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Sharpe Ratio Calculation with Annualized Log Returns

Article Quant Q&A · Author: mbih
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Summary

The document poses a practical question about calculating a Sharpe ratio from a portfolio’s daily observations over a year. The investor has annualized log returns and a risk-free rate for the same year, and proposes dividing their difference by the standard deviation of returns. The main issue is ensuring that the return, risk-free rate, and volatility terms use compatible time scales and definitions.

No answer or worked resolution is included, so the document does not establish a preferred formula, explain how daily volatility should be annualized, or clarify whether the numerator should use arithmetic or log returns. It provides no empirical evidence or caveats beyond identifying the inputs and attempted calculation. Its value is therefore limited to framing a common measurement question rather than teaching a complete Sharpe-ratio method.

Key ideas

  • The question concerns a Sharpe ratio based on a year of daily portfolio observations.
  • The proposed numerator subtracts an annual risk-free rate from annualized log returns.
  • The calculation must use consistent return conventions and time scales for the numerator and volatility.
  • The document gives no answer on annualizing standard deviation or on using log versus arithmetic returns.

Tags

Risk managementStatistics
Full text
# Sharpe ratio of annualized log returns


# Sharpe ratio of annualized log returns












I have returns from the last 12 months on a portfolio, and i have risk free rate for the latest year, on daily basis.

I have annualized the risk free rate, and i am using log returns for the period.

I use the standard deviation function in excel but i cant get the real sharpe ratio.

I am currently using this formula:

$(R^A_T-Rf_T)/\sigma_T$

$R^A_T$ = Annualized log returns

$Rf_T$ = risk free

$\sigma$ = std dev for returns

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