Tuesday, August 11, 2009

Probability and Payout

This is something that relates to the Kelly Formula but at a much more simplistic level.

Basically, it all started when some friend of mine had the idea that if we are 80% sure of a 10% upside, we should be punting big on this event?

Eg. we heard a rumour that the CEO of TSMC saying he wants to buy Chartered for $2.20 (Today closing price $2.00) from the secretary of the CEO of TSMC and he will announce it tomorrow. How should you bet?

Mathmatically, this event can be illustrated with the matrix below.

Probability Payout
0.8 10 8%
0.2 -20 -4%
Expected return 4%

In the first scenario, there is a 80% chance you earn 10% and in the 2nd one 20% chance you lose 20% bcos say for some reason, he did not announce it the day after, or something unexpected happens. In life, nothing is 100%, even if you are the TSMC CEO yourself, you cannot say for sure if you can make the announcement as planned. You might get murdered, or something else etc, Anyways, as such is the case, the expected return is actually about 4%, which is, well, lower than market return of about 5-8%pa.

My initial thought is that we cannot punt this kind of event to help us make big bucks. Given the inherent unreliability of a rumour, the low expected return, it is not exactly a good way to maximize wealth. Of course we can always tweak those probability and payoff to get a good expected return, but using logic and rationality, it is difficult to get a good expected return of more than 15%.

In value investing, I think the matrix looks like this:

Probability Payout
0.4 -30 -12%
0.6 50 30%
Expected return 18%

There is a 40% chance you will lose 30% of your money, but a 60% you make 50% (remember margin of safety and other safeguard put in place?) Your expected return is 18%. If you make enough of these during a lifetime - you are a clear winner.

The caveats here are:

1) your analysis must be quite accurate, ie the intrinsic value is really 50% higher than current price

2) the timeline here is long, it may take 3 years to realized this 18%, which means 6%pa

You might think this is just bcos I am promoting value investing. But if you play around with the probability and payoff you can still get 10+% payout on average, which would translate to only 2-3%pa but still it's positive number.

Back to the TSMC case, you can argue that the 4% when translate to annual return becomes 1200%pa. Spectacular! However the logic would be that you won't get to hear a rumour about a takeover 300 days a year... So looking at the absolute expected return no. regardless of the timeline becomes important. And if you play around with the probability and payoff for this, you do get negative numbers.

So with this in mind, hopefully you can do this simple exercise with your next stock buying and practise more value investing rather than punting!


  1. You may have sketched out why people tend to sell to risk arbitrageurs when takeovers are announced. At least, it reminds me of what people do when that kind of fortune smiles on them.

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