# calculating sharpe and sortino ratio given monthly returns [closed]

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...

1. Your formula for sharpe ratio is correct
2. 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).

• so this sharpe of 0.64 is that the monthly sharpe, then to convert that to an annual sharpe ratio I'd just multiply it by square root of 12? so it's 2.22? – VBACODER Nov 29 '20 at 19:59
• The 2.22 number is computed correctly. Do not annualize using @F0l0w's formula here. – steveo'america Nov 30 '20 at 23:32
• @steveo'america is correct. This'd be 2.22 annualized: web.stanford.edu/~wfsharpe/ws/…. – F0l0w Dec 1 '20 at 0:26

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.