## How to create a Montecarlo simulation in Excel.

Few people know that the fundamentals of the Montecarlo simulations are attributed to Enrico Fermi and Jon Von Neumann, the latter being the creator of the first computer and also mentor to Harry Markowitz at the beginning of his career as a practitioner (this was in the 1940’s). The name Montecarlo was chosen in honor of the famous Monegasque casino, as the models simulate random data combined with various methodologies. These simulations are useful in understanding the characteristics of a financial historical series and the associated probabilities that are often difficult to decipher without data computation. For example, if I invest in a fund that has an average annual return of 5% and a volatility of 7%, what are my chances of having a positive return the following year? And after three years? How about five? These answers can be obtained through mathematical probability calculations, but also, and perhaps more

## The false illusion of converging returns over time

Years ago, a well-known American investment company conducted a study which attempted to explain how returns of long-term financial investments, over the years, converge towards the mean. The period of time examined was 1972-2001, thirty years spanning across the best moment to invest in 1972 vs. investing in the worst moment of 1972, at the beginning of the year vs at the end of the year. According to the study, timing led to negligible differences in average annual yield (if I remember correctly, yields were between 15.1% and 15.7%, different times for the financial markets). Outside of the fact that a difference of 0.6% per year for thirty years is a lot of money, the thing that made me most furious, and you’d think they’d have done the study with at least a crumb of intellectual honesty, was that in 1974, two years after the starting period of review, the

## Why markets are counterintuitive.

A few days ago at a conference I heard the following sentence: “drink food and eat water”. At first, I thought the speaker wasn’t feeling well, but in reality this phrase has a profound meaning: we must chew our food well until it liquifies and water must be kept in our mouths for a long time before ingesting it. The phrase is counter-intuitive and strives to convey that the right way to behave is the opposite of what common beliefs teach us from a small age. Why are financial markets counter-intuitive? Simple. Have you ever met a person who invests in a stock in order to lose money? I haven’t, but I’ve met many people who have lost money in the stock market. Even people who think they’re acting correctly, could be missing things that cause them to make mistakes. If the markets were intuitive, everyone would gain from investing

## Why markets cannot be considered random.

One of the most widespread arguments justifying that financial markets can be considered random is the monkey example: if we assume there are an infinite number of monkeys, each one in front of a typewriter pressing keys at random for an infinite amount of time, surely it can be statistically affirmed that one of them will sooner or later type The Divine Comedy word-for-word. Switching back to S&P500, its history can be reproduced exactly by using one of the infinite random historical series generated by a Montecarlo engine and conducting an extraction of random returns. I’ll add that just because a monkey can perfectly replicate The Divine Comedy, doesn’t make The Divine Comedy an aggregate of random letters that created a masterpiece, it is the fruit of extraordinary genius and intellect. The trends of the S&P500 are equally unrepeatable and generated by a sequence of events that have determined its