The Holy Grail is uncorrelated systems
One good system is a start. Several good systems that do not lose at the same time are something else. Why correlation matters more than the number of systems, why it is harder to get than it looks, and why it fails exactly when you need it.
By Baris Demirci · · Rev00
The idea
Ray Dalio calls it the Holy Grail of investing (Principles, 2017). Hold fifteen to twenty good sources of results that are not correlated with each other, and the risk of the whole falls far below the risk of any one of them, while the average result stays about the same.
For a systematic trader, the sources are systems. One good system is a start. Several good systems that do not lose at the same time are a different thing altogether. The losing stretches of one are partly filled by the others, so the combined account falls less far and recovers sooner.
Why it works
Every system has losing stretches. What matters for the account is whether they arrive together. That is what correlation measures: how closely two systems’ results move with each other, from +1 (always together) through 0 (unrelated) to −1 (always opposite).
The arithmetic is simple enough to draw. Take a number of equally good systems with the same level of risk, give each the same share of the account, and assume every pair has the same correlation. The risk of the mix then depends on just two things: how many systems there are, and how correlated they are.
Two things stand out:
- With uncorrelated systems, risk keeps falling. Ten of them carry about a third of the risk of one. Twenty carry about a fifth.
- With correlated systems, it stops falling early. At a correlation of 0.6, the mix never gets much below four fifths of the risk of a single system, however many you add. Past a handful of systems, adding more of the same does almost nothing.
Correlation matters more than the count. Five genuinely different systems do more than twenty variations of one idea.
Uncorrelated is harder than it looks
Most systems that look different share the same bet underneath. A stock momentum system, a sector rotation, an index trend filter and a stock reversion system all hold US stocks most of the time. When US stocks fall hard, they all lose together. That is one bet with four names.
Real differences come from a few places:
- Market. Stocks, bonds, commodities and currencies are driven by different things.
- Approach. Trend following, mean reversion and other families suit different conditions: one does well in long moves, another in choppy ones.
- Timeframe. A system that holds for one night and one that holds for months react to different things.
- Direction. A system that can stand aside, or go short, behaves differently from one that is always long.
It fails when you need it most
Correlation is not fixed. In calm markets, many systems look unrelated. In a crash, they often start moving together, because everyone is selling the same things at once. That happened in 2008 and again in March 2020. The protection of a diversified mix is weakest exactly on the days it is meant for.
So measure correlation in the bad times as well as on average:
- Look at the worst months of each system and check whether they line up with the worst months of the others.
- Use rolling correlation, over a year or two at a time, and see how far it moves.
- Check what each system holds on the worst days, not only its results.
What it costs
- Each system has to be good on its own. An unrelated system that loses money still loses money. Diversification spreads risk. It does not create results that are not there.
- More to run. Every system needs its data, its orders and its checks. Five systems are five daily routines, not one.
- More to watch lagging. A mix will always trail its best component in any given year. Watching that, and not abandoning the mix for whatever did best last year, is the hard part.
The short version
The Holy Grail is not one perfect system. It is several good systems that do not lose at the same time. Correlation matters more than the number of systems, real differences come from market, approach, timeframe and direction, and correlations rise in a crisis. Measure them in the bad times, not just on average. The Combinator on the systems page shows how our published systems combine, and how closely they move together.
Written for people building their own systematic portfolio management process. Nothing here is a recommendation to buy or sell anything. See the disclaimer.