Finocturne
Investment

Sharpe ratio and risk-adjusted returns

Divide same-period excess return by to compare return per unit of total risk; a historical only describes its sample.

Compare excess return per unit of risk

01 · Make a predictionAt a fixed positive excess return, how does higher volatility affect Sharpe?

Same-period assumptions: risk-free 3%; A return 12%; B return 10%, standard deviation 10%. Match periods and data basis when comparing.

Portfolio A Sharpe0.600
Portfolio B Sharpe0.700

Same-period excess return divided by SD; Sharpe is unitless

S=0.12−0.030.15≈0.6

What did you just see?

For the same positive excess return, lower volatility raises Sharpe. treats upside and downside alike and does not fully describe tail losses.

Historical or assumed inputs

Historical return and describe the sample; expected return and volatility describe a scenario. This tool does not estimate inputs from a price series.

Match periods and reference rates

All three inputs need matching horizons, currencies, and return definitions. Square-root-of-time annualization is justified only under assumptions such as appropriate time independence.

Another example

  1. Enter return 12%, risk-free rate 3%, and volatility 15% on the same horizon.
  2. Excess return is 12% − 3% = 9%.
  3. Sharpe is 9% ÷ 15% = 0.6, a dimensionless ratio.
Show formal definition and formula

The Sharpe ratio standardizes excess return by total standard deviation to compare investments with consistent horizons and methods.

S
Dimensionless Sharpe ratio; historical and assumed inputs have different interpretations.
Rp
Portfolio return.
Rf
Same-period risk-free rate.
σp
Strictly positive same-period return standard deviation; the ratio is undefined at zero.

Common mistakes

Do not silently mix realized historical returns with forecast volatility, or treat a high Sharpe as a future guarantee. Smoothed valuations, skewness, and small samples can distort it.

Frequently asked questions

Does zero standard deviation give infinity?

This tool reports zero standard deviation as undefined, including zero excess return, rather than returning infinity or zero divided by zero.

How should I interpret a negative Sharpe?

Return is below the matching risk-free rate. With negative excess return, more volatility can move the ratio toward zero, so ranking strategies solely by the ratio can mislead.

You can now explore…

  • Compare excess return with volatility
  • Separate historical measurement from assumed inputs
Term reference2 terms

Open a term when you need a reminder. Underlined words in the article work too.