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.


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 the first and who among the last, while the accidents determine different classifications).


Eugene Fama to start, father of efficient market theory, claimed that the market must be based on randomness in order to justify the mathematical/statistical models used to describe it.

For decades, the academics have strongly supported the randomness of financial markets, using various examples like the one where an infinite number of monkeys in an infinite interval of time can write The Divine Comedy, as I explained previously in this blog in the post Why Markets Cannot Be Considered Random.

For the sake of argument, let’s say that a monkey will never succeed in writing The Divine Comedy by putting the right letters in line and compose it by chance. I can now with absolute certainty affirm that the same monkey wouldn’t succeed in writing the De Volgari Eloquentia, another work by the good Dante Alighieri, therefore it cannot be affirmed that the good Dante Alighieri is a lucky monkey who has written masterpieces by chance.


To transpose it back into the world of finance, even if thanks to infinite random historical series generated by endless Montecarlo simulations, you were to find a series that faithfully replicates the S&P 500, it wouldn’t be very likely that at the same time, the exact time series of the DAX, the TOPIX and others would be generated as well.


Why am I saying this. I’m saying this because there certainly are statistical reports, which for lack of a better word we’ll call weak, that bind the stock indices of various countries together, but above all that react in a determined way to the occurrence of events.


Let’s take the September 11, 2001 attack on the Twin Towers. If we look at how the financial markets behaved on that day, a cause created an effect, ie. a 7% loss for the market on that same day.

If I were to look at the historical series 15 years later, and wasn’t aware of what happened on that day, would I be able to say it was a coincidence that the market lost 7% in one day?

Perhaps I would, but the loss was caused by an event, the destruction of the Twin Towers, and so the movement was not random that day (a little like Vettel, who lost the Singapore race due to an accident despite leaving from the pole position).


One could say that in reality the attack couldn’t have been predicted (apart from the group of bombers who surely speculated on the loss of the index that day), and therefore it must be considered a random and unpredictable event.

In other words, what came first, the chicken or the egg?


The answers to these questions aren’t easy and I’d like to know your opinion. Feel free to share what you think directly on social networks or on the blog comments.


I recently read an article that mentioned October as a very volatile month (perhaps the most volatile of all months) where the worst catastrophes took place (see 1987 and 2007) but also the most extraordinary recoveries. A dangerous month for the exchanges but also a month to allow some satisfaction. 


We tried to analyze if in fact there was a seasonality. With a slight bit of skepticism deriving from our knowledge of financial markets, we discovered that there is, if even just a small amount of it, not on a monthly basis but on a quarterly, semester- basis, or better yet over the years (the famous trends).

We’ve taken the monthly returns of the S&P 500 (amongst others, which I’ll spare you the time) from 1927 to today, placing (explained in Chapter X the post: My name is Bond, Corporate Bond!) all month-to-month returns on a box plot to see if October actually represented the black month of financial market-months, but this statement does not hold true on this graph.

Analyzing the percentage of months that have been more positive and months that have been more negative, it doesn’t appear that the month of October is particularly different from the other months. If any anomalies were to be found, they’d be in the percentage of positive months in December (typically an instrumental month for obtaining bonuses from institutional managers and traders) and if a particular month were to be indicated, perhaps we should consider September as the black month of the American stock market, given that the worst return is precisely during this month, and it is the only month where the percentage of positive to negative months is under 50%.


However, don’t believe in the utility of these statistics; to show you just how weak these relationships are we’ve compared the monthly yield reports of each month to another month of that same year to see if there were any exploitable correlations.

As you can see, with respect to the month of October, only July and August offer a regression that is minimally negatively inclined (which means that if one month goes well, the other does the opposite), but the coefficient of determination (which measures the reliability of the analysis) indicates that there is no minimum robustness in this analysis.

This type of analysis is a bit like looking at the sequence of numbers coming out of a roulette machine and hoping that the next day the number from the previous day will come out at 9PM. It does not provide any added value nor any kind of investment strategy, so beware of anyone believing that the seasonality of the financial markets can be summarized onto monthly data.


A quant knows that the more I expand the so-called “time-frame”, that is, the window of analysis for a single period (ie. a week or a month) the more trends come out and can be grasped. The more I restrict the window of analysis (ie. a day, an hour, five minutes…), the more I’ll struggle to capture a trend and fill myself with useless noise.


It can be concluded (obviously this is my personal point of view) that financial markets in the short-term have a trend that can be considered random and non-interpretable, while over longer periods of time, usually intercepted by trend following strategies, it is possible to notice and understand deterministic trends.


Just to point out, a deterministic trend only minimally depends on macroeconomic data, in fact it is the macroeconomic data that is influenced by financial markets.