What is Kelly Fraction

Question

What is Kelly Fraction?  Explain.

Answer 1

The Kelly criterion is to bet a specific fraction of your wealth in order to maximize your expected growth of wealth. We utilize φ to denote the random variable taking value 1 along with probability p and −1 along with probability 1 − p and f to signify the fraction of our wealth which we bet. The growth of wealth after every toss of the coin is then the random amount ln(1 + fφ).
Therefore expected growth rate is p ln(1 + f ) + (1 − p ) ln(1 − f ).
That function is plotted in figure for p = 0.55.

Figure: Expected return versus betting fraction.

This expected growth rate is maximized through the choice
f = 2p − 1.
It is the Kelly fraction.