Annualizing Daily Return Volatility for a Portfolio Sharpe Ratio

Summary

The document describes a portfolio investor’s uncertainty about which standard deviation belongs in an annual Sharpe ratio when returns are recorded daily over a long historical period. The investor compares the dispersion of annual returns across years with an annualized estimate based on daily volatility, and also considers averaging yearly volatility estimates. The question further raises whether to use an average annual risk-free rate or transform rates using the number of trading days.

No answer or accepted method is included, so the document supplies no resolution or empirical evidence favoring one calculation. It does show why the alternatives can differ: annual returns vary substantially across the sample, and averaging yearly estimates is not automatically the same as measuring the full daily return series. The described square-root-of-time conversion is an assumption-based annualization, and the document does not discuss serial correlation, compounding, changing risk-free rates, or the precise return convention needed for a consistent Sharpe calculation.

Key ideas

• The document compares standard deviation across annual returns with annualized volatility estimated from daily returns.
• Averaging yearly volatility estimates is a distinct calculation from measuring volatility across the entire daily sample.
• The investor considers using either an average yearly risk-free rate or a transformed rate in the Sharpe ratio.
• The document presents the question but contains no answer validating a preferred calculation.
• Serial dependence, compounding, and return conventions are not addressed.

Tags

# How can I calculate the annual Standard Deviation for Sharpe Ratio of Daily Portfolio Returns?


# How can I calculate the annual Standard Deviation for Sharpe Ratio of Daily Portfolio Returns?












I'm somewhat confused with regards to calculating the annual standard deviation and Sharpe ratio for my portfolio of daily returns.

I have daily data ranging from 1960-2020 and use Excel to make some calculations. I have attempted 2 ways of doing it and don't know which makes most sense.

- I calculated the annual return for each individual year, from that I took the standard deviation of those 61 years (return: 12.10*, st. dev.: 25.70**)

- I calculated the annual return for each individual year, next I calculated the standard deviation for each individual year - but they're really low (less than 1). I got confused and tried to multiply these by the square root of 253 (assuming 253 trading days/year). The average of those 61 data points is 13.40 (st. dev.).

After that I want to calculate the Sharpe ratio using the avg. annual return (12.10%) minus the avg. risk-free rate (which I think I can either estimate with the square root of 253 or just take the avg of the yearly risk-free rate - I'm inclined to do the second).

But which standard deviation would be correct to use here?

*annualizing the daily returns by averaging all daily returns and multiplying them with the square root of 253 (trading days) got me 12.16

**annualizing the daily st. dev. by averaging all daily st. devs and multiplying them with the square root of 253 (trading days) got me 15.03. Also note that the returns do fluctuate quite a lot through the years, ranging between -53% and +77%.

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