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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## Are financial markets Random or Deterministic?

Allow me the concession of not having a definitive answer; this question has haunted investment operators for many years. LET’S START WITH THE DEFINITION: Random Markets state that the market’s performance moves without any pre-established patterns and is not tied to external factors that modify the trend, or the trend of the market day after day. By definition, in a random market it is not possible to profit from the interpretation of the market itself (would be as random as trying to profit from the sequence of numbers that come out of the casino roulette). Deterministic Markets describe the belief that their performance is influenced by external factors that modify their course, so by knowing what these external factors are, it is possible to make a profit (the results of a motor race for example, are deterministic, in the sense that you can know in advance who will be among

Read more## 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

Read 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

Read more## 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

Read more## 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

Read more## Blessed Correlation. Damned Correlation.

The concept of correlation and Daniele Bernardi’s vision. Everyone knows the concept of correlation, and everyone has surely seen a Cartesian plan where two funds are depicted growing over the long term, while in the short term are inversely related to each other as seen on the image above (on today’s post). In 2009 I took part in a Risk Management course in London organized by Paul Wilmott (who also recently attended an annual conference of mine in Venice, www.quant.it) and Nicolas Taleb, author of best sellers Fooled by Randomness, and The Black Swan. Nicolas Taleb showed me (for the first time in my life) a graph like this: The correlation is negative in this case as well, but the funds are going down (following the same principle for which they should rise in the previous image). This second image opened my eyes to how much we tend to overestimate

Read more## Now let’s talk about Standard Deviation from a “non-standard” point of view.

The Standard Deviation is an indicator that looks at dispersed data around a position index; it is one of the few statistical indicators that are able to measure fluctuation around the mean. In finance, especially in Italy, this indicator has become increasingly used to assess the risk of a financial instrument, illustrating that the higher the standard deviation, the higher the risk the investor runs. This association is very approximative and misleading; the standard deviation is not an indicator of risk but one of uncertainty since when it’s very high, estimates on a given financial instrument are not too reliable, and when it is low, they can be considered more accurate. First introduced by Pearson, the standard deviation is nothing but the square root of the variance, see Wikipedia for the mathematical formula. The main issue with the standard deviation from a financial use point-of-view, is not so much the

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