Calculating Sharpe and Sortino Ratios from Monthly Returns
Summary
The document considers how to calculate year-to-date Sharpe and Sortino ratios from a series of monthly portfolio returns and a stated risk-free rate. The questioner subtracts the risk-free rate from the arithmetic average return and divides by the standard deviation, but reports a result that appears implausibly large. The replies explain that the decimal return inputs produce a Sharpe ratio around 0.64, rather than a value in the tens; the apparent error is a percent-versus-decimal scaling mistake.
One response also points out that unusually large positive monthly returns make the sample positively skewed and can pull the mean above the median. This is a useful arithmetic check, but the exchange does not work through a Sortino calculation or clarify annualization conventions, risk-free-rate period matching, or downside deviation choices. Its numerical illustration is fictional and should not be treated as performance evidence.
Key ideas
- Sharpe calculations require consistent units for returns and risk-free rates.
- Entering percentages as decimals prevents a scale error in the ratio.
- The example's unusually large positive months raise the mean and create positive skew.
- A high mean relative to the median can signal that outliers influence the summary statistics.
- The exchange does not specify Sortino downside deviation or annualization conventions.
Tags
Full text
# calculating sharpe and sortino ratio given monthly returns
# calculating sharpe and sortino ratio given monthly returns
suppose I have (fictitious) monthly returns:
```
Jan-20 = 5%
Feb-20 = 7%
Mar-20 = 50%
Apr-20 = 4%
May-20 = -8%
Jun-20 = 0%
Jul-20 = -3%
Aug-20 = 12%
Sep-20 = 25%
Oct-20 = 3%
Nov-20 = 30%
```
and I wanted to calculate the Sharpe and Sortino ratio for the YTD of the portfolio.
Is the following correct:
If we assume a risk free rate of say 0.85% then the arithmetic average portfolio return is 11.36% and the std deviation is 16.29%. So is the Sharpe Ratio = $\frac{(11.36\% - 0.85\%)}{16.29\%} = 64.52$ this seems way too high...
Similarly with the Sortino ratio I get a number that seems absurdly high...
## Answer by F0l0w (score 1, accepted)
https://quant.stackexchange.com/a/59649
- Your formula for sharpe ratio is correct
- Given that dataset, your mean and std dev are overall fine
The sharpe ratio is 0.64. Meaning, you achieve 0.64 return (over the risk-free rate) for each unit of risk you confront. You must consider that this year is (obviously) an outlier.
For instance, look at the descriptive statistics of your dataset, where it is clearly positively skewed due to the outliers to the right (50%, 30%), while your median is just 5 (median is not affected by extreme values).
## Answer by user51037 (score 4)
https://quant.stackexchange.com/a/59645
You probably entered it wrong. you must enter the following:
```
(0,1136 - 0,0086)/ 0,1629 = 0,64518
```
If you want to do it via Excel. I can send you a finished calculation that I had to do for a paper at university. That would be for daily returns, but that is of no importance.
If you would like to try it yourself, let me know and I would be happy to explain how.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.