Trading interview, often as a follow-up to a probability question.
How much do you bet?
The question
You have an edge: a bet wins 60 percent of the time at even money. What fraction of your capital do you stake?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
The Kelly fraction is 20 percent, and most people should bet a fraction of that.
Kelly for an even-money bet is 2p - 1, so 0.2 with p = 0.6.
Kelly maximises the long-run growth rate of log wealth, not expected wealth, which is why it does not tell you to bet everything despite the positive edge.
Full Kelly is very volatile and assumes your edge estimate is exact. Since 0.6 is itself an estimate, half Kelly or less is the practical answer, giving up a little growth for much less variance.
Saying 'all of it, the expected value is positive' fails the question. So does refusing to bet.
What it is testing
Understanding growth rate versus expectation and the fragility of an estimated edge.
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