A useful rule of thumb (which I teach my students in week 3), which can be derived from the sampling distribution of a mean estimate, is that for statistical significance you need at least N data points where N:
N = 4* (s / m)^2
Where m is the average value and s is the standard deviation.
[This assumes that a T-statistic of 2 is significant, which is true at 2.5% significance for more than ~60 observations, i.e. you can be 97.5% confident that the true mean was greater than zero]
This implies that the more profitable your trades are (bigger m), and the more consistent their profitability (smaller s), the more confident you can be and the fewer trades you need.
Consider for example the following series of 100 trades: +$300, -$250, $300, -$250 ....
The mean is $25 and a quick visit to Excel confirms that the standard deviation is $275 [depending on whether we use the 'sample' or 'population' version of the statistic]. Plug into the formula;
N =4 * (272/25)^2 = 4 * (11)^2 = 484
So we'd need almost 500 trades to be at least 97.5% confident that our backtest results weren't just down to luck.
Of course this theoretical result assumes there are absolutely no issues with your backtest such as:
- overfitting
- survivorship bias
- data snooping
- source of return you are exploiting vanishing
- under-estimating costs
For this reason I'd generally multiply the figures above by at least a factor of 2, if not more.
GAT
