Optimal Kelly Bet Sizing for a Mean-Reversion Signal
You have an opportunity each day to trade an ETF mean-reversion signal. Each day the trade either wins or loses:
- With probability $p = 0.54$, you earn $+1\%$ on the capital you deploy.
- With probability $q = 0.46$, you lose $-1\%$ on the capital you deploy.
You choose a fraction $f \in [0, 1]$ of your total bankroll to invest in the trade each day. The remaining fraction
- f$ sits in cash and earns nothing.
1. Derive the fraction $f^{*}$ that maximizes the expected log-growth of your bankroll over one day, $E[\log(W_1 / W_0)]$.
2. What is the maximum expected log-growth at $f^{*}$?
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