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Risk-Adjusted Returns: Sharpe Ratio, Sortino, and Alpha
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Risk-Adjusted Returns: Sharpe Ratio, Sortino, and Alpha

Measuring how much return you get per unit of risk taken

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Return Without Context Misleads

Two strategies can post the same annual percentage while exposing you to wildly different drawdowns. Risk-adjusted metrics ask a disciplined question: how much pain did you take per unit of reward? They do not replace judgment — they stop headline numbers from hiding leverage, concentration, and gap risk.

Start with a simple split: excess return versus a baseline (often a short-term government yield), and risk measured as dispersion of returns or sensitivity to a benchmark.

Return distributions (schematic) Low dispersion High dispersion Same mean return possible — very different paths. Risk-adjusted view: reward per unit of undesirable variation
Wider return clouds imply more uncertainty even when averages match.

Sharpe: Excess Return per Unit of Volatility

The Sharpe ratio divides average excess return over the risk-free rate by the standard deviation of returns (often annualized with consistent scaling). It is widely quoted because it is simple and comparable across strategies — but it treats upside and downside swings the same.

  • Values near zero suggest little compensation after adjusting for volatility.
  • Values materially above one often attract attention — and should trigger scrutiny for data mining or non-stationary regimes.

Always align the risk-free series with your return frequency and currency.

Sharpe ratio structure E[R − Rf] mean excess return ÷ σ(R) std dev of returns Annualize numerator and denominator with the same assumptions (e.g., √252 for daily equity returns). Sortino replaces σ with downside deviation if you want to ignore upside volatility.
Sharpe is a ratio — garbage inputs (bad returns series) produce garbage ratios.

Sortino and Treynor: Different Denominators

The Sortino ratio uses downside deviation in the denominator — volatility of returns below a target or zero — so positive surprises are not “punished” as risk. The Treynor ratio divides excess return by beta, emphasizing compensation for systematic exposure rather than total volatility.

Neither is universally “better.” Pick the denominator that matches the risk you actually fear.

Alpha and Information Ratio

Jensen’s alpha (in a CAPM framing) measures return above what beta would predict. The information ratio scales active return by tracking error — how consistently you deviate from a benchmark. A noisy strategy with occasional jackpots may look worse than a steadier one when you care about implementation risk.

Applying Metrics in Crypto

Crypto return series are non-normal: fat tails, regime shifts, and funding mechanics on perpetuals. Report both rolling Sharpe and maximum drawdown. If you trade on GaiaEx, include fees, funding, and liquidation proximity in your simulation — otherwise your “alpha” is a spreadsheet fantasy.

A Practical Checklist

  • Define the return series (log vs simple) and stick to it.
  • Pick a risk-free proxy that matches your horizon.
  • Document whether statistics are full-sample or rolling.
  • Never optimize purely for Sharpe in-sample without a holdout regime.