# 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?

## 2 Answers

You can test if your mean return and variance are significantly different from benchmark statistics. Steps how to do it are described here "Chapter 9: Testing differences between two means, variances or proportions".

• The link doesn't work. – user16651 Aug 18 '16 at 19:17
• The significance level should reflect a Bonferroni Correction for the number of strategies you tested before coming up with this one... Otherwise the result may reflect Data Dredging. – noob2 Aug 18 '16 at 19:24

"The Statistics of Sharpe Ratios" by Andy Lo is the standard reference for the widely used test for performances: the Sharpe ratio.

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) $$t\mbox{-test}=\sqrt{N}\cdot \frac{\mbox{mean}(R) - r_f}{\mbox{std}(R)}=\sqrt{N}\cdot\mbox{Sharpe Ratio}.$$

Of course this relies on the i.i.d. of the performance. It is not the case if you obtain different statistics on daily, weekly and monthly resampled timeseries of your dataset. These points are discussed in Andy Lo's paper.

If you want to go further on the nonparametric aspects of testing the Sharpe ratio, you can follow this link on the Cross-Validated stackexchange.