Posted on August 13, 2009 - by Jay

Probability and Payout

Photo by walknboston

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. Read more…

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