How Prediction Correlation Relates to Portfolio Sharpe

Summary

The document asks whether the correlation between a stock-return predictor and realized returns can determine the maximum Sharpe ratio of a portfolio built from that predictor. It frames the question around an optimally constructed and leveraged position, supposing the predictive relationship is known when the portfolio is formed. The author expects perfect prediction to allow unbounded leverage and therefore an unbounded Sharpe ratio.

No derivation, answer, or empirical evidence is included, so the document does not establish a formula linking correlation and Sharpe. The question highlights that predictive correlation alone may not specify a portfolio’s risk-adjusted performance: assumptions about return distributions, forecast calibration, trading constraints, costs, and the portfolio construction rule would matter. It is best read as a prompt for analysis rather than a demonstrated result or implementable strategy.

Key ideas

• The document asks how a predictor’s correlation with realized returns relates to attainable portfolio Sharpe.
• It considers an optimally constructed portfolio whose predictive relationship is known in advance.
• The author conjectures that perfect prediction could imply unbounded leverage and Sharpe.
• No formula, derivation, or evidence is provided, and additional modeling assumptions would be needed.

Tags

# Relationship between predictive power and Sharpe ratio


# Relationship between predictive power and Sharpe ratio












Let's say I have an algorithm that can predict the future return of a single stock. The covariance between its prediction and the real return of a stock is $\rho$. Based on this predictor, I can construct an optimal portfolio with appropriate leverage that maximizes expected return over long-term. Let's say $\rho$ is known during the construction of the portfolio. With reasonable assumption, can we express the sharpe ratio of the portfolio $S_{max}$ in term of $\rho$? I would expect $S_{max} \to \infty$ when $\rho=1$ since you can achieve the infinite return by maximizing the leverage to $\infty$ when you know the future.

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