# Double Simple Moving Average Crossover - Backtesting DAX

First lets backtest the DAX for yield outperformance, similar as we did with the index crossover. Again we are backtesting the last 3750 trading days (15 normal years) and searching the highest yield p.a. Because we now have 2 variables (SMA short & long) and the yield for them we can display them as 3D graphic and get a topology for the SMAs, as in figure 1. Because of better visibility there is a topview graphic in figure 2, where the yield performance is visible as color.

Again we tested every timewindow size up to 1000 days, for each of the two simple moving averages. Because using an SMA short timewindow bigger then the SMA long timewindow doesnt make sense respectively produces an inverse result, these yields where not calculated (the single color triangle in the graphics). We see that the yield performance when using high long SMA values decreases at about 500 days, for 1000 days you can hardly find an SMA short combination that gives a good yield. It can be seen there is a ‘golden triangle’ of SMA Pairs where the high yields are located, in the range of middle SMA timewindow sizes. The simple moving average pair with the highest yield is the 281 / 235 combination which gives about 26.5%.

Benchmark versus Buy & Hold yield on trading the DAX

Which SMA Pairs brought more yield then Buy & Hold? To make this visible alle Pairs which yield is below the Buy and Hold performance were removed, as you can see in figure 3. You can see that this is a triangluar shape, and inside that is again a golden triangle with the best yields, cornered by SMAs ^{125}⁄_{25} - ^{275}⁄_{250} - ^{500}⁄_{50}. In figure 4 you can see this area in a zoomed view und in fig. 5 in 3D.

Lets look at the top SMAs performance in comparison with the Buy & Hold strategy (fig. 6). Strangely the performance makes a very strong leap upwards at day 1800 - why is that?

For this lets look at the chart of the SMAs relative to the DAX index and keep an eye on the crossovers in fig. 7. You see that you cant really discriminate the crossings from the lines because they run so close together. The reason for the sudden leap lies at day 1850, where a strong price rise in the DAX happens, and shortly before the SMA signals a ‘buy’ at the local minimum, and after that a ‘sell’. So it was a perfect timed trade - or just lucky ;)

But of course we searched for the luckiest SMA Pair, and that why this Pair has the best yield. But the focus should be on SMAs which use the longterm movements of the market, and not be lucky in short time trades.

If you look at figure 5, the whole upper corner of the golden triangle (where the ^{281}⁄_{235} pair lies) draws it yield performance from this leap, the others just have a bit worse timing on this trade.

So lets look at the second highest mountain, and look if we find an SMA Pair there which doesnt had such lucky results, but more constant good performance. We find it at the mountain top a bit left from the golden triangle with the values ^{351}⁄_{97}. We see in the chart in figure 8 that this moving average pair doesnt have extreme leaps, but earns its yield outperformance by signalising the big downward trends correctly and gets ca. 25% p.a.
Optimal simple moving averages against yield underperformance for trading the DAX

Now we got the SMA Pairs with the best final yield on the SMA map. But what about the continuity of the results? If a strategy falls behind its benchmark for a longer period, you are going to lose your faith in it, even it turns out to be great at the end. Its psychological much more pleasent to be never below the benchmark. Normally you would calculate the votality for an investment, but with our goal (beating the market) the benchmark index is the important line, its good if the simple moving average strategy hardly drops below that.

To quantify this, we look at the days of underperformance, we sum up the negative distance from the benchmark and calculate the average daily underperformance for each SMA, the result can be seen in figure 9. Figure 10 shows an zoom into the area of the golden triangle.