I’d like to present a lesson by professor Ruggero Bertelli on the subject of deterministic statistical indicators as they compare to classic indicators of mean and variance. LET’S SEE IT IN ACTIONAssuming we have an investment that in the first year earned 10%, the following year lost 10%, the third year earned another 10% and the fourth year lost 10%, what would be the return on investment at the end of the four years? THINK ABOUT YOUR ANSWER BEFORE YOU KEEP READINGIf your answer was zero, perhaps you forgot that returns are not linear, and losses are not equal to the returns necessary to recover them. If I’ve lost 50%, to return to the initial value I would have to earn 100%. If I lost 10%, to get even, I’d have to make almost 11% back, as you can see from the image below. At the four-year mark, I’d find

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## 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

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