Comparing Overlapping Systems (Part 1)

I have this oscillator that comes in handy. The details of the oscillator are unimportant, but I’ve found three different ways to use it as a signal to enter into a short-term (“swing”) trade on SPY. The duration is anywhere between one and twelve days, depending on the system being used, the exit etc.

My problem was this: the systems all trade SPY. Two use mean reversion (one long, the other short), and the third uses long momentum. The systems overlap! How do I determine which systems to trade?

If you are using multiple trading triggers or systems on the same instrument, it’s really important to know how these systems will work together. Is it better to use just one system and discard the others, or should you use all of them and divide up your resources (if necessary) between the systems?

How do you go about comparing these systems in a meaningful way? Here’s what I did.

Referencing the lead image, trade #1 is a mean-reversion long position. It entered at the open of June 8th, 2007, and exited at the close of June 12th for a win. System #2, the long momentum system, entered at the close of June 12th, and exited at the close June 24th for a win. System #3, which is a shorting mean-reversion system, entered at the close of June 16th, and exited at the close of June 18th. Again, for a win. Obviously I’m going to pick a scenario that shows me winning!

From the chart, we can see these systems have the potential for overlap, but don’t work in the same way. We need to compare them individually against each other, and also see how they work together.

First, we need some data! Preferably with some pretty graphs. I don’t know about you, but I feel wealthier just looking at a positive equity graph.

I exported my backtest daily equity data from the three systems and imported it into Google Sheets. With a hypothetical account of $30,000 and a fee of $0.02 per trade, I graph four strings of data: the three systems each using the entire account independently, and the systems combined, each using 1/3 of the account.

(click to enlarge)

The long MR system is clearly more profitable than the rest. It also trades much more frequently. Using all three systems with 1/3 of the account allotted to each – the green line – is less profitable than just sticking with the one system.

End of the story? Of course not.

Let’s look at our risk. These systems will not all have the same risk profile. If one is less risky than the other, we could conceivably allot more cash to the system, or use leverage.

 system: long momo short combined leveraged combined
time in market 36.62% 20.59% 10.24% 58.19% 58.19%
tot return 87.39% 23.37% 27.07% 44.21% 164.88%
ann. return 238.63% 113.51% 264.44% 75.97% 283%
Max Drawdown -8.06% -5.76% -3.14% -2.98% -7.96%
AR/MaxDD 29.59 19.69 84.08 25.53 35.60

The table above shows some performance metrics. I’ll discuss that “leveraged column” in a moment.

I’ve calculated the percentage of time each system is in the market, as well as for the combined systems. The long-MR system is trading most frequently, which makes sense when we look at our equity graph. The “ann. return” is the annualized return. I’ve taken the total return percentage and divided by percentage of time in the market. This allows us to compare systems more easily, if we have to decide to chop one of them.

The “maximum drawdown” row is the one I find interesting. Yes, the long-MR system makes the most money and trades the most often, but it also has the worst drawdown of the three systems. Meanwhile, the combination of three systems shows the best maximum drawdown value. Because the systems are only partially correlated, one system can be a winner while another is a loser. Success from one system during under-performance of another helps reduces volatility for the equity curve.

The MaxDD of the combined system is much less than the Long-MR system. Approximately 2.7 times less in fact. If we had been willing to allocate $30,000 to our long-MR system and experience a MaxDD of -8.06%, then we could trade 2.7 times as much using the combined system. We’d make 2.7 times the profit, and┬ástill experience roughly that MaxDD of the long-MR system.

That’s where that leveraged column comes in. If we uses 2.7x leverage, our risk (MaxDD) is about the same, but our profit is substantially larger. We don’t even have to use real leverage. I would feel pretty good about using a 2x or 3x leveraged ETF with the same account size, allocating a third of the account to each system.

The leveraged combined systems (red) and the long-MR system (blue).

(click to enlarge)

There’s one more thing we need to think about though. What if these systems are highly correlated? What if they overlap each other most of them time? If they are, we would essentially be throwing two buckets of money at the market instead of one, which doubles our risk. We need to look at the overlaps. Perhaps one system overlaps the other so much that we could just dump it. I will discuss that in more detail in the next post.

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