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A New Look at Momentum

Published in Automated Trader Magazine Issue 28 Q1 2013

Time series momentum strategies are about as old and ubiquitous as the CTA community that uses them, yet there has been surprisingly little recent academic work done in this space. Notable exceptions to this are two papers produced in 2012 and 2013 by Dr. Nick Baltas and Prof. Robert Kosowski of Imperial College London. Automated Trader talks to the authors about their work and some of the conclusions, which run counter to established thinking.

Automated Trader: What are the origins of your work in the field of time series momentum?

Nick Baltas: It has its origins in work I was doing a couple of years ago when I was preparing for my PhD and Robert was my supervisor. At the time, there was not a vast amount of material on momentum strategies in published academic literature. We felt that there was potential for making the strategy more robust as regards both volatility estimation and signal generation.

Automated Trader: What started as one paper now appears to be two. Why?

Robert Kosowski: In March 2012 we decided to split the original paper into two parts partly for reasons of space, but more importantly because we felt that there were further issues to be examined that would naturally cover distinct features of time-series momentum strategies. The paper 'Momentum Strategies in Futures Markets and Trend-Following Funds' examines matters such as the prevalence of time-series momentum strategies among CTAs by using benchmark strategies that have high explanatory power in the time-series of CTA index returns. It also considers (and rejects) the hypothesis that high flows of capital into CTA strategies cause capacity constraints.

The second paper, 'Improving Time-Series Momentum Strategies: The Role of Trading Signals and Volatility Estimators' is primarily focused on the mechanics of the time-series momentum strategy. In particular, it considers how two specific changes might enhance the overall profitability of a momentum strategy. One change was that the introduction of a more efficient volatility estimator could reduce unnecessary portfolio rebalancing and thereby also reduce transaction costs. The paper also examines how the quality of the momentum trading signal affects performance and posits an alternative model that in addition to long/short signals incorporates a stay flat/exit signal.

We feel that both papers are of interest to practitioners (including fund of funds) and academics.

Automated Trader: What was the motivation for investigating capacity constraints in the first paper?

CTA performance since 2009 has generally been weak, with various conventional CTA indices (e.g. BarclayHedge, Newedge indices) reporting negative yearly returns for 2009, 2011 and 2012. Yet over the same period flows into CTAs have been positive. That would superficially suggest that there are capacity constraints in the industry. We therefore decided to test this hypothesis, and in order to do so we needed to find some strategies that had explanatory power for CTAs that could be used as a proxy for their activity.

Automated Trader: Surely determining that those strategies should be momentum-based was a given, in view of their well-documented proliferation among CTAs?

Nick Baltas: That may be a widespread assumption, but it is interesting that previous studies which have asserted this have not actually provided any empirical evidence in support. We decided to remedy this by building a time series momentum strategy that we applied across monthly, weekly and daily time frames (which we termed Futures-based Trend-following Benchmarks or FTBs1) and regressing this against a CTA index.

Dr. Nick Baltas

Dr. Nick Baltas

Automated Trader: What was your methodology for constructing the FTBs?

Robert Kosowski: We first tested for and found evidence of return predictability in the lagged returns across monthly, weekly and daily frequencies of our dataset. We then created a series of overlapping portfolios that were rebalanced at the end of each day/week/month, and tested for momentum profitability. The results showed that the momentum strategy generated an economically significant alpha and return at all three frequencies and were in the majority of cases significant at the 1% level. Several combinations of lookback and holding periods exhibited Sharpe Ratios greater than 1.25.

The underlying FTB momentum strategy was constructed on a simple rule: if the return of an asset for the lookback period (J) was positive we would go long (short if the return was negative) and hold the position for the holding period (K). We generated results for the strategy across a combination of lookback (J) and holding period (K) ranges (in both cases 1, 3, 6, 9, 12, 24 and 36 days/weeks/months accordingly).

Automated Trader: Which markets were in your dataset and which CTA index did you use?

Nick Baltas: Our futures dataset consisted of daily open, high, low and close data for 71 futures contracts provided by TickData ranging across commodities, equity indices, currencies and bonds from December 1974 to January 2012. (We used spot data from Datastream to backfill futures series for instruments such as equity indices for which futures data was unavailable for the entire period.) We rolled over contract months so that we were always trading the most liquid contract, based upon daily tick volume. In order to check the capacity constraint hypothesis, we also collected open interest data for the US-traded futures contracts of our price dataset from the CFTC, which covered 43 of the 71 futures contracts.

For the CTA index we collected monthly return and assets under management (AUM) data for all the CTAs reporting into the BarclayHedge database. After de-duplication and the removal of discretionary funds we were left with 1348 systematic CTA funds which accounted for 87.5% of the total AUM of the CTA industry at the end of the sample period. As a precautionary measure against outlier bias, we restricted the dataset by date to ensure a sufficient sample size.

We then used this data to construct an index that was weighted by AUM (AUMW-CTA), as well as using AUM weighting to calculate the aggregate flow of capital in our systematic CTA universe at the end of each month.

Prof. Robert Kosowski

Prof. Robert Kosowski

Automated Trader: What conclusions did you reach?

Robert Kosowski: When we regressed the AUMW-CTA index against the time series momentum strategies the R2 exceeded 37%2, with the strategies remaining significant across all three time frames at the 1% level. This supported the hypothesis that CTAs follow momentum strategies at various time frequencies. As a check on the validity of the FTB strategies as appropriate benchmarks, we regressed the AUMW-CTA index against two other benchmark models (see items (a - FH7) and (b - FH9) in side bar 'Other benchmarks used for CTA performance') resulting in R2 values of 26.54% and 29.83% respectively. We also regressed it against a combination of FH9 and the FTB strategies, which generated an R2 of 51.65%.

For additional robustness we tested several other combinations of factors, and in most cases all three FTB strategies were largely significant at the 1% confidence level. We also calculated a 60-month rolling adjusted R2 for the FH7 benchmark model, FTB and FH9+FTB specifications to cross check the stability of the explanatory power of the FTB strategies for CTA returns over time. The rolling R2 for the FH9+FTB barely dipped below 50 for the entire period and was above 60 for significant phases. Overall, the results demonstrated that the FTB time-series momentum strategies have highly significant explanatory power for CTA index returns.

Our objective in establishing a link between time series strategies and CTA returns was to support the use of CTA fund flows to examine potential capacity constraints in momentum strategies.

Automated Trader: So how did you use this to conclude that net inflows of funds to CTAs were not responsible for their lacklustre performance 2009-11?

Nick Baltas: We regressed the individual FTB strategies against lagged CTA fund flows for all futures contracts, ex-commodities, commodities only, currencies only, equities only and interest rates only. While the t-statistics3 showed that, on average, lagged fund flows had a negative effect on future momentum strategy performance, it was at a statistically insignificant level. Furthermore, the slope coefficient of the regression was in no case economically significant. It is important to stress that we carried out the above analysis using data over the past 30 years and we are not looking specifically in detail in the most recent three years. In order to address situations where fund inflows might be held as cash for a period, rather than immediately used as margin, we performed further tests to check whether inflows that occurred when open interest was increasing were negatively related to momentum strategy performance. The results did not change our original conclusion, as we found no relationship between the sign of the performance flow relationship and changes in open interest.

Other benchmarks used for CTA performance

In addition to the FTB strategies detailed in the main article, a number of other benchmarks were used when analysing CTA returns:

(a) the hedge-fund return benchmark 7-factor model by Fung and Hsieh (2004) (FH7, hereafter), which incorporates three primitive trend-following (PTF) factors for bonds, foreign-exchange and commodity asset classes

(b) an extended Fung and Hsieh (2004) 9-factor model (FH9, hereafter) that incorporates the remaining two PTF Fung and Hsieh (2001) factors for interest rates and stocks, since Baltas and Kosowski's FTB strategies tend to capture return continuation in all asset classes.

As a further check, we also simulated what would happen if the entire AUM of all systematic CTAs were invested in the monthly FTB strategy, specifically comparing the number of contracts that would be required for this purpose and the open interest at each corresponding point. We conferred with industry practitioners to arrive at realistic portfolio weightings for each category of underlying instrument (currencies, equities etcetera) and also to determine a margin to equity ratio.

Based upon this, we calculated the percentage of months between January 1986 and December 2011 in which each of 43 futures contracts for which CFTC open interest data was available would have exceeded their corresponding open interest. The results were an almost exact fit with public data about the relative liquidity/illiquidity of futures contracts. None of the oil/gas complex, S&P 500, soy products, wheat, cocoa, coffee, cotton, gold or copper had any months where our modelled total capacity of the CTA industry would have exceeded available open interest.

Those that did exhibit 'exceedance' were those such as currencies (mostly traded as forwards rather than futures by CTAs anyway) and contracts with known liquidity limitations such as lumber, palladium, platinum, the Dollar Index and less popular stock index futures. The one surprise, initially, was the two year T-note which showed 60% 'exceedance' (all other US Treasury note and bond futures showed 0%), but we then realised that this was because prior to 2002/2003 most CTAs traded this maturity on a cash basis rather than using futures.

Automated Trader: Sounds compelling, but if capacity constraints are not responsible for recent weak CTA performance, what is?

Robert Kosowski: Two possible alternative reasons are an absence of sufficient price trends for individual securities, and increased absolute correlation between futures markets which reduces any diversification benefits.

Regarding the absence of price trends, it could be argued that high monetary/fiscal policy uncertainty between 2009 and 2012 may have affected market sentiment and caused price trends during this period to reverse more frequently than in the past. This hypothesis of course has yet to be rigorously tested.

Hat Tip

Our thanks to Radovan at Quantpedia (www.quantpedia.com) for alerting us to Nick and Robert's work in this area.

In order to investigate the intertemporal correlation structure of the futures markets, we performed a rolling window principal component analysis on the 71 futures contracts in our dataset. The analysis showed that the average explained variance of the first principal component rose dramatically after the Lehman collapse, peaking at the end of our sample period at 45%. This might therefore support the hypothesis that the underlying data generation process has changed since the financial crisis and that the degree of market co-movement has increased, which is something we also intend to study in future research.

Automated Trader: In your second paper ('Improving Time-Series Momentum Strategies: The Role of Trading Signals and Volatility Estimators') which markets did you use for testing and what was your motivation for researching alternative trading signals?

Nick Baltas: As regards markets, we used intra-day (30 minute intervals) futures prices for six commodities (Cocoa, Crude Oil, Gold, Copper, Natural Gas and Wheat), two equity indices (S&P500 and Eurostoxx50), two FX rates (US Dollar Index and EUR/USD rate) and two interest rates (Eurodollar and 10-year US Treasury Note) for a period of 10 years - November 1st 1999 to October 30th 2009. We adjusted the data for rollovers so we were always trading the most liquid contract. We intend to extend this dataset to a larger cross-section and longer period in an updated version of the paper in the next couple of months.

One motivation for our research was the recent poor performance of CTAs as markets have largely moved sideways (possibly as a result of national monetary policies). These conditions have always been challenging for momentum strategies anyway, so these recent events were a motivation to develop a signal that did not just flag entries but also abstentions from trading or reduced exposure. The key was to do this in a parsimonious manner without introducing anything too complex.

The traditional approach has simply been to use the sign of past return over a lookback period as a signal to go long/short, which doesn't take into account any of the information between the beginning and end of that period. We therefore wanted to test approaches that made use of that additional information, while also incorporating econometric features of the price paths.

Automated Trader: Which were?

Robert Kosowski: We looked at four possible signals (though some of these may change or be replaced as the research evolves) in addition to the traditional sign of past return signal (SIGN):

• A moving average indicator (MA)

• A price trend based signal from a previously published paper4 (EEMD)

• A signal we developed based upon the t-statistic of the slope coefficient from a least-squares fit of a linear trend on the price path (TREND)

• A more robust version of TREND (SMT) refined using a methodology from a previously published paper5

Automated Trader: What effect on trading activity did the last two signals have?

Nick Baltas: Both signals flag abstention from trading when the statistical significance of the least squares regression trend is weak, so they reduce the amount of trading activity. For example, a 12-month lookback period resulted in trading activity about 87% of the time using the TREND signal, and 63% of the time using the SMT signal.

In comparison with the traditional SIGN signal, this resulted in superior returns. For instance, the SMT signal using a six month lookback period and a one month holding period generated a 28.36% annualised mean return, compared with 15.97% generated by SIGN signal, with both results strongly significant at the 1% level. While this was encouraging, one potential issue was that the signals would switch between the various states (flat, long , short), which might have the effect of increasing the turnover of the portfolio. Some practitioners suggested that we try a modified signal that used the ratio of positive to negative returns over the look-back period, which is something we might introduce in a later version of the paper as an additional non-correlated signal.

Automated Trader: Which volatility estimators did you evaluate for portfolio rebalancing of instruments, and which of these did you regard as the most effective?

Robert Kosowski: We examined a total of eight, ranging from simple standard deviation to more sophisticated estimators that took account of factors such as overnight gaps and underlying drift in the price process. Our objective was to find an estimator that introduced the minimum noise and thereby generated the most persistent volatility and in turn minimised unnecessary portfolio turnover.

The two that stood out were realised variance/volatility (RV) and the Yang Zhang6 (YZ) estimator. The former uses the sum of squared intraday log returns. However, it assumes that there are neither price jumps nor serial correlation in the time series. It has also been demonstrated that microstructure noise affects the estimation accuracy of realised variance/volatility when the sampling period is less than five minutes, though this was not an issue in our research as we were using 30 minute sampling intervals.

The Yang Zhang estimator, which we finally selected as optimal for our purposes, uses a linear combination of techniques:

• Standard deviation estimator

• A standard deviation estimator that uses overnight log returns as an input, as opposed to close to close log returns

• The Rogers and Satchell7 estimator, which allows for a non zero drift in the underlying time series

While its use of intra-day price movements gives the RV estimator greater efficiency than the YZ, we nevertheless opted to use the YZ for our testing of momentum signals across our portfolio because we believed that it constituted the optimal balance across efficiency, turnover and the need for higher-frequency data.

The combination of the YZ estimator and the SMT signal resulted in a substantial decrease in portfolio turnover (and hence also trading costs) across a broad range of lookback and holding periods. For instance, for a six month lookback and one month holding period this combination generated 19.3% turnover versus a 44% and 49.8% turnover when the SIGN and MA signals respectively were substituted. Similar outperformance applied across other metrics including dollar return and downside-risk Sharpe ratio8 (which penalises negatively skewed return distributions).

Footnotes

1. Available for download at http://www3.imperial.ac.uk/riskmanagementlaboratory/baltas_kosowski_factors in order to facilitate further research on this topic

2. R2 or the coefficient of determination represents the proportion of variation in the response that is explained by the regression model. Mathematically, the general form of this relationship is: R2 = (SSTO − SSE)/SSTO where SSTO is the total sum of squares in the response about the mean, and SSE is the sum of squares in the response about the regression line.

3. t-statistics

4. Wu, Z. and Huang, N. E.: 2009, Ensemble Empirical Mode Decomposition: A noise-assisted data analysis method, Advances in Adaptive Data Analysis 1, 1-41.

5. Bryhn, A. C. and Dimberg, P. H.: 2011, An operational definition of a statistically meaningful trend, PLoS ONE 6(4), e19241.

6. Yang, D. and Zhang, Q.: 2000, Drift-independent volatility estimation based on high, low, open, and close prices, Journal of Business 73(3), 477-491.

7. Rogers, L. C. G. and Satchell, S. E.: 1991, Estimating variance from high, low and closing prices, Annals of Applied Probability 1(4), 504-512.

8. Ziemba, W. T.: 2005, The symmetric downside-risk Sharpe ratio, Journal of Portfolio Management 32(1), 108-122.