Bill Rempel, a.k.a. NO DooDahs!

Low de-trended correlation of equity curves isn’t the be-all, end-all of system combination. It’s important, yes, but it’s just one thing that needs to be considered. The primary thing that needs to be considered is the return profiles of the systems that are under consideration for combination.

I last discussed this issue in Benefits of Diversification, and there are internal links in that article to other discussions, all of which are worth following.

Let’s assume that I have three systems tested, two of which (call them A and B) are rip-offs, er, adaptations, of public domain systems, and one of which (call it C) is something I cobbled together based on some anomalies in publicly available academic research. Here are the correlations of their de-trended monthly-evaluation equity curves:

A to B: +78.3%
A to C: -39.5%
B to C: -14.6%

On the surface, it seems like Blend(A,C) is an exceptional candidate. However, when I compare Blend(A,C) to Blend(A,B), I find that:

Blend(A,C) [negative correlation] is superior in 10-year Average Gain/Annual Std Deviation of Gain, mainly because the Annual Std Deviation of Gain is very low – significantly below the market (S&P 500) value for the test period. I also find it superior in Sharpe Ratio (at Risk Free = 4.5%). Different risk-free rate hurdles make for different relative evaluations of the two systems (see the Sortino note below).

Drawdown (DD) is merely comparable for the two blends.

Sortino Ratio is dependent on where the Minimum Acceptable Return (MAR) is set – if the MAR is 19.5% annual, then the two blends are equivalent, with lower MARs evaluating Blend(A,C) [negative correlation] as superior, and MARs above 20% evaluating it as inferior.

However, the Blend(A,B) [positive correlation] is superior in Average Gain, CAGR (compounded annual growth rate), Monthly Std Deviation of Gain, and CAGR/DD.

Huh?!?

How could this be!?!

The answer lies in the return profiles of the different systems (A, B, C). C is a good system, but its CAGR is significantly lower (17%) versus that of A (31%) or B (28%).

Diversification of systems with low correlation results in lowered volatility of returns, i.e., the result will be more stable than expected from a simple averaging of the return streams. This also means less degradation of CAGR than one would expect from a simple averaging of returns. However!, this is merely a marginal improvement, and the relationship of the variance to the CAGR gives a “tell” as to how much room for improvement still exists.

When combining systems of drastically different CAGR amounts, the blend will necessarily have a CAGR lower than the max CAGR of any component. So the FIRST step in combining systems, or picking systems to consider combining, is that any candidates for combination should have a CAGR that is relatively close to the CAGR of one’s “best” system.

An Asset Allocation Example

Over the long term, domestic stocks (S&P 500) return around 7-9% annualized on price and 9-11% on total return, ballpark, with an annual standard deviation of returns almost twice that high.

Bonds have had, over the long term, returns in the low-to-mid single digits, depending on the era measured.

Real Estate returns about 6% annualized, long-term, if unlevered.

Commodities are in the same general ballpark if unlevered, i.e. low-to-mid single digit returns.

Because all of these “asset classes” (really different trading strategies) have low correlation in the long term, AND they have comparable CAGR in the long term, a combination of these can actually produce a CAGR that is very close to, or even an improvement on, that of domestic stocks, with LESS VOLATILITY.

Mebane Faber at World Beta, a daily read and RSS of mine, has a “Tactical Asset Allocation” model which uses trend-following techniques on a base of five asset classes. He links to his own SSRN research paper on his blog, but for convenience, here’s another link to it. For purposes of this discussion, the “money shot” is Exhibit 12 on Page 14 of the PDF file – which shows that a passive, buy-and-hold asset allocation can provide approximately the same return as the domestic stock market, with less volatility.

That’s what I’m talking about! Now, if we change our mindset from one that says “buy and hold this asset class” to one that views buying an asset class as just a variety of trading system, then buying and holding multiple asset classes is analogous to blending multiple trading systems.

Please also keep in mind the irony of calling the purchase, inside of a stock brokerage account, of a REIT ETF that trades on the NYSE an “asset allocation to real estate.”

When I test for combinations of trading systems, I am looking for sets of systems that all deliver returns I find acceptably high, but have low enough de-trended correlation that, when I combine them, I get a final product with maximal return and minimal volatility!

Bottom Line

Blending strategies is complicated, and there are a few different moving parts to be considered. However, if done properly, with selections of strategies that have similar CAGR and as low a correlation as possible, it can be very effective in improving risk-adjusted returns.