Questions / Quant trading, Sizing & risk
Fractional Kelly
In an idealised repeated even-money bet, you estimate a 60% win probability. What fraction of wealth is full Kelly? Enter a percentage.
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Show the answer and worked solution
Answer: 20% (1/5)
- Let f be the wealth fraction staked. Wealth changes by factors 1+f on a win and 1−f on a loss.
- Expected log growth is 0.6 log(1+f) + 0.4 log(1−f). Setting its derivative to zero gives 0.6/(1+f) = 0.4/(1−f).
- Solving gives f = 0.6 − 0.4 = 0.2, or 20%, under the idealized probability and repeated-bet model.
Interview shortcut. Even-money Kelly is the edge: p − q = 0.6 − 0.4.
Takeaway. The sizing objective and payout odds matter, not just the chance of winning.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.