Probability vs Expectation

I came across this concept of Probability vs Expectation when I was reading Nicholas Taleb’s Fooled by Randomness and he has explained it very lucidly (I do not recommend this book to anyone). Although all traders and investors know this concept intuitively, I have never seen anyone act upon it. Although I must admit that my dad was once planning to do something very close to it. 

I will take the same example as in the book, modify it a little and explain it here. Once during the author’s trading days he was asked in a meeting whether he was bullish or bearish and he said that he was bullish and a little later he said that he had shorted the market. 

These are two contradictory things and he was asked to explain himself. He said that although he did think that the market will go up, if it goes down it will go considerably down and therefore greater money is to be made from that unlikely considerable downwards movement than a likely small upward movement. 

I don’t know what the author had in mind but it is akin to being in a bull run where everyday the market moves up a little and then waking up one morning to read about the finance minister and SEBI’s outlash on PNs and the next thing you know the whole market is down 10% 

The key idea here is although the probability is greater the expectation is still lower. I myself am a long term investor and have very little faith in short term predictions of say 3 months on the market but the concept in itself is quite interesting. 

I have heard my dad telling me once that these market crashes are inevitable and every month one should buy a ‘cheap’ PUT so that when once in a year the market falls spectacularly that PUT is worth a gold mine and covers up for all the remaining 11 months when the market followed its due course. He was talking about low probability and high expectation and I think a lot of investors do think about this but not really do anything about it. 

I myself have never tried buying PUTs hoping that the market crashes and certainly do not recommend it to anyone but it is certainly a thought that is worth a thought. And while one is at it why not buy a ‘cheap’ Call as well just to take care of the ridiculous 1000 points upward moves too! 

Manshu Verma 

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2 thoughts on “Probability vs Expectation”

  1. What can I say, when I first saw the market crashing in around the beginning of 2000 it was a black swan, next time it was a grey one, third time it was just white! The point is that whether a swan is black, grey or white most of the time depends on what is the most optimistic or most pessimistic scenario one can think of.

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