Choosing Discrete or Continuous Returns for the Sharpe Ratio

Summary

The document addresses whether the Sharpe ratio should use discrete returns or continuously compounded returns. Its answer distinguishes the context: discrete returns are customary for client reporting, while the choice generally has little impact in a backtest. A second response describes the inputs as the realized portfolio return and standard deviation over the period.

The guidance is brief and does not give a derivation, example, or quantitative comparison of the two conventions. It also leaves details such as return frequency and annualization unspecified. The practical takeaway is to use a convention appropriate to the reporting purpose and apply it consistently, while recognizing that the stated equivalence in backtests is a general observation rather than a guarantee for every dataset or horizon.

Key ideas

• The document recommends discrete returns for client-facing Sharpe ratio reporting.
• It says the return convention usually makes little difference in backtesting.
• The ratio uses realized portfolio return and standard deviation over the measurement period.
• The guidance does not specify frequency, annualization, or conditions where the conventions may diverge.

Tags

# Sharpe ratio: discrete or continuous returns?


# Sharpe ratio: discrete or continuous returns?












The Sharpe ratio is known as $$SR=\frac{\mu-r_f}{\sigma}$$ Are these values calculated from discrete or continuously compounded returns?

## Answer by Helin (score 5, accepted)

https://quant.stackexchange.com/a/30472

For client reporting purposes, it is customary to use discrete returns. For backtesting, it pretty much make no difference.

## Answer by vonjd (score 1)

https://quant.stackexchange.com/a/30471

These are the realized return and standard deviation for the portfolio over the period.

Source: Paul Wilmott on Quantitative Finance, sec. ed., p. 329-330

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.