can anyone explain the kelly formula for postion size . How to judge probability?

Answer 1

Dear Natasha,

I will give an answer, though it would be helpful if you were more specific in your question.

You can think of the Kelly formula as giving a position size S in terms of the fraction of an investor's total bankroll. It is related to her probability P of a winning investment, and ratio R of the amount gained on a winning investment divided by the absolute amount lost on a non-winning investment. (The investor would then multiply S by her total bankroll to determine the actual investment amount, since S is only proportion).

The formula appears as S = P - (1 - P) / R .

Although I haven't gone through the derivation of the formula, my understanding that it is designed to maximize wealth over time, assuming reinvestment (i.e., maximizing long-run return). The absolute amount invested will vary up and down with changes in the bankroll over time. Drawbacks of this method are that the investor's bankroll can vary wildly, and many investors will not have the stomach to apply such a formula to their total wealth, nor have the lifespan to reach the "long run."

Judging probabilities could be done by some combination of models using historical data and consultation with experts. You would make probability assessments for your investments in a manner similar to probability assessments about the weather or a medical procedure, for example.

Note that the Kelly formula above applies most readily when investment gains and losses are fixed. Generalizations of this formula have been devised, but you will need to do some research if you are interested in them.