Questions / Quant trading, Sizing & risk
Log-optimal sizing with a no-change state
A fraction f of wealth is invested in a one-period trade returning +100% with probability 0.4, −50% with probability 0.4, and 0 with probability 0.2. The rest stays in cash. Over 0≤f≤1, what f maximizes expected log wealth? Enter a percentage.
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Answer: 50% (1/2)
- The derivative vanishes when 1/(1+f)=0.5/(1−f/2). This gives f=0.5; concavity of the log objective makes it the maximum.
Interview shortcut. Log-optimal: 0.4/(1 + f) = 0.2/(1 − f/2), so f = ½.
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