Annualized Sharpe Ratio from monthly data

[Hank Moody]

Anyone know the correct way to compute the annualized Sharpe ratio from historical monthly or quarterly data?
Do you first annualize the components then compute the ratio, or do you compute the ratio on raw data and adjust the final calculation?
Thanks,

 

[jmh530]

If returns are normally distributed and iid you basically do either. Convert the monthly return and standard deviations to annual and do the ratio, or do the ratio and multiply by the square root of time.
In practice, returns are neither normal nor iid so technically you shouldn’t do that.

 

[Hank Moody]

How would you convert the monthly returns to annual? 12 x monthly, or CAGR? How would you annualize the STDEV?

 

[jmh530]

Multiply by 12 for log returns, CAGR for arithmetic.
For stdev, you just have to realize that you multiply by 12 for variance, so for standard deviation you multiply by the square root of 12.
Hence if you multiply by 12 on top and divide by the square root of 12 on the bottom, you would adjust the Sharpe ratio by the square root of 12.

 

[Hank Moody]

thanks! I flunked Quant in Level II.