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Chandan Dubey
Chandan Dubey
Articles (150) 

Performance of Traders Is Noise

September 14, 2012 | About:

I highly recommend the book “Fooled by Randomness” by Nassim Nicholas Taleb.

The book deserves long pauses between readings to chew over the subject matter and digest the implications. It is possible that one does not agree with Taleb’s assumptions and the subsequent fruits of his deductions but the exercise is recommended nevertheless. The article is heavily influenced by the book.

I want to describe here a very surprising fact that I came across while reading the book. Given that I am a Ph.D. student of theoretical computer science, I am surprised indeed that I had not observed this fact myself.

"The wise man listens to meaning, the fool only gets the noise." - Nassim Taleb

Taleb comes up with a very apt example for distinguishing noise from meaning and gives us scientific reasons for not looking at our portfolio every second.

Let us construct an investor who has a 15% return per annum with 10% error rate, i.e. his return in any given year will be between 5% and 25% with very high probability. The mathematicians model this with a bell-shaped curve, and the distribution is called "Gaussian" after the German mathematician Carl Gauss.


In the graph above sigma equals 15% and mu equals 10%. What this means is that with 68% probability the investor will see a return between 5% and 25%, and with 95% probability will see a return between -5% and 35%. This is nothing out of ordinary. Over a large sample space many things behave this way.

For example, if one plots the height or IQ of every man in the world; they will all look very similar to the bell shaped curve. Most of the people are around the average, and to find someone who has a very high or low reading in either of these is hard.

Now let us go back to our investor who earns 15% return with 10% volatility per annum. This translates to a more than 93% probability of making a positive return in any given year. In other words, if our investor could start every year with exactly the same situation then out of 100 years he will have more than 0% return in 93 of them.

This, as you will agree, is a great return. But what happens if we look at the performance on smaller time scales? The following table lists the same greater than 0% return with 93% probability per annum seen on smaller and smaller scales ("Fooled by Randomness," page 57).

Time scaleProbabilityNoisePerformance
1 year93%5043
1 quarter77%5027
1 month67%5017
1 day54%504
1 hour51.3%501.3
1 minute50.17%500.17
1 second50.02%500.02

It is amazing that a 93% probability of earning more than 0% per annum, when seen every second looks no different from a 50% probability of earning more than 0%. Notice that a stock can either go up or down and if we assume that a stock can go either way with equal probability then a return of more than 0% happens with probability 50%.

Seen from a different angle (noise versus performance), over one year we observe roughly 0.86 part noise for 1 part of performance. Over one second we observe 2500 part noise for every one part performance! Over the short term, only noise is visible.

Given that investors can look at their portfolio and positions in real time, this is bad news. Some behavioral economists estimate that a negative emotional stress is not equivalent to a positive one. In fact, a negative stress can have up to 2.5 times magnitude as a similar positive stress.

If our investor tracks his portfolio every second, he will have 43,217 pleasurable seconds vs 43,182 unpleasurable ones in a day. Given that the pleasurable seconds do not completely offset the unpleasurable ones, at the end of each day, he will feel emotionally drained. The same investor following the same strategy will experience 19 good years out of 20 years of his investing life !

There are faults with the model described above. Nothing in investing is as clean as this. It is wrong to assume that a portfolio will behave in such a way i.e., 15% return with 10% variance per annum. But that is not the point. The lesson here is that over short term - the noise outperforms performance by a big margin. This also leads us to conclude that the performance of traders is noise and "pure" performance can only be achieved by a long term investors.

About the author:

Chandan Dubey
I invest because I want to be free by the time I reach 40 years of age i.e., 2025. My investment style is to find a small number of bets with large margins of safety. I pay a lot of attention to management and their incentive. Ideally, I like to buy owner operator businesses. I am fortunate to have a strong inclination towards studying. I aid my financial understanding by extensive reading in psychology, economic, social sciences etc.

Rating: 3.9/5 (16 votes)


Bregan - 5 years ago    Report SPAM
While you have a good point in this article, your end conclusion is overly absolute and based on too simplistic reasoning.
Cdubey - 5 years ago    Report SPAM
@Bregan: I agree. The last line is a bit of stretch.

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