Introduction

(Thinking Probabilistically & Counterintuitively)

No, you cannot definitively predict the future of financial markets, especially in the short term. However, you can project future outcomes in terms of their probability. These forecasts permit you to be better prepared for possible risks.

Traditional spreadsheets enable you to calculate how changes in particular variables impact your overall model. For example:

1. You may make an estimate of the point (i.e. the most likely value)1 for uncertain variables.
2. Perhaps, the spreadsheet allows you to calculate a range (but not the probability) of values based on best, worst, and most likely scenarios.
3. Similarly,  standard “what if” scenarios result in a single point estimate, rather than the probability of a particular outcome.

Monte Carlo Simulation

In contrast, a Monte Carlo simulation permits you to model real-life systems including the probability (i.e. the odds) of a variety of possible outcomes given specific assumptions about future conditions (i.e. constraints). Monte Carlo simulation was named after the casinos in Monte Carlo, Monaco. Casinos showcase a number of ‘games of chance’ such as slot machines, roulette wheels, and dice. All of these games are intended to exhibit random behavior.

Each Monte Carlo simulation picks values from a probability distribution of uncertain variables (i.e. assumptions) and, thereby, calculates the potential scenarios of a particular model. For each uncertain variable, you must define in advance its probability distribution. Typical distribution types include normal, triangular, lognormal, or uniform. Given enough historical data, your computer program may have a distribution fitting function that simplifies selecting the distribution type.2

Monte Carlo simulations consist of thousands of trials (i.e. random samples). The trial results include the mean forecast value and the certainty of a particular value. Nassim Nicholas Taleb describes these as the exploration of “alternative histories”.3

There are a number of computer programs that permit you conduct a Monte Carlo simulation. Many Fortune 500 companies and business schools use high-end programs like Oracle’s Crystal Ball.4 However, there are also a number of open-source programs and websites like Portfolio Visualizer that enable typical individual investors to perform “what if” analysis for their investment portfolio.

A Caveat

It is not sufficient to simply look at the frequency of historical total returns in order to calculate future returns. You must consider the sources of returns. Speculative returns are mean reverting. And, the growth of corporate earnings is very closely correlated with the growth of the overall economy.

But, you need to know the future dividend yield, not the historic dividend yield. The mistake both companies frequently make is raising future expectations based on past returns, when they should be doing the opposite.5

Thinking Counterintuitively

Too often, investors assume that when the economy is healthy, future stock returns will be high. It may sound counterintuitive, but the opposite is true. In economic boom times, future returns are actually lower. During economic downturns, future returns are higher. That is due to the linkage between risk and return.

During economic recessions, risk seems high; therefore, stock returns must be high enough to attract investors. Long term investors welcome recessions as an opportunity to purchase stocks at lower prices. Conversely, during economic booms, stocks are more attractive and therefore yield lower returns.

Anyone who has studied Microeconomics 101, recognizes that this as a basic function of supply and demand determining market price. That is not an argument for active market timing. Rather, it is a positive reinforcement for investing in a contrarian manner. The best means of doing so is through periodic rebalancing of your portfolio. When you rebalance, the drift of your portfolio from its asset allocation targets necessarily means that you will buy more stocks when bonds are priced high and vice versa.

Summary

Coming soon!

For More on this Topic

Taleb, Nassim Nicholas. Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets.

Updated on January 31st, 2019