Managed futures strategies use quantitative models to invest in price trends. These strategies seek to capitalize on the well-supported observation that security prices follow trends that stem from behavioral biases among investors. Put simply, trend-following strategies systematically buy securities that have been increasing in price and sell securities that have been falling in price. The ability of this approach, also known as momentum investing, to deliver returns for investors has been established over decades of academic research.
However, for a strategy based on widely understood theory and public data, manager approaches can vary considerably, resulting in dissimilar outcomes depending on their choices in strategy design. This paper focuses on one of those choices: How many securities should a managed futures portfolio hold?
As a managed futures investor, we seek to generate long-term positive returns, diversify investor portfolios through low correlations to traditional asset classes and deliver strong positive performance during long-term bear markets. One of the trade-offs we face is the potential marginal benefits of expanding our strategy to include more securities versus the potential marginal costs of using less-liquid securities.
Indeed, the PIMCO TRENDS Managed Futures Strategy seeks to provide a diversified source of return to client portfolios. It uses a carefully controlled opportunity set that seeks to minimize transaction costs and maximize diversification potential.
Investment universe
The depth and breadth of the investment universe are critical elements in building a robust managed futures strategy. On this topic, we discuss a key question investors must answer: Does incremental diversification by trading an additional asset outweigh the incremental transaction costs?
There are clear benefits to combining imperfectly correlated assets in a diversified portfolio. But those benefits do not extend equally to every new security. For example, if 25 similar investments with 0.75 correlations with one another (think 25 different equity markets) were pooled in a portfolio, the diversification benefit would quickly diminish as more securities were added beyond the first few assets (see Figure 1). The third asset matters much more than the 25th.
If we extend this to 50 assets, where the next 25 also have 0.75 correlations with one another but a lower correlation – 0.25 in this example – with the first 25 (a proxy for adding an additional asset class), then again there is a clear initial benefit with declining marginal contribution (see Figure 2).
This analysis illustrates two critical points: An investor should add assets to the portfolio that exhibit low correlations to existing assets, and, if the trading costs are relatively higher, the bar for diversification must be higher as well. To make these concepts more concrete, we look at two asset classes common to trend-following programs: commodities and equities.
In commodities, global benchmark contracts trade with significantly higher volumes than more specialized contracts. For example, average volumes for West Texas Intermediate crude oil are about 30 to 40 times greater than for lean hogs (see Figure 3). The two contracts have very different fundamental drivers and low historical correlations, and thus there is diversification when trading both markets (see Figure 4).
However, a trend-following investor trying to trade $100 million of lean hogs will pay a much higher transaction cost than one trading $100 million of oil. In practice, if a large fund tried to trade hogs in the same volume that it traded oil, transaction costs would swamp the diversification benefits. To control for this, most managers will put a cap on the size of a position they can have in smaller markets.
This is a sensible way to manage the trade-off between diversification and transaction costs. Yet it means that looking only at the number of markets in which a manager trades is misleading without knowing how big a share of their portfolio these smaller markets can be. If the position of lean hogs can be only a fraction of the size of the oil position, then its portfolio impact will be small. In practice, the assets under management (AUM) of a manager’s trend-following strategy can be a more important driver of risk-adjusted returns than the number of markets.
Next, let’s look at equities. S&P 500 futures trade with a daily dollar volume of roughly $150 billion. That is more than 10 times greater than the volume of Dow Jones Industrial Average (DJIA) futures contracts, which is roughly $10 billion (see Figure 5). The two contracts are highly correlated, at 0.97 using daily returns (see Figure 6), indicating that the addition of DJIA futures to a trend-following program is unlikely to add any diversification value. It is likely to add cost, however, particularly during times of market turbulence and reduced liquidity.
Number of trades matters more than number of markets
With the PIMCO TRENDS Managed Futures Strategy, we seek to strike the right balance between the number of markets, the maximum size of each market and the frequency with which we can trade in each of those markets. One way to quantify this approach is to look at the effective number of uncorrelated trades in the portfolio. As an example, suppose you traded a certain number (N) of assets. If they were perfectly correlated, that portfolio would have 1 uncorrelated trade. And conversely, a portfolio of perfectly uncorrelated and equally sized trades would have N uncorrelated trades. The practical reality is that the number of trades in a portfolio is somewhere between 1 and N, depending upon the correlations and volatilities of the various markets and the relative position sizes in the portfolio.^{1}
For the earlier example of 25 assets with 0.75 correlation, and then another 25 assets also with 0.75 correlation to one another and 0.25 correlation with the first 25 assets, the effective number of uncorrelated trades is 1.7. In other words, even though there are 50 assets in the portfolio, from a risk and diversification perspective, it’s equivalent to having 1.7 uncorrelated trades of similar size. For an intuitive understanding, imagine the assets within each group are pretty highly correlated, so each group of 25 assets is essentially just 1 trade. If the two groups were uncorrelated, we would expect effectively 2 trades. But given that the two different groups had a low correlation of 0.25, the number of effective uncorrelated trades is slightly lower.
Size matters
The pursuit of uncorrelated trades can lead managers to less-liquid securities. In fact, the “discovery” of positive expected returns from trend-following can be a tempting source of evidence of diversification potential in the marketing of trend-following strategies. But as portfolios grow in terms of assets, the potential contributions to expected returns and diversification from securities that are lightly traded diminish.
Figure 7 shows an example of how size constraints can affect a portfolio of common listed global rates, equities and commodities futures. We have estimated the natural maximum position for three different sized portfolios trading a given security in a simple hypothetical trend-following model running at 10% volatility to be 1% standalone volatility contribution (maximum size = 1%/volatility). Of course, lower-volatility assets would have larger maximum sizes, thus contributing portfolio risk similar to the higher-volatility assets.
Across each portfolio, we calculate the fraction of total open interest across the entire futures curve that the 1% position would represent. We then calculate the number of trading days required to exit a 1% position, assuming trades are limited to 10% of daily average volume. Reading the table from left to right, the portfolio is relatively unencumbered by size at $1 billion but could encounter significant challenges in some of the smaller securities as AUM grows. At one extreme, this analysis suggests that it would take 51 days for a $25 billion portfolio to unwind a 5% position in white sugar, assuming that the portfolio was active across the entire futures curve, and those trades would constitute 58% of open interest.
This reality doesn’t prohibit large managers from using smaller markets, but it implies that large portfolios are likely constrained in how they use them.
Our approach
Trend-following seeks to produce positive returns that are uncorrelated with equities and bonds by capitalizing on investors’ behavioral biases. Given we are taking advantage of small, systematic biases, the probability of being right on any one position is not that high. This means the potential key to success in such a strategy is having as many different positions as possible. However, certain positions are not very well captured by markets. A position in DJIA futures is not additive to a portfolio that already trades S&P futures. When we look at building our portfolio and adding new markets, we are seeking to maximize the number of uncorrelated positions as opposed to just the number of markets.
As we implement this framework in the PIMCO TRENDS Managed Futures Strategy, we leverage the company’s existing execution infrastructure. Our dozens of dedicated traders have access to both algorithmic and more direct execution options across developed and emerging markets rates, currencies, commodities, credit and equities.
^{1} The actual definition of the number of uncorrelated trades is technical and requires more space than we have here to explain fully, but can be understood by thinking of the principal components of the portfolio covariance matrix. This allows one to identify the truly independent parts of the portfolio and quantify their significance. For instance, when a small number of principal components have a large degree of explanatory power, the effective number of uncorrelated trades will be low.