In part 1, we examined the original version of a strategy that trades crossovers of two triple exponential moving averages. At least on the S&P 500, the original version of the strategy was unprofitable, and the reverse strategy, while profitable, significantly underperformed merely buying and holding the index. We suggested some ways to improve it:
One of the obvious ways to try improving the strategy might be to add some exit conditions, trailing stops, or market filters: being in the market all of the time is rarely an optimal setting. Another way to improve the strategy might be to avoid the binary buy/sell, all-or-nothing form of expression in favor of something a little more nuanced.
In Binary and Polynary Trading Strategies, we laid out the case for developing strategies that can increase exposure gradually, rather than simply issuing all-or-nothing buy and sell signals. This crossover strategy looks like an ideal candidate for applying just such a gradualist or polynary approach, so that’s what we did.
The logarithmically scaled chart above shows the S&P 500 (dashed blue), the reverse of the Vervoort Crossover strategy we discussed in part one (red), and the polynary version described below (green). Trades are executed at the close, and no transaction costs are included.
The polynary version of this strategy has two steps. First, it generates short and long signals based on the difference between the two moving averages: in this context, the crossing of one average over or under another isn’t a particularly significant event (in stark contrast to the original binary version), since the strategy will have been steadily reducing allocations as the difference between the two averages decreased. Second, the strategy takes that signal and expresses it as a ratio of prior maximal and minimal signals, with a rolling window of prior signals that allows the strategy to “forget” old extremes – without such a window, the strategy allocates too conservatively and underperforms in trending markets. Another worthwhile wrinkle would be to exponentially weight more recent signals.
As you can see, these revisions significantly improve absolute returns and generate a smoother sloping equity curve, albeit one punctuated by occasional sharp drawdowns. This strategy looks like it would be further improved by an abnormal market filter like the one we developed last year – that October 2008 drawdown is particularly extreme, and while the strategy has recovered such losses almost immediately, very few living, breathing human traders would have the discipline to stick with a strategy after watching it give up several years of gains in the space of a couple weeks.