Two-asset Kelly

Nifty futures have excess return 4.5% and volatility 20%; a rupee gold position has excess return 3% and volatility 15%. (a) Compute the Kelly weights and maximal excess growth for correlation $\rho = 0.1$ and $\rho = -0.3$. (b) Compare with the excess growth from holding each asset alone at its own Kelly fraction. (c) Show in general that for two assets with equal excess return $m$, volatility $\sigma$ and correlation $\rho$, the total Kelly exposure is $2m/(\sigma^2(1+\rho))$, and interpret $\rho \to 1$ and $\rho \to -1$.