# How to compare Sharpe Ratios of different investment strategies (holding periods)

I am doing the momentum analysis and am trying to see, what strategy (based on trading frequency) yields the highest Sharpe ratio for different investment amounts. The trading frequencies I use are yearly, bi-yearly, tri-yearly .. to monthly. I always hold the portfolio for 12 months, thus, I have overlapping portfolios.

1. When I calculate Sharpe for each of this strategies, I get Sharpe Ratios based on different periodicities. Are such ratios safe to compare, or should I always calculate lets say "Annual Sharpe Ratio" and compare those?

2. Is it possible to get monthly Sharpe Ratios from a vector of yearly returns? Lets say, I have 12-month returns for 15 years, each year. How can I calculate a monthly sharpe ratio from that?

To answer your second question: From the year returns, you can compute the monthly returns by making $(1+R_{t+2})/(1+R_{t+1})$ and then compute the monthly sharpe ratio, or alternatively, just compute the annual sharpe ratio and divide by $\sqrt{12}$. Should yield the same.