Kelly Criterion

The first time I heard about Kelly Criterion was many years ago when I was reading a book about horse racing. When I met Max, I started to notice that he talked about Kelly Formula several times. Recently, Youhang talked about Kelly Criterion related to the investment size. After checking Wikipedia, I learned more about Kelly Criterion.

K = P – Q / B

K – Fraction of current bankroll to wager
B – Odds received on the wager (winning ratio)
P – Probability of winning
Q – Probability of loosing = 1 – P

For example, if the winning ratio is 10/9 (11.11%), which is the average annual return for the stock market index; P and Q are 1/2 (50%). Using the above formula we can calculate the Kelly fraction as 5%.

K = 0.5 – 0.5 / (10/9) = 0.05 = 5%

For another example, if the winning ratio is 100/94 (6.38%), which is the average annual return for the bond market index; P and Q are 1/2 (50%). Using the above formula we can calculate the Kelly fraction as 3%.

K = 0.5 – 0.5 / (100/94) = 0.03 = 3%

I am not very sure about the correctness of using the Kelly Formula. If the above calculations are correct, then one should at least invest 20 independent stocks and 30 independent bonds in order to meet the Kelly Criterion.