Comparing Sharpe Ratios Across Return Frequencies

Summary

The discussion addresses comparing strategies that trade at different frequencies while holding overlapping portfolios for the same horizon. Its central recommendation is to express Sharpe ratios at a common periodicity, such as monthly or annual, before comparing them. The answer also suggests deriving shorter-period returns from a sequence of longer-period returns and relating Sharpe ratios across frequencies with a square-root-of-time scaling rule.

That scaling is valid only under restrictive assumptions, including returns that aggregate consistently and little or no serial dependence. Annual observations alone do not reveal the intervening monthly return path, so they cannot generally be converted into actual monthly returns; consecutive annual total returns instead describe multi-year growth when combined. Overlapping holdings can also induce dependence in measured returns, affecting Sharpe estimates. The document provides no worked example or evidence that these issues were addressed, so frequency conversion should be treated cautiously.

Key ideas

• Sharpe ratios should use the same return periodicity when strategies are compared.
• Square-root-of-time scaling relates Sharpe ratios across frequencies under appropriate assumptions.
• A sequence of annual returns does not identify the actual monthly returns within each year.
• Overlapping portfolios can create dependent observations that affect Sharpe ratio estimates.

Tags

# How to compare Sharpe Ratios of different investment strategies (holding periods)


# How to compare Sharpe Ratios of different investment strategies (holding periods)












I am doing the momentum analysis and am trying to see, what strategy (based on trading frequency) yields the highest Sharpe ratio for different investment amounts. The trading frequencies I use are yearly, bi-yearly, tri-yearly .. to monthly. I always hold the portfolio for 12 months, thus, I have overlapping portfolios.

- When I calculate Sharpe for each of this strategies, I get Sharpe Ratios based on different periodicities. Are such ratios safe to compare, or should I always calculate lets say "Annual Sharpe Ratio" and compare those?

- Is it possible to get monthly Sharpe Ratios from a vector of yearly returns? Lets say, I have 12-month returns for 15 years, each year. How can I calculate a monthly sharpe ratio from that?

Thank you for your help.

Miha

## Answer by phdstudent (score 3)

https://quant.stackexchange.com/a/22591

To answer your first question: You need to make all sharpe ratios annual, or quartely, or monthly to be comparable. All of them must have the same periodicity.

To answer your second question: From the year returns, you can compute the monthly returns by making $(1+R_{t+2})/(1+R_{t+1})$ and then compute the monthly sharpe ratio, or alternatively, just compute the annual sharpe ratio and divide by $\sqrt{12}$. Should yield the same.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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