What is the proper way to caluclate sharpe ratio for the long short portfolio? When I calculate daily return with no cost, I use this formula: (return for long k.mean()+ (-1)*(return for short k.mean())/2 So can I use this formula to get daily sharpe ratio?: all daily return with no cost/all daily return's std If this is wrong, what is the right formula? And how can I get the annualized sharpe ratio of long short portfolio? I tried this: one daily return/all daily return's std for each date and divide by date number
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1$\begingroup$ Isn't the Sharpe ratio just a function of a series of historical returns? $\endgroup$– TickaJulesMay 14, 2022 at 17:30
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$\begingroup$ (1) Find the daily returns (2) Find their mean and standard deviation and compute the (daily) Sharpe Ratio (3) Annualize the sharpe ratio by multiplying by $\sqrt{252}$ the sqrt of the number of trading days per year $\endgroup$– nbbo2May 15, 2022 at 22:48
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1$\begingroup$ Can you clarify what your formula means? What is k.mean, where is the variance? (return for long k.mean()+ (-1)*(return for short k.mean())/2 $\endgroup$– Ralph WintersMay 16, 2022 at 14:36
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1 Answer
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Let's assume stock "A" yields a 5% return and stock "B" yields a 6% return, they both have standard deviations of 10% (per annum) and a correlation factor of 0.5. You decide to short stock "A" and long stock "B", let's assume you short "A" for an equivalent of 50% of your portfolio's value and use the proceeds (including your portfolio's value) to buy "B" for an equivalent of 150% of your initial margin. You have weights -50% in A and 150% in B.
By doing -50% * 5% + 150% * 6%, you will find your portfolio's return. Your standard deviation for only two stocks can be simply calculated by finding the square root of the "portfolio variance formula", keep in mind that you must know your correlation factor.
return : 6.5%
std : 3.5%
risk free rate: (let's say 2%)
Then, Sharpe = (6.5% - 2%) / 3.5% = 1.29
If your values are daily, then the sharpe ratio can be roughly annualized by multiplying with the square root of 252 (number of trading days).
