Choosing Strategy Metrics That Account for Market Beta

Summary

The document asks how to score a trading strategy in a supervised machine learning framework while accounting for exposure to the market. It compares raw strategy returns and a conventional Sharpe ratio with excess returns and a Sharpe ratio based on returns net of the market return. It then proposes two beta-adjusted alternatives: subtracting a penalty proportional to absolute beta, or dividing the excess-return Sharpe ratio by absolute beta.

The discussion is a question rather than a worked analysis, so it provides no evidence that either proposed score is standard or performs well. It also leaves unresolved how to estimate beta, choose the penalty, handle near-zero beta, and make candidate strategies comparable. The listed formulas treat market return as a benchmark or risk-free proxy, which may not be appropriate in every setting. The document is useful as a starting point for distinguishing market exposure from volatility, but selecting a metric would require a clearly defined objective and validation against out-of-sample performance.

Key ideas

• Raw returns and Sharpe ratios do not directly isolate a strategy’s market exposure.
• Excess returns subtract market returns, while a beta estimate measures sensitivity to market moves.
• The author proposes penalizing absolute beta or scaling an excess-return Sharpe ratio by inverse absolute beta.
• The proposed formulas are questions for evaluation, not validated standard metrics.
• Metric choice requires attention to beta estimation, tuning, comparability, and the strategy’s objective.

Tags

# Supervised metric including beta?


# Supervised metric including beta?












I am working in a supervised ML framework. I'd like to define one metric to evaluate a strategy. Naturally I was initially enclined towards overall returns or sharpe ratio. I'd like to implement a metric that take the market beta into account.

I was thinking about penalising by beta, but I am not sure it is a standard appraoch (plus it needs some tuning). Is there a standard approach for taking into account market beta in portfolio evaluation metric ?

Below are some of the metrics considered:

Overall return: Re

Market return: Rm

Excedent return : Re - Rm

Sharpe ratio: Re / std(Re)

Sharpe ratio considering market as risk free: (Re-Rm)/(std(Re-Rm))

I was thinking about these:

Beta penalised Sharpe ratio: (Re-Rm)/(std(Re-Rm)) - lambda * abs(Covar(Re,Rm)/Var(Rm))

Sharpe ratio multiplied by inverse absolute beta: (Re-Rm)/(std(Re-Rm)) * 1 / abs(Covar(Re,Rm)/Var(Rm))

Does these make sense ? Does it need to include some sort of scaling to be comparable (power 1/2, 1 or 2 ?) ?

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