Equal-Weight Portfolio Sharpe Maximization as Binary Selection

Summary

The document formulates a portfolio selection problem: maximize the Sharpe ratio while requiring every included asset to receive the same weight and every excluded asset to receive zero. It represents the decision with a binary vector that marks selected assets, then normalizes that vector so the selected entries become equal weights. The objective uses expected returns and the covariance matrix to measure portfolio return relative to risk.

The author asks how to solve this discrete optimization problem, noting that an attempted transformation for a binary programming solver did not succeed. The document gives no algorithm, solver formulation, or empirical result. It also does not specify additional portfolio constraints or discuss estimation error in expected returns and covariances. Its contribution is the problem setup: subset selection determines the portfolio, while the equal-weight rule fixes weights once that subset is chosen.

Key ideas

• A binary decision vector can encode which assets enter an equal-weight portfolio.
• Normalizing the selected entries produces equal weights for included assets.
• The objective maximizes expected portfolio return relative to portfolio volatility.
• The document poses the optimization problem but provides no solution or results.

Tags

# Maximising sharpe of portfolio with equal weights


# Maximising sharpe of portfolio with equal weights












I want to maximise $\frac{w^T\mu}{\sqrt{w^T\Sigma w}}$ with $w_i$ either 0 or $\frac{1}{\#\text{nonzero weights}}$.

This is the same as maximising $\frac{\tilde{w}^T\mu}{\sqrt{\tilde{w}^T\Sigma \tilde{w}}}$ with $\tilde{w} \in \{0, 1\}^N$, then setting $w:=\frac{\tilde{w}}{||\tilde{w}||}$.

I've tried looking at some transformations of the problem to try solve with `cvxopt` (which supports binary programming), but no success.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.