Double Exponential Moving Average Crossover - Backtesting DAX

First we will test the exponential averages with double crossover system on the DAX index. Again we use the last 3750 trading days and test each combination of SMA values 1- 1000 (the yields where the ema short was higher than the ema high were left out again). Figure 1 shows the results of the backtest with the yield on the Z axis and as color. Figure 2 shows a topview of the backtest.


				
					Abb. 1: EMA Pair Performance for den DAX

Abb. 1: EMA Pair Performance for den DAX


				
					Abb. 2: EMA Pair Performance (Top View)

Abb. 2: EMA Pair Performance (Top View)

The results look very similar to the backtesting with the simple moving averages, there is a triangular mountregion in which the very good yields lie. And in contrast to the SMA backtest the region is not as bumpy, they seem to come in clearer waves und contain less turbulences. The best EMA pair (175 / 152) gives an yield of 22.2%, thats a bit below the results of the best simple averages which had 26.5%. Benchmark vs Buy & Hold trading on DAX

The yield of the buy and hold strategy is at 9.4% p.a., to benchmark this all results below that are left out in figure 3.


				
					Fig. 3: EMA Pair Performance bigger then B&H

Fig. 3: EMA Pair Performance bigger then B&H


				
					Fig. 4: EMA Pair Performance bigger then B&H (Zoom)

Fig. 4: EMA Pair Performance bigger then B&H (Zoom)

You can see that the dest EMA pairs lies again in the golden triangle, figure 4 shows a zoom of that. The waves are also good visible in figure 5. In comparison to the golden triangle of the simple moving averages it seems simpler to hit a good SMA pair, because the low yield regions lie nearly completly at the border at EMA short timewindows below 50 days.


				
					Fig. 5: EMA Pair Performance bigger then B&H (3D Zoom)

Fig. 5: EMA Pair Performance bigger then B&H (3D Zoom)


				
					Fig. 6: Performance comparison SMA281/235 vs B&H

Fig. 6: Performance comparison SMA281/235 vs B&H

The performance comparison with the DAX as benchmark in figure 6 shows that the exponential moving average pair 281 / 235 draws the outperformance by correctly signaling the downward trends.


				
					Fig. 7: EMAs 175 and 152 with DAX curve

Fig. 7: EMAs 175 and 152 with DAX curve

Optimal exponential moving average against yield underperformance on trading the DAX

In figure 6 you couldnt really see much days of underperformance compared to the buy & hold DAX, but it would be interesting also to see the distribution of underperformance for the EMAs.


				
					Fig. 8: EMA Pair Underperformance for the DAX

Fig. 8: EMA Pair Underperformance for the DAX


				
					Fig. 9: EMA Pair Underperformance Zoom

Fig. 9: EMA Pair Underperformance Zoom

The average daily underperformance (in fig. 8) looks really different in this backtest then with the simple averages. The exponential moving averages seem to be stronger underperforming with higher long EMAs (compare fig 6 of the double sma crossover index backtest) but the region of the middle timewindows (including the golden triangle) seems better.