Armanino Blog

Monte Carlo Simulations: What The NCAA Tournament's First Ever #1 Seed Upset Can Teach Us

by Scott Schwartz
March 28, 2018

As companies strive to accurately align executive equity compensation with company performance, an increasing number of companies are granting market or performance-vested restricted stock rather than time-vested restricted stock. Performance-based restricted stock awards vary in their terms and complexity, but they are often dependent on the company's stock price performance over a given period of time. As such, determining the fair value of these awards necessitates a forward-looking simulation of what the stock price will be at various points in the future in order to determine the quantity and timing of the equity awards that will be earned. The best method for accurately determining the future stock price in a dynamic world with multiple changing variables is a Monte Carlo simulation. Whereas a traditional Black-Scholes model is a static model with fixed assumptions, a Monte Carlo simulation is more dynamic and robust, as it takes into account the variability of a variety of factors.

The Monte Carlo simulation gets its name from the Monte Carlo Casino in Monaco, due to the importance of random variables, risk, and probability in the model. While the model relies on certain assumptions such as historical stock returns and stock price volatility which can be good predictors of future stock prices, there are many unpredictable external factors that can affect a company's stock price. Unlikely outlier events happen in the real world and the inclusion of a normally distributed random variable in a Monte Carlo simulation allows for the occurrence of these unpredictable events in the simulation. While these unlikely outcomes can happen in any single iteration of the simulation, the simulation is run with tens of thousands of iterations and the results are averaged, which leads to more accurate predictions.

In the annual NCAA Basketball Tournament, a #16 seed has beaten a #1 seed only one time out of 136 total games (UMBC over Virginia in 2018, ruining my bracket). Usually these games are lopsided blowouts as the #1 seeds have more talent, better records, and have faced more difficult competition than #16 seeds. However, basketball team performance is not static and can vary from game to game. For a #16 seed to defeat a #1 seed, they must play significantly above their normal level of play while the #1 seed must play far below their typical level of play. This almost never happens, but it is within the possible range of outcomes. In a single game or a single iteration of a Monte Carlo simulation, unlikely events can occur. However, if every game were played 10,000 times and the results were averaged, the #1 seeds would have a higher average score than the #16 seeds. The Monte Carlo simulation is the equivalent of playing those games 10,000 times. While it lacks the excitement and unpredictability of a single elimination tournament, accurately predicting a company's future stock price results in an accurate estimate of the present value of the stock award. The Monte Carlo model is the most accurate prediction model. When it comes to determining the fair value of performance-based equity awards, accuracy wins every time.

Armanino has performed numerous valuation analyses using Monte Carlo simulations to help its clients determine the fair value of their performance-based stock awards. Contact the Armanino CFO Advisory team to discuss valuation and equity management options.

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