Kelly fraction for a 75% even-money bet

Question

A repeatable wager pays even money (win $1$ per $1$ staked) and you win it with probability $0.75$ . To maximise long-run growth of your bankroll, what fraction of the bankroll should you stake each time?

Short answer

$50\%$ . The Kelly fraction for net odds $b$ is $f^* = \frac{pb - (1-p)}{b}$ . With $b = 1$ and $p = 0.75$ this is $0.75 - 0.25 = 0.5$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Market Model and Risk-Neutral Valuation
Optimisation Problems
Constrained Optimisation and Lagrange Multipliers

Start with a free lesson: Options is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free