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Options, Risk Math, and Psychology · Risk Math Deep Dive

The Sharpe ratio, interpreted

Define Sharpe ratio, compute it for a sample strategy, and read the thresholds professionals care about.

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Options, Risk Math, and Psychology

Risk Math Deep Dive

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Lesson 40 of 75Options, Risk Math, and PsychologyRisk Math Deep Dive

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Define Sharpe ratio, compute it for a sample strategy, and read the thresholds professionals care about.

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Sharpe ratio: return per unit of swing

The Sharpe ratio is a single number that captures how much return you earned for each unit of volatility you endured. The formula: Sharpe = (your return − risk-free rate) / standard deviation of your returns. The risk-free rate is what you'd earn parking cash in a treasury bill — usually 4-5% lately. The standard deviation measures how bumpy your equity curve is. Bigger swings = bigger denominator = lower Sharpe.

Wick points at a chalkboard with the Sharpe formula and a worked example of 15% return, a 5% safe rate and 10% swings giving 1.0, showing return per unit of swing.Sharpe ratio(Return - safe rate)÷ swings (std dev)(15 - 5) / 10 = 1.0
Wick saysSharpe measures how much return you earned for each unit of bumpiness.

Why this matters. Two strategies can both return 20% a year. Strategy A has a smooth curve with a 10% standard deviation. Strategy B has wild swings with a 30% standard deviation. Say the risk-free rate is 4%. Strategy A's Sharpe = (20 − 4) / 10 = 1.6. Strategy B's Sharpe = (20 − 4) / 30 = 0.53. Strategy A is better. Same return, less pain, more compounding. Sharpe lets you compare strategies on a fair basis — by the QUALITY of the return, not just the size.

Wick compares two cards: smooth strategy A at Sharpe 1.6 and bumpy strategy B at Sharpe 0.53, both returning 20%, showing Sharpe rates the quality of a return.Smooth A20% return,10% swings.Sharpe 1.6Bumpy B20% return,30% swings.Sharpe 0.53
Wick saysSame 20% return, but the smoother strategy earns a much better Sharpe.

Rough thresholds professionals use. Sharpe under 0.5: not worth the effort — buy a treasury bill. Between 0.5 and 1: marginal — could be luck or a small real edge. Between 1 and 2: solid, real-world tradeable. Between 2 and 3: excellent, the territory of well-run hedge funds. Above 3: rare in live capital and usually a sign of overfitting in a backtest. For a retail trader on a $500 account, beating Sharpe of 1 over a long sample is a real accomplishment.

Wick looks worried at a meter whose needle sits deep in the coral 3+ zone for a backtest Sharpe of 4.5, showing that too clean a result deserves doubt.Under 0.53+: overfit?Backtest Sharpe 4.5?
Wick saysA Sharpe above 3 in a backtest is often a sign of overfitting, so be skeptical.

Recap: Sharpe = (return − risk-free) / standard deviation. Above 1 is good. Above 2 is institutional. Above 3 is probably overfit. Always compare strategies on Sharpe, not just headline returns.

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1. Strategy returns 15%, the risk-free rate is 5%, and the strategy's annual standard deviation is 10%. What's its Sharpe ratio?

2. A backtest reports a Sharpe ratio of 4.5 over five years. What's your first instinct?

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