# Test statistical significance of a trading strategy

I have created a trading strategy which operate every single day on the DAX 30, for the last 1700 trading sessions (some years). I have the daily returns of my strategy and also the daily returns of my index. I'm using R, therefore i can get sd, mean, var ecc...

The big issue that impresses the market watchers and financial types is the ability to consistently make above-market returns.

What are the main important instrument to test the significance of a trading strategy?Is it sufficient a simple t-test? Which type (paired, unpaires ecc..)? What are your suggestions?

This ratio is close to the standard t-test: does the mean of my i.i.d. random variable of performances $R$ is significantly not zero (or better than the risk-free rate $r_f$)? $$\mbox{Sharpe Ratio}=\frac{\mbox{mean}(R) - r_f}{\mbox{std}(R)}.$$ To be compared to (where $N$ is the number of points used to compute the mean and the std) $$t\mbox{-test}=\sqrt{N}\cdot \frac{\mbox{mean}(R) - r_f}{\mbox{std}(R)}=\sqrt{N}\cdot\mbox{Sharpe Ratio}.$$