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Sharpe Ratio Question

I have a list of daily returns and I want to calculate an annualized Sharpe Ratio (without risk free return) for.

My question is how to annualize the daily returns and standard deviation?

Also the model did not trade everyday. So do I count the non traded days as "zeros" or it does not matter?

Let use this as an example:

over 1 year period, 150 days were traded.
mean return of 150 days: $1000.00
standard deviation of 150 days: 3000.00

Also in excel do you use "STDEV" or "STDEVP"? I used STDEVP.

Thanks for your help :)
How are you calculating a Sharpe ratio without the risk free rate? Also, I think you want to multiply the standard deviation by the square root of 365.
He's right - without the risk free rate, it's not really a Sharpe ratio. It's more like a coefficient of variation.
Also, how you annualize depends on how you are bearing risk - if you are holding a position even on the days you don't trade, you have exposure and you should count those days, because the market could move, which obviously would affect your mean and st dev. If you have a position every day, you annualize the daily mean (log returns, now) by multiplying by 252, the number of trading days in a year, not 365, because the market isn't open and doesn't move every day. The st dev is multiplied by the square root of 252. If you are out of the market and have no position most of the time, then you annualize by multiplying by a lower day count.
Also, most people use STDEV, not STDEVP. It's always a sample, not a population - you didn't count every trade, change in the bid - ask, etc.
To annualize your standard deviations, multiply by the square root of the number of trading days. In the case you described, you would multiply by the square root of 150.

You should use the STDEV() to figure out your standard deviations. STDEVP() is capable of interpreting TRUE FALSE and STRING cells, which don't apply to your case. For more info on the differences: Differences between the Excel statistical functions STDEVPA and STDEVP

- Frank

Thanks Frank. I switch to STDEV() and it did not really change the results.

I just want to be clear about the SQRT(). The system traded 150 days out of the entire year 252 (trading days). So do I use the 150 or 252? Another poster wrote 365. I am confused.

Also if you were measuring results across multiple years... How would that work?

Thanks for all your help.
Thanks for all the responses.

It is an intra day trading system so on the days there are no trades there is no exposure. In that case you suggest using the SQRT of 150, not 252.