## Monte Carlo Simulation -How can it help investors?

We face an element of risk in almost every decision we make which often leaves us feeling uncertain and ambiguous. Although we have unparalleled access to information, we can never predict the future. A method that can help ease this risk is the Monte Carlo simulation that allows you to see all the possible outcomes of a decision and its associated risk. It can help you, as an investor, to make better decisions at uncertain times.

## Background

The Monte Carlo simulation was developed in the 1940s by Stanislaw Ullam, a brilliant Polish-American mathematician who was in charge of the Manhattan Project (R&D for WWII nuclear weapons). While recovering from a brain surgery Stanislaw spent many hours playing solitaire. He was soon drawn to trying to devise the game through the distribution of cards and predict the probability of winning.

Stanislaw’s analysis of trying to predict the outcomes led him to develop the Monte Carlo simulation. It was named after the glamorous gambling casinos of Monaco, France.

## What is the Monte Carlo Simulation?

The Monte Carlo approach is a computer-based method that uses statistical sampling to build a model of a possible range of results (a probability distribution) for those factors that have an element of uncertainty.

The results for the uncertain elements are calculated over and over using a set of random values at each time. The values entered as samples into the simulation as input ate chosen at random from the probability of income distribution. These sample sets are called iterations. The simulation produces a distribution of possible outcomes and these outcomes are recorded.

The Monte Carlo simulation is used by many different sectors and industries from project management to energy and engineering. But it is especially applicable to the finance and business sectors due to its emphasis on random variables. The simulation can be used to calculate the probability that the costs of a certain project will exceed its budget and the probability that the price of an asset will go up or down.

In addition to this, the model can be used to determine the investment default risk and assess the performance of derivatives such as options.

## Why should we use the Monte Carlo Simulation?

Simply put, the Monte Carlo simulation helps you make better decisions. It helps predict future outcomes based on different scenarios. The technique used in the simulation allows us to measure the risk in quantitative analysis. In addition to providing the outcomes in a given scenario, it lets us know the likelihood of each outcome occurring.

In terms of investing, the Monte Carlo simulation lets us identify all the risks associated with a particular investment. It gives us a range of outcomes so it can show you outcomes for conservative investments and incredibly risky ones. There is also a middle ground for the portfolio which is the outcome of a neutral investment and is particularly useful to investors who want to assess the risk of options.

## How is the Monte Carlo Simulation useful to investors?

The Monte Carlo simulation helps investors assess their portfolios and make investment decisions. Modern technology has now made it easy to perform a Monte Carlo simulation with the just a few clicks. The investor needs to enter a relevant time period between 1-25 years along with a downside floor constraint or an upper target value.

The simulator then generates 10,000 possible outcomes by playing out each simulated version in the future from the lowest to the highest risk based on values entered. However, it is important to remember that the simulator does not take into consideration real-world events such as crashes or unexpected events. Reality can differ from the simulator but it is still a powerful tool in understanding the trade-off between risk and the upside.

There are many websites that can help you perform a Monte Carlo simulation such as Vanguard that offers a ‘Retirement Nest Egg Calculator’. Vanguard uses the Monte Carlo simulation to provide the possible outcomes of a retirement portfolio. It takes into account your balance sheet, spending, and asset allocation and tries to determine the probability that your investment revenue will last the duration of your retirement.

(Image Credits: Vanguard)

Another great website is Personal Capital that also uses the Monte Carlo simulation to assess portfolios. The tool calculates the standard deviation and annual returns on the portfolio based on set targets. The result provides you with three market scenarios, the best possible case, the worst possible case and midpoint between the two. The tool aims to show how a diversified portfolio can be catastrophic when there is a bad market.

## Disadvantages of the Monte Carlo simulation

Like all things, the Monte Carlo simulation has its shortcomings as well because no one can predict the future. The simulations are particularly disadvantageous during a bear market. This is because the outcomes are based on constant volatility and can create a false sense of security for the investors. In reality, however, stock markets are very unpredictable and the Monte Carlo simulation does not hold good for these scenarios.

Moreover, the simulation is unable to factor in the behavioral aspect of the stock market. The Monte Carlo simulation could not predict accurate outcomes during the volatile stock markets of 2008. Therefore the simulations only show an approximation of the true value and can sometimes show very large variances.

## Conclusion

The Monte Carlo simulation is used by many investors to gauge the performance of their investments so they can make more informed decisions.

While you cannot trust the outcomes of the simulation with complete certainty, they do provide a viable way to understand the trade-off between risk and investment. It is a great tool for advisors when assessing the potential risks associated with the client’s portfolio. By changing the investment horizon and the upper and lower targets of the simulation, you can have a better understanding of how you can affect and change the outcome of your future investments.