Kelly across many independent bets

Question

You can run 4 independent (uncorrelated) strategies at once. Each has expected excess return \mui, volatility \sigmai, and a per-strategy Sharpe of 0.5. How should you size each one, and what is the combined growth rate and Sharpe?

Accepted Answer

When bets are independent, their covariance matrix is diagonal, so the Kelly problem separates: you size each strategy at its own continuous-Kelly fraction, ignoring the others, fi^ = \frac{\mui}{\sigmai^2}. Independence means each additional strategy adds risk and return that don't overlap, so the growth rates simply add: g{	ext{total}} = \sumi \frac{\mui^2}{2\sigmai^2} = \sumi \frac{Si^2}{2}, where Si = \mui/\sigmai is the per-strategy Sharpe. For four strategies each with Si = 0.5: g{	ext{total}} = 4 	imes \frac{0.5^2}{2} = 4 	imes 0.125 = 0.5\ 	ext{(units of growth)}. The key result …

Kelly across many independent bets

Your answer

More Market Making questions