There is a simple method of approximating trend follower positioning in real-time and without lag. It is based on normalized returns in liquid futures markets over plausible lookback windows, under consideration of a leverage constraint, and uses estimated assets under management as a scale factor. For optimization and out-of-sample analysis, the approach can be enhanced by sequential estimation of some key parameters, such as the momentum lookback, the normalized momentum cap and the lookback for realized volatility calculation. Trend follower positions are an important factor of endogenous market risk due to the size of assets under management in dedicated funds and the informal use of trend rules across many trading accounts.

Kestner, Lars, (2020), “Replicating CTA Positioning: An Improved Method”.

The below are mostly quotes from the above paper. Cursive text and text in brackets have been added for clarity and to interpret the research findings for the purpose of trend following.

The post ties up with this site’s summary on endogenous market risk.

### A brief reminder of trend-following basics

“Trend following has existed for a very long time…The most basic trend-following strategy is…going long markets with recent positive returns and shorting those with recent negative returns…In each decade since 1880, time series momentum has delivered positive average returns with low correlations to traditional asset classes…[and] has performed well in 8 out of 10 of the largest crisis periods over the century…Time series momentum has been profitable on average since 1985 for nearly all equity index futures, fixed income futures, commodity futures, and currency forwards.”[Hurst, Ooi, and Pedersen]

*A post on the basics of trend following can be found here.*

“Trend following strategies gained interest in recent decades as a noncorrelated diversifier to more economically-sensitive asset classes. Performance of trend following CTAs [commodity trading advisors, typically hedge funds that focus on derivatives contracts] during the financial crisis of 2008 was strong, resulting in __growth of assets under management__. As assets have grown, the trading sizes of these managers has become larger relative to the total market. This __has led to market analysts attempting to forecast the aggregate size of positions and also the potential changes __in their positions.” [Kestner]

*Assets under management of trend-following hedge funds have peaked around USD340bn in the 2010s and have been estimated at USD280bn for 2020. The actual amount of assets managed by trend following strategies across all types of institutional investors, including discretionary traders that use trend following tools, is almost certainly much higher.*

“We show that __Managed Futures, Global Macro and Fund of Hedge Funds strategies can be partly explained by a…volatility-adjusted time-series momentum signal__…exposure. Moreover, [this] exposure is a significant determinant of hedge funds returns at the fund level, for Managed Futures and Global Macro but also, and more surprisingly, for the other styles.” [Chevalier and Darolles]

### How to replicate trend-following strategies

“Performance explanation and attribution… of systematic strategies… is an important task as investors attempt to understand an asset or portfolio’s behavior [and] the impact these strategies have on various financial markets. Risk parity, option overwriting, volatility targeted equity indices, and trend following strategies gain the majority of this attention…__We focus on the dynamic trading of trend following strategies and detail an improved method for estimating their actions across markets__…A simple replication model employed on 16 futures markets explains over 75% of the variation in a trend following benchmark…__we can use our replication model to estimate positions by specific market and the expected trading flows when individual markets move__.” [Kestner]

“Analysts usually resort to factor-based techniques where portfolio returns are regressed on known investment returns from broad asset benchmark returns and intra-asset class strategies, using statistical techniques to minimize fitting errors. This analysis is ripe for misattribution as portfolios can change instantaneously while the estimation techniques need additional data to determine these changes.” [Kestner]

“We present __a replication model that explains the majority of variability in a trend following CTA benchmark__… For our benchmark, we use the SG Trend Index, a sub-index of the SG CTA Index that aggregates the performance of managers trading trend following strategies… We limit our trading to 16 of the most liquid futures markets originating from four market classes. The model will trade equity, interest rate, foreign exchange, and commodity futures. The number of markets and sectors in our replication model is much smaller than a typical diversified trend follower would trade.

- We begin by
__calculating the average weekly return over a set lookback window__. Trading positions will be larger when the momentum intensity is higher. - Next,
__we normalize average returns by a measure of realized return volatility and multiply by the square root of the number of weeks in the lookback window__. This result is the relative position size for a market on any given week. The volatility normalization creates a like-for-like ability to compare returns of low volatility markets such as government bonds with higher volatility markets such as crude oil, while the window scaling normalizes the results of varying the lookbacks. - We also cap these exposures at defined thresholds to avoid situations where most of the portfolio’s variance is created in just a few outlier market moves.” [Kestner]

“__We investigate the robustness of our replication model by varying three parameters: the momentum lookback, the point where we cap the maximum signal (the normalized momentum cap), and the lookback for the realized volatility calculation__… The chart below graphs all 125 parameter combinations sorted from lowest R2 to highest R2. The two jumps in the graph can be described generally as where the momentum lookback shifts from 4 weeks to 8 weeks and then from 8 weeks to 16 weeks… We find that the benchmark is best approximated by momentum lookbacks around 32 weeks, normalized momentum caps around 1.0, and volatility lookbacks of 90 days. __Changing momentum lookbacks has the largest sensitivity to replication success__.” [Kestner]

“__We use an ensemble method to improve fit further__. __While the returns of trend following CTAs are correlated, the strategies these managers utilize will vary across trend speeds__. Combining a range of parameters in our replication model improves our results by better matching how the actual managers trade – across trend speeds. When we average the performance of our 3 models (momentum lookbacks of 16, 32, and 52 weeks; normalized momentum cap of 1.0; volatility lookback of 90 days) the R2 to the benchmark climbs above 75%. Expressed graphically, we see the tight relationship between the replication model and the benchmark on both time series and return scatter graphs.” [Kestner]

### How to estimate positioning

“Trend followers buy on market strength and short on market weakness, with algorithms determining when to trade…__Because we…generally understand the investment process of trend followers, we can estimate their positions more accurately in real-time and without lag__.” [Kestner]

“[Having] identified a model to replicate trend following CTA returns, we can estimate the risk exposures that trend following managers have to each of our 16 markets…Below is the percentage exposure per $1 notional allocated to the benchmark aggregated by sector [for the 2015-2019 period]. That is, a +100% exposure to equities would approximate a $1 long position per dollar invested in the benchmark (or managers comprising the benchmark).” [Kestner]

“If we [use the assets] under management [by CTAs related to] the SG Trend Index, we can utilize the output of our replication model and estimate the position sizes by market traded. The chart below estimates the total dollar size in longs or shorts to each of the four equity markets.” [Kestner]

### Quoted additional sources

Chevalier, Charles and Serge Darolles 2019), “Trends everywhere? The case of hedge fund styles”. Journal of Asset Management 20, 442–468 (2019). https://doi.org/10.1057/s41260-019-00141-5

Hurst, Brian, Yao Hua Ooi, and Lasse Heje Pedersen (2017), “A Century of Evidence on Trend-Following Investing” https://ssrn.com/abstract=2993026 or http://dx.doi.org/10.2139/ssrn.2993026