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Titanomachia aka the battle of momentum models: In the end it’s all about exposures

29 October 2020

GAM Systematic’s Dr Daniele Lamponi says experience and attention to detail are crucial in successfully harvesting alternative risk premia, and models must adapt to changing market conditions.

  • Successfully harvesting alternative risk premia (ARP) requires a thoughtful understanding of risk and performance drivers.
  • In order to continue extracting ARP efficiently, models need to adapt to changing market conditions: however, we believe it is not a Clash of the Titans, where new models replace old ones, but an evolution.
  • Cross-sectional and trend-following momentum models exhibit meaningfully different exposures which we can explore with statistical risk factors. Understanding these may allow managers to enhance ARP portfolios through intentional design choices in portfolio construction.

The new against the old. The Clash of the Titans (Titanomachia) represents one of the greatest moments in ancient mythology, where new deities, the Olympians, fight old deities, the Titans. Jumping to the modern day and models for investing in global capital markets: are momentum cross-sectional models fighting trend-following models1? We think the battle is misplaced, and it is not about new and old, but more about something else: exposures. And as in the Titanomachia some Titans might finally decide to join the Olympians.

As we have argued many times, the process of successfully harvesting single risk premia requires experience and continuous attention to detail; there is no exception for momentum models. In fact while it might appear easy to employ some generic momentum models to extract risk premia from multiple markets, it is much more complex to decide which contracts one should consider and how one should weight and integrate them into an actual strategy. The complexity arises because of the multiple choices one has to face while designing and implementing an algorithm, concerning for instance data, investable universes, signals and portfolio construction methodologies. As discussed previously2 the result of the variety in these choices is dispersion in the outcome (ie in performance).

Momentum is a well-known and robust investment strategy, with an impressive out of sample track record. It can be measured by a multitude of indicators, in its simplest form as the total return over one year and thus ranking past winners and past losers. It has been known for a long time, mainly implemented in the single name equity market as cross-sectional strategy (eg [Chan1996] and [Jegadeesh1993]), and in the last few decades by Systematic CTA managers in its trend following (or time series) format ([Hurst2013] and [Moskowitz2012]). In cross-sectional models momentum scores are ordered, for example high to low, and the strategy is long the top securities and short the bottom securities. The strategy therefore has a resulting zero net notional exposure. In trend-following models the strategy is long (short) securities with respectively positive (negative) momentum. In this case the net exposure varies through time and might be positive as well as negative. Exhibit 1 compares basic algorithms for the two methodologies.

EXHIBIT 1. Schematic summary of time series and cross-sectional methodologies. 
Panel A. The Time series methodology generates long / short positions according to the sign of the trend (momentum indicator). 

 

Panel B. The Cross-sectional methodology generates long / short positions according to the sign of the trend (momentum indicator): securities are ranked and the signal is generated by subtracting the rank median.

Source: GAM. For illustrative purposes only.

This categorisation of momentum strategies in cross sectional and trend following is often used by practitioners in order to compare methodologies and investment strategies. And this is in fact one of the multiple choices the developer of systematic momentum strategies has to face.

However, while this may constitute two different ways of implementing a momentum strategy, what is more important is the specific exposures the strategy is taking. A categorisation cannot replace a sound understanding of the exposures the algorithm is generating through time, and these are driven by multiple choices, in particular the investable universe (ie the set of securities one is investing in) and the portfolio construction methodology (ie how signals are used and contracts weighted). The analysis and understanding of return drivers and portfolio characteristics is of paramount importance, and this is where analytical skills and experience make the difference. This is true for both investment managers and allocators. The first rely on a back test whose main scope is the study and analysis of past exposures and risks. The latter’s job is to perform a careful due diligence, diving into the details of the algorithm and its exposures. Both tasks require a specific knowhow and skillset. As an example, for illustrative purposes, here we consider two momentum strategies in the bond market: the first uses a trend-following approach while the second uses a cross-sectional approach. The investable universe is constituted by long-term bonds in developed markets (Exhibit 2). The signal is simply the total return over 12 months.

EXHIBIT 2. The investable universe, composed by interest rate future contracts on developed market government bonds with an approximate term of 10 years.

Source: Bloomberg, GAM.

The backtests of the two strategies are reported in Exhibit 3 and show that both strategies generated positive returns over the last 20 years. In this setup the trend-following strategy outperformed the cross-sectional one.

EXHIBIT 3. Backtested performance of trend-following and cross-sectional momentum strategies from 2000-2019 (returns and volatilities are annualised).

Total Return Indices

Source: GAM. Data from 31 December 1999 to 31 October 2019. Past performance is not an indicator of future performance and current or future trends.

However, these equity lines are of little use3 as, at the risk of being repetitive, past performance is not a good indicator of future performance. Our purpose is to understand performance and risk drivers. Why has the strategy performed and when? To answer this question we focus here on a particular methodology based on statistical risk factors. These are data-driven risk factors explaining the returns of the investable universe ([Lamponi2020] and [Meucci2009]). Although not all of the statistical risk factors have an economic interpretation, some of them might be easily interpreted. For example, should we identify a statistical risk factor with all weights positive we could interpret this as the asset class risk premium (in this case, interest rate / duration risk). This is, for instance, the case for the first statistical risk factor, which is the one explaining most of the variability of returns in the dataset. Again we can identify the third statistical factor as spread North America versus Europe as it is long US and Canadian bonds and short German and British ones, with very small positions in the other contracts.

Exhibit 4 presents the investment strategy risk contributions over the backtested period arising from exposure to statistical risk factors. It points out a remarkable difference between the two methodologies; while the trend-following strategy risk and performance have been driven by the dynamic exposure to the first statistical risk factor (Panel A), the cross-sectional strategy risk and performance have been more diversified, at least in a statistical sense (Panel B). The strategies have thus generated performance in a very different way. Exhibit 4 shows that the main driver of risk and performance of this simplistic trend-following strategy has been dynamic exposure to interest rates, while the cross-sectional strategy has relied principally on the dynamic exposure to the spread North America versus Europe. All exposures are dynamic in the sense that the strategy can be long or short at times, adjusting to different market conditions.

EXHIBIT 4. Comparison of trend-following and cross-sectional risk and performance drivers. Six data-driven statistical risk factors are used.

Panel A. Percentage risk and performance contribution for the trend-following strategy.

Panel B. Percentage risk and performance contribution for the cross-sectional momentum strategy.

Source: GAM. For illustrative purposes only.

But differences in investable universes or alternative and / or more involved portfolio construction methodologies might also have a large impact. For example the introduction of different tenors in the investable universe, such as the US 2 and 5-year treasuries or the euro Schatz4 and Bobl5, allows other risk drivers to emerge, such as duration risk, to which the strategy might dynamically allocate. Again, adding constraints during the portfolio construction can change the loads on risk and return drivers. For example, we consider here the impact of constraints on security weights on the aforementioned trend-following strategy. As an example, we have simulated the case where a hypothetical investor would like to have a more balanced East-West portfolio. In order to achieve its scope she doubles the allocation of Australian and Japanese contracts. Exhibit 5 shows that during the considered period such a portfolio would have been more diversified and relied less on the dynamic exposure to the asset class risk premium to generate risk and performance.

EXHIBIT 5. Percentage risk and performance contribution of the trend-following strategy once additional hypothetical constraints are added to the investable universe. Six data-driven statistical risk factors are used.

Source: GAM. Past performance is not an indicator of future performance and current or future trends.

Constraints on weights can finally lead to different risk exposure, reducing the utility of the classification of trend-following versus cross-sectional models.

So, Titans against Olympians? It is not a matter of definition but the exposure one wants to achieve. In the end, it is the attentive and thoughtful analysis of return drivers, backed by long term experience, which leads to the efficient harvesting of alternative risk premia.

1Historically trend following models have been predominantly used in a macro framework by CTA while cross-sectional models have been used in the single equity space.
2D. Lamponi and A. Schorr. ARP: There is no such a thing as generic algorithms. GAM Insights 2019.
3Equity lines can give very useful hints and indications of return and risk drivers; however the return they represent per se is of limited value.
4Interest rate futures contract on a notional German government note with a remaining term comprised between 1.75 and 2.25 years.
5Interest rate futures contract on a notional medium-term German government bond with a remaining term comprised between 4.5 and 5.5 years.

Bibliography

Chan, L. K., N. Jegadeesh, and J. Lakonishok (1996). Momentum Strategies. The Journal of Finance, vol. 51 (5), pp. 1681-1713.

Hurst, B., Y. H. Ooi, and L. H. Pedersen (2013). Demystifying Managed Futures. Journal of Investment Management, vol. 11 (3), pp. 42-58.

Jegadeesh, N. and Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal of Finance, vol. 48 (1), pp. 65–91.

Lamponi, D. (2020). Trend following vs cross-sectional momentum: a data driven statistical factor comparison. The Journal of Investing, vol. 29 (6), pp. 61-74 .

Meucci, A. (2009). Managing Diversification. Risk, vol. 22 (5), pp. 74-79.

Moskowitz, T. J., Y. H. Ooi, and L. H. Pedersen (2012). Time series momentum. Journal of Financial Economics, vol. 104 (2), pp. 228–250.

Important legal information
The information in this document is given for information purposes only and does not qualify as investment advice. The mentioned financial instruments are provided for illustrative purposes only and shall not be considered as a direct offering, investment recommendation or investment advice. Opinions and assessments contained in this document may change and reflect the point of view of GAM in the current economic environment. No liability shall be accepted for the accuracy and completeness of the information. Past performance is no indicator for the current or future development.