I am looking at a data set of 60 monthly returns (last 5 years) and want to calculate an annualized Sharpe Ratio.
The usual way of doing this is to calculate the monthly Sharpe Ratio first, and then multiply it by a scaling factor. This scaling factor is the square root of 12 if returns are not serially correlated.
In my data set however, the returns exhibit statistically significant autocorrelations. I am aware that Lo (2002) suggests to use a scaling factor which accounts for the first 11 autocorrelations (specifically, autocorrelations for time lags 1 to 11).
My question revolves around the calculation of the autocorrelations for the purpose of annualization: Do I calculate the first 11 autocorrelations for the biggest possible periods (in my case it would be 60 - 11 = 49 months)? Or do I calculate autocorrelations for 12 month periods?
I tried to retrieve the correct way to do this from Lo (2002), but this uncertainty remains for me after reading through the paper and similar Q&A threads I found.