Optimal investment – multiple assets

We will use an example with various equities. E. Chan (2008) illustrates how to arrive at a multi-asset application of the Kelly Rule, and that the result is equivalent to the (potentially levered) maximum Sharpe ratio portfolio from the mean-variance optimization. 

The computation involves the dot product of the precision matrix, which is the inverse of the covariance matrix, and the return matrix:

mean_returns = monthly_returns.mean()
cov_matrix = monthly_returns.cov()
precision_matrix = pd.DataFrame(inv(cov_matrix), index=stocks, columns=stocks)
kelly_wt = precision_matrix.dot(mean_returns).values

The Kelly Portfolio is also shown in the efficient frontier diagram (after normalization so that the absolute weights sum to one). Many investors prefer to reduce the Kelly weights to reduce the strategy's volatility, and Half-Kelly has become particularly popular.

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