows you to estimate the risk linked with a particular decision by using a probability distribution. The results are calculated a few hundred thousand times and every time a random set of values is used. On the completion of the several iterations, a distribution of possible outcome values is plotted. The Monte Carlo simulation attaches a probability for each outcome and is thus considered to provide a better view of estimating risk and in risk analysis.

So how is Monte Carlo Simulation used in finance? It is often used in the evaluation of project investments, project finance, valuation of fixed income instruments and derivatives, portfolio evaluation and in project planning. However, what may interest our readers more is how this can be used in personal finance. 

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The Monte Carlo Simulation Method

The Monte Carlo method uses various scenarios of uncertainty which can possibly affect how an investment or portfolio can perform over a period of time. The results are usually plotted in the form of a bell curve, with varying degrees of probability for various outcomes. It is most commonly used in investment and retirement planning. Different factors such as the present portfolio value, interest rates, inflation, time to retirement, amount added or withdrawn from corpus, etc are considered as assumptions to arrive at the final result. The correlation between the underlying assumptions is also considered in the computation. The model is computerized, and as mentioned earlier, several thousand iterations are run before arriving at the result.

For example, in retirement planning, let’s assume that there are 2000 iterations, each denoting a scenario. Of this, assume that the simulation reveals that 90% of the time, your retirement corpus is sufficient for your lifetime. This is based on the probability distribution of the various factors and the riskiness associated with this. So as an individual, you should assess if you are ok with the result of 90%. If you think that this is still risky and you would like to increase the probability of the corpus lasting your lifetime, then you can increase the investment amount.

So is the Monte Carlo Simulation a foolproof method? Not really! For starters, if the underlying assumptions are wrong, the output will be incorrect.  Also, after the financial crisis of 2008, there was criticism on the ability of the Monte Carlo method to predict such events. Critics opine that this method cannot factor in infrequent but influential and radical events in the probability analysis. As a result, the output does not reflect the actual outcomes. However, supporters of Monte Carlo Simulation opine that this is a better way of predicting outcomes reflecting real market scenarios, compared to assuming a single rate of return throughout the tenure of investment. There are different suggestions given by experts on how to handle the shortcomings of the Monte Carlo Simulation.

Given that in reality everything is uncertain, this mode of risk analysis continues to be favoured by most financial planners across the world.

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