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posted by: Radnor Financial Advisors

Monte Carlo Analysis- Decision Making Under Uncertainty

A pharmaceutical company deploys most of its $50 million liquid asset-base into developing a coronavirus vaccine. An NBA player decides to play in the final game of the season in a contract year for a non-contender to reach an important statistical milestone. A young professional spends $150,000 and forgoes two years of six-figure earnings to pursue an MBA at a top-10 program. Most of us can probably come up with several examples in our own lives where we have had to make critical decisions under uncertainty. While in many cases it may be difficult to quantify the merits of a particular decision, when the stakes are high enough it is absolutely critical to do so. Through a process called Monte Carlo Analysis, corporate project managers, engineers, financial planners, and other professionals help to answer the question “What should we do?”

Imagine someone comes over to you and offers you $6,100 for every seven you get on a roll of two dice, with a cost to you of $1,000 per roll. You are allowed an unlimited number of rolls. You remember reading (or you calculate yourself) that the probability of getting a seven on a roll of two dice is 1 in 6. While you quickly calculate that the expected revenue of the roll is more than the $1,000 cost, you cannot afford to lose any money and you have a train to catch in ten minutes. You realize you could easily be unlucky and not get a seven 1/6 of the time with such a small sample size and you wish you had a quick way to know how many rolls would be necessary to all but guarantee this as a winning proposition.

This is where Monte Carlo analysis would be useful. Within seconds of entering the various inputs of this deal into a Monte Carlo simulation engine, you could determine the number of rolls necessary to achieve a given probability of making money. The engine would simulate the rolls in advance without you having to commit to the offer and thus allow you to make a more informed decision.

This type of analysis can be helpful in any situation in which there are uncertain variables that would contribute to the outcome of a particular decision. The project manager may not know how much a particular supply may cost in the future, the basketball player may not know the salary cap constraints for his future team, the business school student may not know how long it will take her to secure a position post-graduation, and the financial planner does not know what the stock market will do over the short-term to a retiree’s portfolio. In order to plan effectively for these situations, identifying the probability of success in light of inherent uncertainty is crucial and this is precisely what Monte Carlo Analysis allows us to do.

One of the most popular criticisms of Monte Carlo analysis relates to the difficulty in ascertaining reasonable inputs to the equation. This argument raises the important point that it is not always easy to define the expectations or uncertainty relating to a particular input. While the results associated with repeatedly rolling dice are both predictable and finite, it would be considerably more difficult to ascertain the expected return on large-cap growth stocks over the next 15 years. It is important to note however, that there is a lot more agreement among investment professionals regarding such longer-term capital market assumptions than there is about short-term returns. Moreover, without at least an attempt to capture reasonable long-term risk and return characteristics it would seem impossible to accurately determine the viability or appropriateness of an investment portfolio.

As we navigate some of the most uncertain times in history, we are reminded of the importance of planning appropriately for the unknown. While not every situation we are faced with will require or be compatible with a robust analytical model, measuring the impact of uncertainty in some way remains a crucial component of both our personal and professional decision making.

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Philip I. Fried

Financial Planner

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