Sharpe Ratio Inputs: Portfolio Returns, Annualization, and Compounding
Summary
The discussion addresses how trade sizing, portfolio returns, compounding, and the risk-free rate affect a Sharpe ratio calculated from daily data. The answer recommends treating the portfolio value time series as the basis for returns and risk rather than interpreting the ratio as a direct function of a chosen percentage risk per trade. This frames the statistic around the realized path of portfolio wealth.
For comparisons with annual rates, the response recommends converting daily return and volatility measures to yearly units, using a trading-day annualization convention, and comparing them with a risk-free rate expressed on the same basis. It suggests a long-maturity Treasury yield only as a practical proxy, while acknowledging that it is not the theoretical risk-free rate. It also favors geometric average returns for compounding, while noting that conventions differ. The answer is brief and does not resolve details such as matching the risk-free instrument’s horizon or choosing an arithmetic versus geometric excess-return convention.
Key ideas
- Sharpe calculations should use returns from the portfolio value series over time.
- Trade count and position size do not directly define the measured portfolio return series.
- Daily return and volatility inputs need consistent annualization when compared with annual risk-free yields.
- The response treats a long-maturity Treasury yield as a practical proxy, not a theoretical risk-free rate.
- It favors geometric average returns for compounding but acknowledges that other conventions exist.
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# Questions about Sharpe Ratio calculation
# Questions about Sharpe Ratio calculation
- Let's say I have daily returns. Don't they depend on the risk per trade I am using? Obviously, if I'm risking 2% of equity per trade returns will be drastically different than when I'm using 10%? So if I have a strategy I have to assume a certain % risk per trade in order to calculate Sharpe? Wouldn't it be too easy to manipulate Sharpe by just changing this parameter?
- I'm going to use one of these bad boys for risk-free rate here.
https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield
But which one should I use? Given that I'm working with daily returns, not yearly.
- When inputting daily returns in Sharpe formula should they be compounded or not? Like if I start with \$100 in equity should every daily return be based on \$100 in equity?
## Answer by Oscar (score 1, accepted)
https://quant.stackexchange.com/a/55051
Question1: I think you're confused on what you're actually measuring. Don't think about this in terms of trades, think about it in terms of the total value of your portfolio. At day 1 you have 100 dollars, tomorrow you have 110, 2 days from now 115 and a week from now it's back to 105. How many trades you made during that period, how big those positions are or even how much cash you have is irrelevant. The time series of those portfolio values (100, 110, 115.... 105) is from where you calculate your standard deviation and average return to get your Sharpe Ratio.
Question 2: Even if you're working with daily returns and measure the daily standard deviation it's probably a good idea to transform those into yearly measures (in fact you need to do so in order to calculate your Sharpe ratio). Just take $1-(1+r)^{252}$, where r is your average daily return calculated in question 1, to get your average yearly return and $\sigma_ {daily} * \sqrt{252}$ to get your volatlity as a yearly measure. The interest rates you found are already measured yearly. the correct rate to use is the theoretical risk free rate, so none of them really, but the 10-year rate should be fine for your purposes.
Question 3: Again, not sure what you mean. Do you mean if you should use the geometric or arithmetic mean when finding your average rate of return? I would use the geometric but I'm sure you'll be able to find people with differing opinions.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.