Beta-Adjusted Return and Its Difference from the Sharpe Ratio

Summary

The document raises a question about a proposed beta-adjusted return measure: subtracting beta times a benchmark return from a stock return, then dividing by the stock’s volatility. It compares this expression with the Sharpe ratio, which subtracts a reference return directly before scaling by volatility. The topic is useful for understanding how performance measures account for market exposure and risk.

However, the document contains only the question and does not include an answer, derivation, or empirical comparison. It does not specify whether the benchmark return is risk-free, how returns and volatility are measured, or which convention the proposed metric is meant to follow. Readers therefore cannot use it to settle the definition; further context is needed to distinguish a beta-adjusted excess return from standard Sharpe-style measures.

Key ideas

• The question compares a beta-weighted benchmark adjustment with the Sharpe ratio’s return adjustment.
• Both expressions scale an adjusted return by stock volatility.
• The document does not establish a definitive definition or preferred formula.
• Interpreting either measure requires clarity about the benchmark and return conventions.

Tags

# Beta Adjusted Return


# Beta Adjusted Return












I'm a bit confused about the definition of the 'Beta Adjusted Return', say I have benchmark whose return is $r$ and a stock whose return is $R$, the beta adjusted return is defined as

$$ \frac{R-\beta r}{\sigma} $$

where $\beta$ is the beta coefficient, and $\sigma$ the stock's volatility.

Isn't it related to the Sharpe Ratio, defined by $\frac{R-r}{\sigma} $ ? What definition should we use?

Thanks

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