Strategy vs Asset Diversification

Here’s the proper, albeit math-geeky, way of looking at diversification. Don’t think of it as “holding a variety of asset classes” – instead, think about it as implementing a variety of trading strategies, because trading a different class of asset is really a subset of the idea of trading a different strategy. What we’re after, in order to benefit, is that the strategies have a low correlation.

Strategy Correlation and De-Trending

Of course, all successful trading strategies will have a positive correlation over time. Why? Because they’re all positively correlated with TIME, that’s why! The definition of a successful trading strategy presupposes that the equity in the strategy increases over time!

There are a few folks who will speak of correlations between the de-trended equity curves of various strategies – listen carefully to these people! They have a clue about what they’re doing. Performing a de-trending operation on the equity curves removes the bias of the time element.

Occasionally you’ll hear someone speak of “negatively correlated strategies” – first, determine if they’re speaking about negative correlation in a de-trended strategy. If they are, then listen carefully to these people! They have a clue about what they’re doing. If they aren’t talking about a de-trended comparison, and mention “negatively correlated strategies,” then please, slap them for me.

When looking at correlation over time, we try, given that the strategies are successful ones (thus necessarily positively correlated), to pick strategies that have as low a correlation as possible and combine them. If the data is de-trended, you want to combine strategies with a negative correlation. If the data is not de-trended, then you want to combine strategies with as low a correlation as possible, while recognizing that non-de-trended successful strategies are positively correlated over time.

A Thought Experiment

As a thought experiment, imagine a strategy that returned a straight average of 11% annually with a standard deviation of returns being about 15%. You could expect, over a long period of time (as in a multi-century Monte Carlo simulation), a CAGR (cumulative annualized growth rate) of about 10% from this strategy. In this long-term random simulation, you could expect a maximum equity drawdown (using annual data points only) of about 44%. Sounds a lot like buy, hold, and reinvest dividends on the U.S. stock market, doesn’t it? The reason why I use the stock market as the primary asset class is simple: historically, there is no substitute for exposure to stocks. As a broad asset class, the stock market has returned far more than real estate, commodities, bonds, or cash, over long periods of time. While each other class has some relative advantages, stocks have the relative advantage coming from the highest average annual returns. This is Strategy A - 11% simple annual average with 15% standard deviation of annual returns.

Now imagine three additional strategies, all with a straight average return of 8% annually and 10.9% standard deviation. This is the same ratio of annual return to standard deviation of annual return as Strategy A, and I selected these parameters to isolate the impact of diversification. I specifically selected lower returns because, well, the returns on the other asset classes are lower.

Strategy B has a de-trended correlation of +1.00 to Strategy A, that is, on a de-trended basis, it is going up when A is going up, and down when A is going down.

Strategy C has a de-trended correlation of -1.00 to Strategy A, that is, on a de-trended basis, it is going down when A is going up, and up when A is going down.

Strategy D has a de-trended correlation of 0.00 to Strategy A, that is, on a de-trended basis, it is marching to the beat of its own drummer.

Any 50/50 combination of Strategy A with your choice of B, C, or D will yield about the same average annual return, that is 0.50 * 11% + 0.50 * 8% = 9.5%. Whoopedeedoo.

The real “edge” in combining strategies with low de-trended correlation comes from the reduction in volatility of returns.

Combining a strong strategy like A with a highly-correlated weaker strategy like B reduces the average return and reduces the standard deviation of returns. Since Strategy A and Strategy B both had CAGR/StDev of 0.667, one gets the same CAGR/StDev with Strategy (A+B). If we were to run a Sharpe Ratio at 5% risk-free on Strategy (A+B), we might not be surprised to learn that the blended strategy performs worse than Strategy A does alone, due to the lower return. Max drawdown is slightly improved from Strategy A, however the CAGR/Drawdown ratio is equivalent.

On a risk-adjusted basis, combining strategies with high de-trended correlation makes no sense.

If we combine A with D, a totally non-correlated (on a de-trended basis) strategy that is still weaker (8% versus 11%) than A, we get a better result. We’d now be looking at a CAGR/StDev close to 1.00 and an improved Sharpe Ratio. Drawdown (using annual data points only) is more than cut in half. Note that while the numerical average return isn’t any different for A+D as opposed to A+B, but because of the reduced volatility, we experience a lesser degradation of the CAGR. It’s not a huge difference, but it’s there.

So the combination of a strong strategy with another strategy, even a weaker one, can improve returns on a risk-adjusted basis, provided that the strategies are not highly correlated on a de-trended basis. Less degradation of CAGR relative to average return, less drawdown, less standard deviation, and higher Sharpe Ratio.

If we combine Strategy A with Strategy C, where the de-trended correlation is perfectly negative (note that non-de-trended correlations would be low, but positive, because both strategies return well over time), we get the best possible result. In reality, this is not very likely to happen, finding two profitable strategies with totally negative de-trended correlation, but Hey!, we can dream.

Year-to-year standard deviation drops into the low single-digits. CAGR/StDev goes north of 4.00, and the chances of having a negative calendar year all but vanish. In this extreme example, expect a Sharpe Ratio over 2.0. Booyah!

Benefits of Diverse Strategies

When two strategies are combined, the simple average return of the combination will be the weighted average of the two strategies’ returns. Period.

The standard deviation of the blended strategy will depend on the standard deviations of the two strategies, the amount of de-trended correlation between the strategies, and the weight of the blend.

Combining strategies of different average annual return levels will always result in a blended average return that is lower than the highest average return for any of the components. However, the CAGR is, in itself, a risk-adjusted measure, and if the strategies that are combined have low correlation, the CAGR will not be degraded as much as the blended average annual return is. In extreme examples, perhaps the CAGR is even improved! Remember that CAGR, compared to average return, is a risk-adjusted measure in and of itself.

The main benefit is reduction in volatility of returns. This is why the CAGR doesn’t degrade as much as the annual return, and this is why risk-adjusted measures show improvement. Reduced drawdowns will reduce the “fear factor” that individual investors have, and may keep paying clients from pulling their funds out.

So, for people on Roger’s timeframe, or for people who are looking for performance “throughout the cycle” (whatever that means), adding exposure to alternative asset classes (like commodities) makes sense simply because it reduces volatility, even though it may degrade returns somewhat. After all, the best you can get from cash is a zero de-trended correlation. If one adds a return stream that is similar in magnitude to cash, but has some negative correlation to the current portfolio’s equity curve, then one has an improvement in the blended strategy’s results.

For more active traders that confine themselves to one asset class … consider having some alternative strategies. Perhaps half your equity money in “value investing” strategies and half in CAN-SLIM, or half CAN-SLIM and half Zweig, or half day-trading and half position-trading. Trading the e-mini’s on two or three different timeframes could improve the average risk-adjusted results dramatically.

Something to think about.