Systematic managed futures1 have often been described as mystical. Perhaps because of the lack of transparency that can surround such strategies. As part of our continuing academic and research work at Amplitude, we have prepared an introductory paper aimed solely at de-mystifying one aspect, trend analysis, and in the process we hope to provide a thought provoking read.
One of the key characteristics of alternative funds pursuing managed futures and macro strategies is their overriding commitment to deciphering market trends2. The capacity to identify and interpret prevailing trends quickly and accurately undoubtedly forms the backbone to any successful investment strategy. With this insight, managers are able to formulate investment strategies based on long or short trading positions. Strong market movements can often lead to the increased likelihood of profitable trades, whilst sedate markets with narrow trading ranges can result in the opposite effect.
In examining the behavioural characteristics of trends, we explore existing tools used for trend analysis and discuss their limitations. We then develop the "Trend Indicator" concept (the "TI") which seeks to overcome some of the inherent weaknesses of traditional trend concepts. The TI concept is a valuable tool to explore the inter-relation between market trends and market volatility3.
In this paper, we will demonstrate how the inter-relation between volatility and trend is not as clear as it might seem. Above a certain level of market volatility, the strength of a trend (as measured by the TI) is significantly diminished such that volatility no longer aids trend detection.
We will also use the TI concept to evaluate and analyse two simple theoretical trend following systems based on the Moving Average Convergence Divergence indicator (the "MACD"). The TI is used to test and determine the underlying trading timeframe used by both trend following systems.
Finally, we shall test the TI concept against a live foreign exchange fund with the objective of deducing what investment time horizon the fund is deploying. The result is then compared to the funds own stated investment strategy.
Analysts have developed numerous methods aimed at uncovering the characteristics of market price movements and trends. One such model is the "Average Directional Indicator" (the "ADX") which describes a trading or trending market environment.
The key driver of this model is the relationship between intra-day market highs (HD) and lows (LD) over a defined time period (t). Intuitively, the ADX model measures the magnitude of any increase of daily highs and decreases of daily lows over a certain timeframe.
Mathematically, the model is described with the following series of expressions:
The ADX model can be a valuable tool in understanding trends. In theory, the higher the ADX value, the stronger the trend displayed. However, in isolation this can also be misleading. It is conceivable that the ADX may show a strong market trend where in reality, no such trend exists.
To illustrate this, consider the example in Figure 1.
In an effort to overcome this flaw, we have developed the Trend Indicator (the "TI"). The TI incorporates two significant deviations from the ADX model. Firstly, the TI model considers only the absolute values derived from the linear regression which, in isolation, this does not correct the flaw in the ADX. However, the model also considers the measure of price volatility around the trend line. Volatility in this case is measured by the standard error of the slope.
To demonstrate the integrity and practicality of the TI model, we shall examine its output over a specified time period measured in minutes – TI(n). We use the concept to test the correlation between volatility and trend, but also to test existing strategies.
The mathematical expression describing the TI model is shown below.
n: time scale in minutes (i.e. 30 for 30 minutes, 1440 for 1 day, etc)
t: moment in time when the indicator is calculated (i.e. 14th February 2002 at 16:45)
a: the slope of the linear regression from t-n/2 to t+n/2
sa: the error of the regression
R: a small summand that is added to avoid that single outliers (with nearly no error of the slope) would disturb the result. In this paper R=10-11
Again, the higher the TI value, the stronger the implied trend of the examined data.
Volatility and trends are often referred to in the same context and in some cases, as synonymous. It is also not unusual for volatility and trends to be regarded as strongly correlated to one another. However, as we will demonstrate with the use of the TI concept below, high degrees of volatility do not necessarily denote strong trend patterns. There is compelling evidence to suggest a weaker correlation between volatility and trend exists at higher levels of volatility than commonly assumed.
To demonstrate this assertion, we will examine the relationship between trends and volatility using the TI model as a proxy for the strength of trends. We have used the minute spot price for the USD/EUR exchange rate between 1990 and 20044 as the underlying data for this analysis.
In Figure 2 over, the 1-day (i.e. 1440 minute) spot volatility and TI values for each day between the examined data periods and plotted on the graph. The frequency or density of the observations at each point in time is demonstrated by different colours on the graph.
The graphic in Figure 2 is useful in so far as to illustrate the dispersion of data. It is nevertheless, a challenging illustration to interpret and to reach any firm conclusions. By segmenting the data into strips along individual volatility levels and plotting this data in a normalised form against relative frequencies, a compelling picture begins to emerge (see Figure 4 below).
In Figure 3 over, we have taken one cross section or strip along the x-axis between the volatility values of 0.20% and 0.21% to illustrate the point. The data shown here has been a normalised and relative frequency calculated.
By applying this same methodology at every level of volatility and plotting this against a graph, a picture emerges which is shown in Figure 4 over.
The nature of this relationship between volatility and TI is even more pronounced when one re-organises the data by showing volatility against average TI values. This is shown in Figure 5.
By utilising the Trend Indicator in this way, we believe a more complex relationship emerges between volatility and trend than commonly perceived. During low levels of market volatility, the expected value of the TI increases as volatility increases. But as market volatility reach higher levels, the relationship does not hold.
We have demonstrated that for volatility levels above 0.5%, the expected value of the TI is independent of the market volatility. Furthermore, it could be said that for volatilities above 0.5%, the knowledge of the exact volatility level holds no more information than that the volatility is in fact higher than 0.5%. It should nevertheless be noted that volatility levels above 0.5% during one trading day remains relatively rare.
Having now explored the inter-relationship between volatility and trends, we are now in a position to examine the practical relevance of the Trend Indicator when evaluating simple trend following systems. In particular, we shall limit our analysis of trend following systems to the relatively standard smoothed Moving Average Convergence Divergence indicator (the "MACD").
In a nutshell, the MACD indicator shows us the difference between two moving averages for prices at two points in time (t1 and t2). This result is then smoothed over the value at a third time period (t3). It is intuitive therefore, to expect the MACD indicator to be strongly correlated to the TI if both are measured over similar time scales. We will test this assertion below.
Let's consider two MACD systems over USD/ EUR exchange rate data covering different time periods.
MACD 1: Examines moving averages over 16 and 32 hours and a smoothing time of 10 hours
MACD 2: Examines moving averages over 5 and 10 days and a smoothing time of 3 days
In Figure 6 over, we have plotted the correlation of both MACD 1 and MACD 2 indicators against the Trend Indicator over the same period. Near perfect correlation would suggest lines on or around the 0 correlation coefficient axis.
It is clearly apparent from the graphic in Figure 6 that MACD 1 and the TI are most closely correlated at about 24 hours. Similarly, MACD 2 practically converges with the TI between 4 and 10 days.
From this type of analysis we can deduce the underlying timeframe of trends that each system is designed to recognise. By virtue of the parameters within its system, MACD 1 is designed to identify 1-day market trends, whilst MACD 2 will be better suited to trends over a 1 to 2 week period.
The analytical concepts we have developed and tested in this paper now provide us with a useful tool for analysing existing funds. In particular, we have the tools required to test existing trading funds and to establish the likely strategic hold periods employed by these funds.
To conduct this analysis, detailed information on returns per instrument and strategy is required. This is not always readily available and in some cases the information is proprietary and not disclosed. Nevertheless, for the purposes of this study, we have identified a fund that claims to trade on multiple timeframes in the foreign exchange markets.
In Figure 7, you will see the degree of correlation between the active fund's monthly trading returns against the TI for the USD/EUR exchange rate over different time periods. The data examined for this exercise was accumulated between January 2002 and December 2004.
We can clearly see a strong correlation in the two-day time period and also at the longer time period. This outcome falls nicely in line with the fund's communicated investment strategy and provides a useful test of the credibility of the concepts we have explored in this paper.
Through this research paper, we have considered the nature of trends and how to develop an efficient indicator of them. The Trend Indicator concept was used to probe the relationship between trends and volatility and challenge the widely held belief that both terms are inter-changeable. We have shown that this is not the case.
The paper also looked at simple trend following systems and used the TI to determine their underlying investment timeframes. The concepts were then tested against data from an active trading fund and the analysis revealed that the examined fund operated with two primary trading timeframes. This was in line with the funds stated investment strategy.
We hope this brief insight into trend following concepts has been interesting. We believe the Trend Indicator concept can be a powerful tool for analysing systematic traders and their funds.
Definitions and notes
Amplitude Capital is a London based manager focusing on highly liquid exchange-traded futures including stock indices, commodities, and foreign exchange markets. Its primary strategy is to create superior risk-adjusted returns by identifying and exploiting opportunities through a short-term trading strategy. Transactions are executed via a fully automated system with an average holding period of one to two days. Amplitude's first fund is expected to launch during the second quarter of 2005 following authorisation by the FSA.
The team at Amplitude is diversified with backgrounds in investment banking, hedge funds, management consultancy, software development and quantitative research. Most of the team is focused on trading, research and product development.
Karsten Schröeder is the CEO and joint founder of Amplitude Capital. He oversees all key decisions relating to product development and trading strategy for the Amplitude funds. Florian Leder is a member the Research, IT and Technology team at Amplitude. He is a mathematician by training and is responsible for programming and product development.
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