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Worked examples, in Risk & Portfolio Construction

Sharpe vs Sortino Worked Examples

When returns are symmetric the two ratios agree; when they are skewed they diverge, sometimes sharply. These scenarios are built to show exactly that. All use monthly excess returns annualized with the square-root-of-12 factor; Sharpe divides by total standard deviation, Sortino by downside deviation only. The numbers are computed directly from those formulas and are reproducible in the tool. Start from the baseline scenario, then trace what changes as you shift the volatility shape.

3 examples. Published May 26, 2026. Updated May 27, 2026. By AI Fin Hub Research.

Worked examples

See the inputs and outcome together

Each scenario keeps the starting point, the outcome, and the actual lesson in one place so the page reads like a decision notebook, not a data dump.

  1. 1

    Baseline: symmetric volatility

    A steady strategy whose ups and downs are roughly balanced, so downside deviation is below total standard deviation but not dramatically so.

    Annualized Sharpe 0.69, annualized Sortino 1.04.

    Mean monthly excess return

    0.6%

    Total standard deviation (monthly)

    3.0%

    Downside deviation (monthly)

    2.0%

    Even with symmetric-looking returns, Sortino reads 1.04 against Sharpe 0.69 because downside deviation is two thirds of total volatility. Treat the gap as a baseline fingerprint of the return shape. When you later compare strategies, a Sortino-to-Sharpe ratio near 1.5 like this one is the neutral case, not a sign of skew either way.

  2. 2

    More upside volatility

    Same mean return, but the strategy now has larger winning months. Total standard deviation rises while downside deviation is unchanged.

    Annualized Sharpe 0.52, annualized Sortino 1.04.

    Mean monthly excess return

    0.6%

    Total standard deviation (monthly)

    4.0%

    Downside deviation (monthly)

    2.0%

    Sharpe drops from 0.69 to 0.52 because it penalizes the extra upside volatility. Sortino stays at 1.04 because none of that new volatility is downside. This is the case where Sharpe undersells a strategy.

  3. 3

    Hidden downside risk

    Same mean and same total standard deviation as the baseline, but the losses cluster, so downside deviation is now higher than total standard deviation.

    Annualized Sharpe 0.69, annualized Sortino 0.59.

    Mean monthly excess return

    0.6%

    Total standard deviation (monthly)

    3.0%

    Downside deviation (monthly)

    3.5%

    Sharpe is unchanged at 0.69 and looks fine, but Sortino falls to 0.59 because the loss distribution is the problem. When Sortino sits well below Sharpe, the strategy carries negative skew the Sharpe number is hiding.

Patterns

Holding mean return fixed, Sharpe falls when upside volatility rises while Sortino does not.
When Sortino sits above Sharpe, the volatility is mostly upside and Sharpe is being unfair to the strategy.
When Sortino sits below Sharpe, losses are concentrated and Sharpe is hiding downside risk.
Reporting both ratios from the same return series surfaces skew that either number alone would mask.

Run the numbers next

  • Calculators Risk-Adjusted Returns Calculator

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  • Calculators Returns Distribution Analyzer

    Paste a returns CSV. Histogram, normal QQ plot, skewness, excess kurtosis, Jarque-Bera test, tail-weight index. See why Sharpe alone misleads.

Sources

  1. The Statistics of Sharpe Ratios , Andrew W. Lo, Financial Analysts Journal (2002)
  2. Performance Measurement in a Downside Risk Framework , Frank A. Sortino and Lee N. Price, The Journal of Investing 3(3), 59-64 (1994)

Keep the topic connected

  • Learn Sharpe Ratio

    Sharpe ratio defined, when it lies (skew, fat tails, autocorrelation), and how to read a Sharpe number you didn't compute yourself.

  • Learn Sortino Ratio

    Sortino ratio: same numerator as Sharpe, denominator only counts downside volatility. When it's the right number to look at.

  • Formula Sharpe Ratio Formula

    The Sharpe ratio formula: excess return over the risk-free rate divided by return volatility, then annualized. Every variable defined, with a worked example.