I'm trying to calculate an Ex-Post Sharpe Ratio for my portfolio and I would appreciate verification I'm doing it correctly.
I have my portfolio's daily returns in one column and my benchmark's returns (the S&P) in another. I calculate the differential between the two (Daily_return - S&P_return). Next I find the arithmetic average of the differential, which in my case is 0.15% over 87 trading days. I annualize the average return by (avg_daily_return+1)^252-1, for a value of 46%.
I then calculate the sample standard deviation of the differential returns, for a value of 0.62%. I annualize the standard deviation by multiplying this number by the square root of 252, for a value of 9.95%.
Finally, I divide the annualized daily average return by the annualized daily standard deviation (46%/9.95%) for a Sharpe of 4.59. I believe I'm performing the calculation correctly, but this value seems unreasonably high.