The year 2014 has been proclaimed the return of trend. As divergence spread across financial markets, commodity trading advisors (CTAs) were poised to capture momentum’s rewards. Despite this, the range in performance across CTAs was remarkable. Performance ranged from less than 0% to over 100%. Because most large trend-following managers maintain a high correlation with each other, investors are left wondering why managers they perceived as similar could perform so drastically differently in such an important moment for the strategy. This article returns to the basic tenets of portfolio theory for equity portfolios to examine the origin of return dispersion and cross-manager correlation for CTAs. Similar to how idiosyncratic risks in stocks are reduced by diversification in equity portfolios, the idiosyncratic differences in signal construction, parameter selection, and risk management are reduced by diversification in CTA portfolios. A closer look at performance and return dispersion demonstrates that CTA strategies have more return dispersion on the upside. Despite the high inter-manager correlation in the CTA space, during moments when there are opportunities in momentum, subtle differences in CTA strategy construction seem to matter. This explains why correlation to momentum is easy to replicate, while replicating performance in momentum remains somewhat more elusive. CTA diversification is best demonstrated on the upside.

**Idiosyncratic systematic: portfolio theory revisited**

Behavioural psychologists, sociologists, ecologists, and evolutionary biologists all understand the diversification heuristic and our natural interest in variety. Why do we diversify? To increase our chances of survival, as spreading risk allows us to reduce risks. Turning to portfolio theory, there are both idiosyncratic (diversifiable, those we are not paid for taking) and systematic risks (undiversifiable, those we receive a risk premium for taking). Individual stocks can be quite volatile, but as more stocks are added to a portfolio, idiosyncratic risk can be reduced via diversification. The risk which remains is systematic risk. For equities, systematic risk is derived from a common equity “market” factor. This classic relationship is plotted in Fig.1. Due to an exposure to a common equity factor, a diversified basket of stocks should provide a risk premium (i.e., the “equity risk premium”) over time.

If a long-only investment in equities provides a risk premium, how is this premium realised and how difficult is it to capture? Is there substantial variation (return dispersion)? Consider an equity universe of 1000 liquid US stocks. Fig.2 plots return dispersion against the average return from 1980-2014.

Over this time period, there tends to be larger variation in individual stock returns during times when the overall market is either going up or down strongly.Would diversification have been beneficial during the extreme market scenarios? Following the same approach as in Fig.2, the 1000-stock universe can be partitioned into 100 unique portfolios, each with 10 stocks. Fig.3 plots return dispersion for 10-stock portfolios against the average portfolio return. When compared with Fig.2, return dispersion decreases substantially from around 25% to 8%. However, despite the overall decrease in idiosyncratic risk, larger return dispersion still remains for both large positive and negative market movements.

CTAs primarily seek to capture a momentum premium. Just as with equities, the same questions are also relevant. How is the momentum premium realised over time? Is there substantial variation in how it is captured? The earlier analogy with individual stocks can be extended to CTA portfolios. One individual trend-following strategy based on one signal is conceptually similar to one stock. The strategy roughly captures momentum, but it contains substantial idiosyncratic effects due to individual parameter choices. Similar to building portfolios of stocks, CTA portfolios are collections of strategies, largely capturing time-varying momentum.

To examine how these returns are captured over time, return dispersion (or cross-sectional variation in performance across CTA portfolios) can be compared with the average performance. Using monthly returns from managers in the Newedge Trend Index, Fig.4 plots return dispersion (cross-sectional standard deviation) versus the average return from 2000-2014.

CTA portfolios capture returns with substantial variation, and this variation is more pronounced during periods when momentum strategies are performing strongly. Put more simply, key moments for CTA performance are also moments when the range in performance across managers varies the most. Drawing once again from the stock analogy, CTAs can be viewed as being exposed to acommon “momentum” factor. During extreme returns for this factor (especially on the upside), different managers will have different exposures to this factor.[1] Put in another light, when CTAs perform their best they tend to be the most different from one another.

**Counterintuitive correlation**

Correlation is an important measure for understanding portfolio diversification, but it doesn’t always tell the entire story. High inter-strategy correlations in the CTA space are often interpreted as all CTAs being the same. In theory, just as a long-only equity portfolio is a basket of individual stocks, a CTA portfolio is a basket of strategies applied across futures markets to capture momentum premiums. The average correlation across CTA managers is akin to comparing baskets of stocks with other baskets of stocks. Correlation between baskets of stocks increases with the number of stocks in a basket. For demonstrative purposes, Fig.5 plots the cross-portfolio correlation (average pairwise correlation) between stock portfolios of various sizes (one to 500 stocks) from 1980-2014. It is clear from this figure that as the diversification in these portfolios increases, the correlation across portfolios increases in step.

The same conclusions are also true for CTAs. For any basket of CTA strategies (or a CTA portfolio), as more strategies are introduced into a portfolio, the level of diversification and the amount of cross-portfolio correlation should be expected to increase. The relationship between managers can be examined in two ways. The first way is to measure rolling average pairwise correlation. This approach examines the relationships between portfolios over a certain time horizon. Second, the level of return dispersion across managers can be used to estimate implied correlation for each individual month (or the implied point in time estimate of relationships between portfolios).[2]

When return dispersion is high (low), this would imply that managers are less (more) similar to one another. Using the managers in the Newedge Trend Index, Fig.6 plots cross-portfolio correlation (rolling 12-month average pairwise correlation) and implied correlation (point estimates and 12-month smoothed point estimates).[3] The managers in this set are large and highly diversified, and they tend to focus on trend-following strategies. For this set of managers, average pairwise correlation fluctuates around 70% and is time-varying. This measure can indicate a relatively high degree of similarity between CTAs (consistent with 10 or 20-stock portfolios).

Implied correlation tells a markedly different story. The smoothed version of implied correlation is roughly similar to average pairwise correlation, but point estimates for implied correlation demonstrate periods of severe correlation breakdown between CTAs. This observation suggests that most of the time these managers are similar, but during certain moments appear to be drastically different. In a world focused on month-to-month performance, the actual investor experience may be better represented by the purple line (monthly implied correlation) as opposed to red or blue lines (rolling pairwise correlation and smoothed implied correlation). Fig.7 plots the conditional performance for seven CTA managers during extreme correlation breakdowns (negative implied correlation) and in normal times (positive implied correlation). Subtle differences in CTA strategy construction have the largest impact during extreme correlation breakdowns.

**Portfolio implications**

Through the efficient use of index products, most equity investors can select portfolios roughly the same size as the S&P500. A 500-stock portfolio has cross-correlation with other 500-stock portfolios greater than 99%. Even a 100-stock portfolio has cross-correlation with other 100-stock portfolios at roughly 95%. If CTA managers have an average cross-manager correlation of 70% under some simple assumptions, roughly seven to eight CTA managers would be required to create a portfolio with the same level of diversification as an equity index.[4] There are currently 10 managers in the Newedge Trend index. The 70% cross-correlation between managers in the CTA space is often interpreted as a high level of similarity between managers. This correlation measure may cause investors to under-diversify, something which will be more noticeable during months with large positive returns. When performance is very high, return dispersion tends to be high for CTAs. This implies a breakdown in correlation between managers.[5]

Intuitively this suggests that under normal scenarios with moderate opportunities for CTAs, subtle differences in system construction, parameter selection, and risk management seem to be less important. A closer look at implied correlation (as seen in Fig.6) demonstrates that when there are opportunities for momentum strategies, the subtle differences between systems seem to become important. This leads naturally to two follow-up questions: which managers perform the best during these periods? And is this predictable? Considering the same universe of CTAs, Fig.8 plots the risk-adjusted performance of these seven CTAs during the periods where CTA correlation seems to break down.[6] Despite being similar in aggregate pairwise correlation, performance across these highly correlated CTAs is markedly dissimilar during these moments. This figure demonstrates why understanding CTA correlation may be somewhat counterintuitive. High pairwise correlations may underestimate the importance of diversification in CTA portfolios, leaving portfolios undiversified in critical moments for performance.

**Summary and conclusions**

Using classic parallels to portfolio theory for stock portfolios, this article examines return dispersion and cross-manager correlation for CTA strategies. There are two main conclusions of this study. First, consistent with results for stock portfolios, diversification has clear benefits in the CTA space. Better diversification improves the capture of return premiums for CTA strategies. Second, cross-manager correlation in the CTA space may be high, but this correlation seems to be weaker when there are opportunities for momentum. This suggests that CTA diversification may be best demonstrated on the upside.

**Kathryn Kaminski**, PhD, CAIA, currently holds the position of director, investment strategies at Campbell & Company. She recently co-authored the book Trend Following with Managed Futures: The Search for Crisis Alpha published by Wiley Trading in 2014. She has been a senior lecturer at MIT Sloan, affiliated faculty at SSE, and visiting professor at the Swedish Royal Institute of Technology (KTH). Dr Kaminski’s work has been published in a range of industry publications as well as academic journals. She holds a BS in electrical engineering from MIT (2001) and a PhD in operations research from MIT Sloan (2007). She also holds the CAIA designation as a 100 Women in Hedge Funds PAAMCO CAIA Scholar and she serves on the CAIA Curriculum Committee focusing on hedge funds and managed futures.

**Footnotes**

1. Greyserman, Kaminski, Lo and Yan (2013) derive a style framework for comparing trend following CTAs including a baseline strategy, market size factor, equity bias factor, and trading speed factor.

2. To estimate implied correlation, all portfolios must be assumed to have the same Sharpe ratio.

3. The implied correlation estimates are implied by the cross-sectional standard deviation across managers in the Newedge Trend Index. For this figure, seven large CTAs were used due to data availability.

4. For a portfolio with N assets with stable correlation (ρ), the porfolio correlation (Ρρ) for an equal volatility weighted portfolio is

Ρρ = ρN / (ρ(N – 1) +1). For the average large CTA is ρ = 0.7, to get a portfolio with a cross correlation of 0.95, N must be roughly 7-8 CTAs.

5. Similar to equity portfolios, differences in manager performance could be explained by difference beta exposures to momentum and other factors.

6. Seven CTAs are used due to their return series spanning the entire time horizon.

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## Commentary

## Issue 103

## Return Dispersion, Counterintuitive Correlation

## The role of diversification in CTA portfolios

## KATHRYN KAMINSKI, PHD, CAIA, CAMPBELL AND COMPANY

## Originally published in the April 2015 issue