Comparing Strategies at Equal Risk

Strategy A returned 18% last year. Strategy B returned 11%. A now looks like the better strategy — until you learn A ran at 25% annualized volatility and B ran at 9%. Scale both to the same risk level and B, not A, is the one that would have delivered the higher return. Comparing raw returns across strategies with different risk levels is comparing numbers that aren't measuring the same thing; the fix is to put them on equal footing before comparing.

Scaling to a common risk target

Because a strategy's risk (leverage, position sizing) is a choice separate from the quality of its signal, any strategy can be scaled up or down by applying a leverage multiplier $k$ so its volatility matches a chosen target $\sigma_{\text{target}}$:

$$k = \frac{\sigma_{\text{target}}}{\sigma_{\text{strategy}}}, \qquad R_{\text{scaled}} = k \times R_{\text{strategy}} .$$

In plain English: if a strategy runs twice the volatility you want to compare at, halve its exposure and its return roughly halves too (ignoring financing costs and assuming returns scale linearly with leverage, which holds well for modest leverage changes). This is exactly what the Sharpe ratio already does implicitly — it's return divided by volatility, so it's automatically comparable across risk levels — but risk-equalized comparison makes the scaling explicit and concrete in dollar or percentage terms, which is often more intuitive for a portfolio manager deciding how much capital to allocate.

Worked example: scaling to a common target

Strategy A: 18% return, 25% volatility, Sharpe $= 18/25 = 0.72$. Strategy B: 11% return, 9% volatility, Sharpe $= 11/9 = 1.22$. Scale both to a common 10% volatility target. For A: $k = 10/25 = 0.4$, scaled return $= 0.4 \times 18\% = 7.2\%$. For B: $k = 10/9 = 1.11$, scaled return $= 1.11 \times 11\% = 12.2\%$. At equal risk, B delivers 12.2% versus A's 7.2% — B is clearly the better strategy per unit of risk taken, the opposite of the impression the raw headline returns gave.

What this means in practice

Any time a report ranks strategies by raw return alone, ask what risk level each was run at. This is standard practice in manager selection and in capital allocation across a multi-strategy book — allocators typically scale every strategy's backtest to a common volatility target before comparing Sharpe ratios, drawdowns and returns side by side, precisely because raw headline return rewards whoever took the most risk rather than whoever had the better signal. It's also why leverage alone can make a mediocre strategy's returns look impressive without improving anything about its actual quality.