Frequently Asked Questions In Quantitative Finance

Chapter 2: FAQs 71

The expected growth rate is

pln(1+f)+(1−p)ln(1−f).

This function is plotted below forp= 0 .55.

This expected growth rate is maximized by the choice

f= 2 p− 1.

This is theKelly fraction.

A betting fraction of less than this would be a conserva-

tive strategy. Anything to the right will add volatility to

returns, and decrease the expected returns. Too far to

the right and the expected return becomes negative.

This money management principle can be applied to

any bet or investment, not just the coin toss. More

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

-0.1 0.1 0.3 0.5 0.7 0.9 1.1

Betting fraction

Expected return