Forex Maths & Physics

The Sharpe Ratio — And Why It Lies to You

Ask anyone in finance how good a strategy is and they will quote its Sharpe ratio. It is the single most common scorecard in the industry — and one of the most abused. Understanding both what it measures and how it deceives is essential.

What it measures

The Sharpe ratio is return per unit of risk:

The expected return E[R] minus the risk-free rate R_f, divided by the volatility of returns σ_R. A higher Sharpe means more reward for each unit of wobble. A Sharpe of 1 is respectable; 2 is excellent; anything claiming 5+ on a retail strategy should make you deeply suspicious.

Why it lies — selection bias

Here is the trap. Suppose you backtest 1,000 random strategies. By pure chance, some will have high Sharpe ratios — not because they are good, but because randomness produced a flattering sample. If you then report *only the best one*, its Sharpe is meaninglessly inflated. This is selection bias, and it is everywhere in trading.

The fix — the Deflated Sharpe Ratio

The Deflated Sharpe Ratio (DSR) corrects for how many strategies you tried and how non-normal the returns are. Intuitively, it asks: *given that I tested N strategies, how impressive is this best Sharpe really?* The more you searched, the higher the bar the winner must clear. A Sharpe of 2 from a single hypothesis is strong; the same 2 picked as the best of 10,000 trials may be pure noise.

Other ways the Sharpe misleads

• It punishes good volatility. Big upside moves raise σ_R and *lower* the Sharpe, even though you love them.
• It assumes returns are well-behaved. With fat tails, the same Sharpe hides far more tail risk than it appears to.
• It can be gamed. Strategies that sell insurance (steady small gains, rare huge loss) post lovely Sharpes — until the rare loss arrives.

How to use it honestly

• Always ask how many strategies were tried before this one was chosen.
• Prefer the deflated Sharpe, or at minimum out-of-sample evidence.
• Pair it with a look at the worst drawdown and the tail, not just the average.

The Sharpe ratio is a useful summary, not a verdict. Treat a high number as a question — "is this real?" — rather than an answer.

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