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
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).