70 Frequently Asked Questions In Quantitative Finance
What is the Kelly criterion?
Short Answer
The Kelly criterion is a technique for maximizing ex-
pected growth of assets by optimally investing a fixed
fraction of your wealth in a series of investments. The
idea has long been used in the world of gambling.
Example
You own a biased coin that will lands heads up with
probabilityp>^12. You find someone willing to bet any
amount against you at evens. They are willing to bet any
number of times. Clearly you can make a lot of money
with this special coin. You start with $1000. How much
of this should you bet?
Long Answer
Let’s work with the above example. The first observa-
tion is that you should bet an amount proportional to
how much you have. As you win and your wealth grows
you will bet a larger amount. But you shouldn’t bet too
much. If you bet all $1000 you will eventually toss a tail
and lose everything and will be unable to continue. If
you bet too little then it will take a long time for you to
make a decent amount.
TheKelly criterionis to bet a certain fraction of your
wealth so as to maximize your expected growth of wealth.
We useφto denote the random variable taking value
1 with probabilitypand−1 with probability 1−pand
fto denote the fraction of our wealth that we bet. The
growth of wealth after each toss of the coin is then the
random amount
ln(1+fφ).
