Time-Series vs. Cross-Sectional Implementation of Momentum, Value and Carry Strategies
A new related paper has been added to:
#28 – Value and Momentum across Asset Classes
Authors: Baz, Granger, Harvey, Le Roux, Rattray
Title: Dissecting Investment Strategies in the Cross Section and Time Series
We contrast the time-series and cross-sectional performance of three popular investment strategies: carry, momentum and value. While considerable research has examined the performance of these strategies in either a directional or cross-asset settings, we offer some insights on the market conditions that favor the application of a particular setting.
Notable quotations from the academic research paper:
"In quantitative cash equity strategies, momentum is almost always traded across assets (relative value) whereas in futures trading, momentum is typically applied directionally. Why? Our goal is to better understand the performance of three popular strategies, carry, momentum and value in different implementations: time-series vs. cross-sectional.
We fill this gap by providing an analysis of both the time-series and cross-section using a broad number of asset classes: equity, fixed income, currencies and commodities. We measure the relative performance of directional vs. cross-asset strategies as well as strategies that combine the information in each dimension. We show that these strategies are largely profitable over our sample – and the best performance is when these strategies are combined.
Contrasting Table 1 Panel A and Table 5 Panel A, we have quite different results for the three styles: value works well in the cross-section, poorly in time-series; carry works about equally well in both cross-section and time-series and momentum works well in time-series, but poorly in the cross-section.
At a basic level, assuming linear signals, cross sectional portfolio weights are equal to time series weights minus the cross sectional average. This average can be thought of as a global factor. Therefore, we can think of a cross sectional portfolio as a time series portfolio hedged for the global factor. Pursuing this line of reasoning, time series momentum will outperform cross sectional momentum to the extent that the global factor is trending. Alternatively, to the extent that the value indicator trades reversion to the mean, time series value investing will do better than cross sectional value investing when the global factor returns are negatively autocorrelated.
So how do we interpret the results from our data exploration? As stated above, momentum outperformance seems to go hand in hand with value underperformance in the time series versus the cross section. Although this result is difficult to interpret, we can offer three possible explanations.
The first is that momentum, unlike value, takes the price movements themselves as being informative and, as in such, may be better placed to assimilate any truly novel information about the global factor which may not be captured by the valuation model. In other words, the momentum model may account unwittingly for the factors omitted by the valuation model. This distinction between value and momentum is most prominent in the more correlated asset classes of equities and bonds.
In FX and commodities where a global factor is much less apparent the performance dierences between the cross section and time series is much less. This makes sense, because in moving from time series to cross sectional portfolios we are essentially hedging out a single global factor. If this factor explains less, there will be less to hedge out and less difference between the portfolios (in either direction). This is exactly what we observe. Although this explanation may have merits, it does not help us understand why value performs better than momentum in the cross section.
Another explanation is that major global factors have exhibited very strong trends which have by definition hurt reversion based value predictors. It may even be claimed that the central purpose of stimulative public policies recently was to boost wealth effects by supporting a sustained rally in stocks and bonds, that in turn favored momentum over value in both asset classes.
A third explanation for time series versus cross sectional performance is the correlations of the signals, and how they compare to the correlations of the underlying markets. All else being equal, a cross sectional approach has more to gain when asset correlations are very high, as the above-mentioned global factor will dominate, and hedging this out will increase diversication by boosting exposure to a wider range of other factors. However, if signals are also highly correlated, a cross sectional approach will hedge out most of the (presumably informative) signals as well, potentially canceling out any gain from the diversication. Conversely if asset correlations are high, but signal
correlations low, we will likely lose very little of the information in the signals by forcing them to be cross-sectional as their information already mostly relates to the non-global factors. This could potentially explain the outperformance of time series momentum against time series value in bonds and equities. Although both asset classes are internally highly correlated, the momentum signals on them are even more correlated, so moving to a cross-sectional framework will potentially hedge out more of the alpha from the signals than noise from the market. Correlations of value signals are notably smaller.
While all of the above explanations have appeal, the readers should note that value is traditionally traded in the cross section while momentum is traded in time series. So it would seem that traders have generally come to the "correct conclusions".
By combining simple signals in carry, momentum and value across less than 100 liquid futures, forwards and swap markets we are able to achieve a remarkably stable strategy over 25 years with a Sharpe ratio of close to 2, returning an approximately eight-fold increase on a hypothetical 15% volatility investment. This can be considered a genuine return, as the strategy has very low funding costs. Is this too good to be true? Why is not every investor trading these styles in combination?
We tried our hand at six possible explanations.
Selection bias is a partial answer. Why did we choose these styles and not others? Because, by and large, they have worked consistently over time and across asset classes. However, in defense of our results, not many styles make sense across such diverse asset classes; so the selection pool is not large.
What about potential over-tting? There was no fitting in this exercise, although some potentially creeps in from experience. Why do our value predictors look back much further than the momentum predictor? Because momentum has worked better at medium frequencies, whereas value is clearly a long-term game. How obvious would this have been 25 years ago?
Survivorship and selection bias of assets is also a problem. Toxic emerging markets may be excluded. This study excluded Argentina but included the likes of Russia, Greece, Indonesia. This kind of bias will likely favor value and carry through the removal of markets where turmoil has caused major assets to exit.
Momentum suffers from another potential bias. Back in 1990, many markets we would include now were much smaller. The ones that make it into our study have likely grown over this time, often via a strong long-term up-trend. By adding data for markets which are now big, but were once small, we likely give a positive bias to momentum predictors.
Another, perhaps more appealing explanation for the performance is simply that few firms have the appetite and patience to trade something so simple. It is easy to forget the arguments in 1999 that value had been replaced by growth, in 2008 that carry was toxic, and in 2011-13 that momentum was finished. These are long-term signals whose performance oscillates over time, with each style experiencing negative performances for at least three years. It is difficult to stick with underperforming strategies this long."
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