6 December 2013 - 15 minute read

Trend following is a well-known investment strategy, in which market forecasts are based solely on recent price movements. We document the performance of such strategies ran on a portfolio of large futures markets since the mid-1980s, and consider if there is any dependence on trading speed. In general we find trend-following systems to be effective in forecasting future price movements, but we observe a significant and persistent decline in the forecasting ability of those with the fastest turnover.

There is a long history of practitioners within financial
markets using technical analysis to take investment decisions based on patterns
in historical price data. These ideas became popular within futures markets,
where professional investment advisors operate under the rubric of “Commodity
Trading Advisor”, or “CTA”.

The CTA acronym has now become almost synonymous with trend-following
or momentum strategies, where the pattern in question is simply whether a
market price has risen or fallen in recent history. This tendency for prices to
trend is described in statistical terms as “auto-correlation” of returns.

It is only in recent history that trend following on major
asset classes, via futures markets, has gained the attention of the academic
community [1]. The focus of academic work has been on equity markets, where
momentum is most commonly embodied as a cross-sectional effect, and is used to
predict relative, rather than absolute, returns of stocks [2, 3]. In this guise
it still exploits the existence of auto-correlation in returns, relative to the
market.

The evidence for momentum in equity prices is strong enough
that it is now accepted as one of the standard equity “risk factors” that can
be used to explain the returns of any stock or portfolio, along with the
market, value, and size factors [4, 5]. As it becomes better documented,
returns from momentum signals are increasingly deemed to be “beta” rather than “alpha”
in the world of equities.

In this study, we document the performance of trend-following
strategies over different time horizons, on data from the mid-1980s until
today. Within financial markets, great efforts are being made to achieve the
fastest possible communication speeds with exchanges, contributing to a
perception that fastest is always best.

We, however, find evidence that fast has not always been
best in the world of trend following and futures markets, where we see a significant
decline in the performance of the fastest strategies even before transaction
costs are accounted for.

First, we outline the markets that we use to document this effect
and the rules of our trend-following investment system, then we document our
results, before concluding with a discussion.

## Data and methodology

**Futures**

We use the front contract for 20 futures markets that are 1) representative of their sector; 2) highly liquid and global in their reach; and 3) have a long history. The markets used are listed in Table 1.

## Table 1: The 20 futures in our trend-following portfolio

These are now all traded on the CME except: (1) Eurex, (2) TSE, (3) OSE, (4) HKFE, (5) SFE, (6) LIFFE, (7) LME. (8) We synthesise prices for a Copper futures contract with a fixed expiry date, rather than a fixed time to expiry as found on the LME.

It is tempting to synthesise futures prices prior to these
start dates in order to perform a longer historical simulation. For the purpose
of this study, we wish our results to be free from any uncertainty regarding the
validity of such an extrapolation. Similarly, we restrict ourselves to results
since January 1984, when most of our markets have started, in order to avoid the
effects a changing number of assets can have on the portfolio-level
performance.

**Investment system**

We use an exponentially weighted moving-average (EWMA) cross-over system (the difference between a fast and a slow EWMA of the price) to determine whether the system goes long or short in a market ‒ we are long when the fast average is above the slow and vice versa.

The positions are scaled by the inverse of a 20-day exponentially weighted estimate of volatility, which keeps the volatility of the final return time series approximately constant over time with a single market, and equal between markets.

As well as the per-market returns, we consider the results of a portfolio of 20 markets. The portfolio is simply an equally weighted, linear combination of the per-market return streams. Recall that each market achieves approximately the same volatility due to the scaling of positions, and we achieve approximately equal sector risk because we have five markets per sector. We remain free to apply a final overall scaling to all positions in order to achieve a desired volatility at the portfolio level.

Returning to the moving-average cross-over system, there are two important parameters: the short and long periods of the EWMAs. These determine the effective look-back time and holding period; although, this is not how the system is specified.

We will consider three trend-following systems of different speeds: “fast”, “medium” and “slow”, which have a turnover of 1, 6, and 13 weeks, respectively [6]. The fast system is correlated 26% and 5% to the medium and slow systems, respectively, with the medium and slow systems having a 34% correlation to each other. Note that our systems trade every day, regardless of speed.

Another way of implementing a momentum strategy is to look at the past return for some look-back period and then hold a position ‒ long or short according to the sign of the return ‒ as implemented in [1]. In the final section, we check our results against this alternative implementation, and generally find the results to be similar at the same turnover level.
Throughout this study we focus on gross performance in order to document the historical properties of futures price series. We do not attempt to translate these results into a net return ‒ that is, we are not including transaction costs, fees or any earned interest in our simulations.

## Results

First, we look at the results of the portfolio of 20 markets. In Figure 1, we see that all three strategies have performed well, with annualised Sharpe ratios of 0.81 or higher for this 30-year period. We can see, however, that the performance of the fast strategy has declined, having initially outperformed the others, but remaining flat since 2004.

## Figure 1: Gross performance and realised volatility for our trend-following strategies

Returns are not compounded and volatility is determined by a 100-day exponentially-weighted estimate. The Sharpe ratios are 0.87, 1.12 and 0.81 for the fast, medium and slow strategies, respectively, for the 30-year period. The standard error on the Sharpe ratio is approximately 0.2 for 30 years of data. The realised volatility is around 10.5% for all three strategies.

This is even clearer once we compute the Sharpe ratio for different time periods, as can be seen in Figure 2 and Table 2. The fastest strategy has seen a significant decline in performance, and we can rule out with a probability <0.0001 that the Sharpe ratio in the first and last 10-year periods have come from a distribution with the same mean.

## Figure 2: Gross performance in six separate five-year periods for our trend-following strategies

The standard error of these estimates is shown in grey around the results of the medium-speed strategy. Dashed lines give the average Sharpe ratio for the individual asset return; these appear to mimic the performance of the portfolio, indicating that the decline at the portfolio level is due to the decline of performance of underlying assets and not an increase in between-asset correlation.

## Table 2: 10-year gross Sharpe ratio for our trend-following strategies

Where Δ is the difference between the first and last 10-year periods, and t and p are the corresponding t-statistic and p-value. The p-value estimates the probability of achieving the observed Δ value under the null hypothesis that the true performance did not change in these two 10-year periods, and the difference is just due to sample error. All strategies have seen a decline in performance, but this is most significant for the fastest system.

Second, we examine the performance of the systems at the market level. The decline in risk-adjusted performance at the portfolio level seen in Figure 2 could be due to: 1) increased correlation between the constituent market returns, which would reduce diversification and cause the system to scale down its positions in order to achieve the same annualised volatility at the portfolio level; 2) a decline in per-market performance; or 3) a mixture of both.

In Figure 2, we see that the average per-market performance has declined in an identical fashion to the portfolio performance, confirming that 2) is the main cause of the portfolio-level decline. To double-check this we also consider how the correlation of the per-market return has changed over time.

We find the average correlation is ~4% (1984-1988) and rises to ~7% (2009-2013), and this is true for the three different trading speeds. The risk-adjusted performance of an equally weighted portfolio of *N* assets can be estimated as:

where *R*_{a} is the average risk-adjusted performance of the markets.

With this equation we estimate the effect the increase in correlation has on the portfolio level performance, and we find the multiplicative factor goes from 3.4 to 2.9. Thus, had the per-market results not changed over time, the increased correlation would alone cause a relative decline of about 15%. This is not much compared to the relative decline that we actually observe ‒ 100% for the fastest system.

## Further analysis

We consider an alternative implementation of a trend-following strategy, where instead of a price moving-average cross-over signal, we simply look at the past return for some look-back period and use this to determine the sign of our position.

The system then holds inverse-volatility-weighted positions for a certain holding period, with a number of positions open at any time if the holding period is greater than one day. We sum the return of these positions to evaluate our daily portfolio return.

We restrict ourselves to the parameter space where the holding period is half of the look-back period. We find look-back periods of two weeks, one quarter, and one year, and holding periods of one week, 33 days, and six months, which approximately correspond to the fast, medium, and slow EWMA cross-over strategies, respectively. They have similar turnover levels (one, six and 13 weeks) and have about 80% correlation to the corresponding EWMA strategy. The results are shown in Table 3.

## Table 3: Sharpe ratios for the alternative implementation of trend-following strategies

We see the same features with performance declining overall, and most significantly for the fast strategy. We therefore conclude that our results are robust to the exact implementation details of a momentum driven strategy.

We next consider the robustness of our results to the markets that we have used, as listed in Table 1. We extend our potential portfolio by another 18 markets (five in fixed-income, commodities and stock indice; three in currencies [7]) and we randomly choose a subset of 20 markets from these 38 and repeat the analysis for the fast, medium and slow EWMA cross-over systems.

In Figure 3, we plot the median and 15-85 percentile ranges for the results from 1,000 random portfolio choices for each speed of system. We find the overall result robust to the selection of the markets ‒ the performance is seen to decline, particularly for the fastest strategy.

## Figure 3: Gross five-year performance for randomly selected portfolios

For each portfolio 20 markets are selected at random from a total list of 38. The median results are plotted for each strategy speed, and the 15th to 85th percentile ranges from 1,000 realisations.

We do not want our analysis to rest heavily on synthesised data, but we consider one very long time series: that of the Dow Jones Industrial Average (DJIA). While this index was first calculated in 1896, futures on the index have only existed since 1997; therefore, we synthesise a rolled futures series using dividend yields and interest rates going back to 1900.

We then simulate the hypothetical results of trading our original fast, medium, and slow EWMA trend-following strategies on this DJIA price series. We find results over this very long time period that support the hypothesis that performance has declined for the fastest strategy in Table 4.

## Table 4: Trend-following strategies simulated on synthesised Dow Jones Industrial Average futures since 1900

The Dow Jones Industrial Average futures have only existed since 1997 we synthesise a rolled futures series using dividend yields and interest rates going back to 1900.

The medium strategy has seen a less sharp decline than the fast strategy, and the slow performance is fairly flat. For reference, the standard error on a 30-year Sharpe ratio is approximately 0.2.

## Discussion

Momentum is increasingly getting the stamp of approval from the academic community as one of several factors that can explain both the risk and return of equity prices [5] and more generally the returns of asset prices [1]. Its existence is controversial as illustrated by the words of Eugene Fama:

“Of all the potential embarrassments to market efficiency, momentum is the primary one"

At the same time as receiving academic attention, mainstream institutional investors have embraced momentum strategies. This is illustrated by the growth of assets in the CTA industry and the proliferation of products that seek to profit specifically from a momentum or trend-following effect.

In this study, we have gone beyond just documenting the existence of a trend-following effect in futures markets, and have explored how consistent it has been through time. In particular, we find evidence that the strength of fast trend-following strategies has declined significantly over time. Our results are robust to the markets we use and the parameterisation of the system.

A glaring omission from this study is the issue of transaction costs which could be a major factor in the ultimate profitability of these strategies. Instead, we have concentrated on the raw effect size, and have not attempted to make any claims as to the potential economic usefulness of it.

In order to understand the economic significance, it is necessary to consider brokerage fees, market impact (or slippage) and any other associated costs. Furthermore, in the context of this study, it would be necessary to understand how these costs have varied through time. Since this would require many more assumptions, we decided that it would detract from the simplicity and clarity of this research; although, we appreciate that costs could be substantial.

We have also not included interest in these simulations. Investors in CTA funds typically earn interest on cash that they do not require to margin positions. This can be around 90% of assets and would therefore improve the performance results significantly. This is true especially in the past when rates were higher than are today. We have also not included management or performance fees in the simulations as they are not relevant for this study, having had a consistent effect over time.

We have not speculated about the causes of the decline in performance, but many would note that it coincides with a rise in assets under management in the CTA industry. Three possible explanations for a weakening of the momentum effect are:

- A growing volume of assets seeking to profit from the effect. The exact mechanics of how this might weaken performance are beyond the scope of this discussion, but such an argument would be based on the premise that the more people who know about an “opportunity” in financial markets, the less likely it is to persist. This explanation is consistent with the growth of the CTA industry.

- A reduction in transaction costs. An efficient market perspective would argue that predictable effects can exist, provided they are not exploitable after costs. Viewed from this perspective a steady reduction in transaction costs over the past 40 years could explain the reduction in effect size. While the experience of the authors as practitioners within the CTA industry is at odds with an efficient market perspective, nothing in this paper discredits this being either a partial or complete explanation.

- A change in the behaviour of market participants. The first two possible explanations are endogenous to those who seek to exploit this effect. It is possible that some exogenous change is responsible. Indeed, the recent poor performance of trend-following strategies has been attributed to the intervention of central banks curtailing trends in markets [6].

These three explanations are purely speculative and as such we do not seek to suggest which, if any, of them is the most plausible. It is also not possible to extrapolate our results into the future with any confidence. All we can say is that the strength of the momentum effect has not been historically stable, and so we have no reason to think it will be in future. Taking all the data at face value the outlook is unclear, except that our results suggest that fast is not always best, and perhaps patience is rewarded.

### References

[1] T. J. Moskowitz, Y. H. Ooi, L. H. Pedersen, Time series momentum, Journal of Financial Economics, vol 104, 228-250, 2012.

[2] N. Jegadeesh, S. Titman, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal of Finance, vol 48, 1993.

[3] A. W. Lo, A. C. MacKinlay, When Are Contrarian Profits Due to Stock Market Overreaction?, Review of Financial Studies, vol 3, 175-205, 1989.

[4] M. M. Carhart, On Persistence in Mutual Fund Performance, Journal of Finance, vol 52, 57-82, 1997.

[5] E. F. Fama, K. R. French, Size, Value, and Momentum in International Stock Returns, Journal of Financial Economics, vol 105, 457-472, 2012

[6] We define the turnover of a system as: the ratio of the mean absolute position to the mean absolute five-day change in position, roughly indicating how many weeks it takes to close a position but ignoring small trades back and forth on a daily level.

[7] Lean hogs, silver, natural gas, soybeans, aluminium, Eurostoxx 50, DAX, Kospi, Nasdaq, Hang Seng, Euribor, short-sterling, bobl, US 5-year T-notes, schatz, Australian dollar, Mexican peso, New Zealand dollar.

This article contains simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under- or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity and cannot completely account for the impact of financial risk in actual trading. There are numerous other factors related to the markets in general or to the implementation of any specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results and all of which can adversely affect actual trading results. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any investment will or is likely to achieve profits or losses similar to those being shown.