# Double Exponential Moving Average Crossover - Backtesting DAX

Now lets test the american S&P500 index with the exponential moving average double crossover method. Again 3750 days of data, and timewindows of 1 to 1000. In figure 1 you see the 3D results of the yields for each EMA pair, figure 2 shows the 2D topview.

It is interesting that this backtest yield map is even smoother than the exponential moving average on the DAX one. There are just a few big waves, and like no turbulences in this backtest. The highest annual yield is 16.23% produced by the pair 125 /120, the buy & hold strategy only delivers 6.5%. The ‘golden triangle’ region with the best results is very clear and homogeneous and good results can even be found in the long combinations. Benchmark with Buy & Hold on trading the S&P500

So how does the yield map look if you take the buy and hold performance as benchmark.

You see the clear triangle shape and at the spike the little golden triangle with the highest yields for this backtest. In fig. 5 you see the 3D view of the small triangle, you can clearly see the seperate waves.

The performance progession in this backtest can be seen in figure 6 together with the buy and hold performance. The exponential average nearly perfectly times the ext at day 2250, and at day 500 and reaches so a good outperformance.

You can see the curves of the two exponential moving averages in fig. 7 together with the S&P500. Optimal exponential moving averages against yield underperformance on trading the S&P500

The daily average underperformance compared to the SP500 performance index is visible in fig. 8 and 9. The under performance very homogeneous in its structure, there is a very strong region at the little timewindowsand one at the little timewindows. The upper part of the golden triangle is nearly affected.