Calculating Sharpe Ratios with Excess Returns and Consistent Frequencies
Summary
The document discusses computing and comparing Sharpe ratios for gold, Treasury returns, and a stock index when observations have different frequencies. The reply recommends calculating each asset’s excess return at a common monthly frequency by subtracting the corresponding monthly risk-free rate from each monthly asset return. The average excess return and volatility should then be estimated across the same observations for the ratio.
It confirms that annualizing monthly mean returns and volatility uses different scaling factors, while referring readers elsewhere for the choice between simple and logarithmic returns. To study how the horizon affects Sharpe ratios, it suggests comparing rolling one-year windows with the full twenty-year period. The brief response does not specify how to convert the Treasury data to monthly risk-free rates, handle serial correlation, or account for estimation uncertainty in rolling windows. It also leaves the return convention question unresolved, so the calculation requires a consistent choice of simple or log returns.
Key ideas
- Compute asset excess returns by subtracting the risk-free rate at the same monthly frequency.
- Estimate the mean excess return and volatility over matching observations.
- Annualize monthly means and standard deviations with different scaling factors.
- Compare rolling short-horizon Sharpe ratios with a full-sample ratio to examine horizon effects.
- The reply does not resolve the choice between simple and logarithmic returns.
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# How to calculate sharpe ratio # How to calculate sharpe ratio I have end of month Gold prices, Returns of treasury (in percentages) & end of day NASDAQ index over 20 years. I want to compute risk adjusted returns by finding sharpe ratio. Im confused how do i go about calculating them. - For these 3 assets, i need to bring them to the common scale - so i calculated monthly gold return & equity returns by computing percentage change and then annualize them by multiplying by 12. So i get monthly return %age - then i use the formula of sharpe which is to calculate mean of these returns and divide them by std deviation. For gold and stock market, since i have calculated monthly returns ill multiply the mean by 12 and sigma by sqrt 12 to adjust it to monthly - What is the risk free return to be used. For example, for over 20 year period, the risk free return of any instrument will vary. So do i simply average it out? - I take the entire 20 years as duration, but im realizing that to analyze short term vs long term , i perhaps need to take 1 to N years rolling sharpe ratio and then show how equity & gold is more volatile and smoothens out over a long time range. So to achieve this, do i simply reduce the time range over which i compute sharpe ratio? My qs: - For #1, is the approach to convert them to annualized returns correct? Whats the ideal way? - For #2- Ive seen some websites using log returns and they dont mention pros/cons of using the same. Is my formulation correct? - Is the rational correct to measure effect of time horizon on sharpe ratio? TIA ## Answer by KaiSqDist (score 0) https://quant.stackexchange.com/a/79634 Not sure if I understood your questions perfectly but - Yes, that is fine. - See Discrete returns versus log returns of assets - You should calculate the individual excess returns (monthly returns minus the monthly riskless rate) across all 240 data points, take the average of all of them as the expected excess return to be used in computing the Sharpe. You should repeat for the volatility. - There isn't a right or wrong, you can do both and show the Sharpe ratios across 20 for 1 year or 1 for 20 years.
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