# Looking Back on Trend Following – Part 3

*Analyze CTA trading style using AWTR; simple linear regression of CTA rolling returns; trend-following vs non-trend-following results; data.*

In the previous post in this series, we examined the relationship between the Average Weighted Trend Ratio (AWTR) and the rolling returns of the SG CTA Trend Index. We found a relatively strong relationship between the two time series, especially at higher values of AWTR.

While this relationship may be an interesting factoid for your next financial engineering cocktail party (which admittedly tend to be rather dull affairs), it’s not particularly useful for a portfolio manager in his day-to-day work.

So what practical uses might the AWTR have? In this post, we’ll take a look at how we might perform style analysis using AWTR. Can we use the AWTR to identify trend-followers and non-trend-followers? Can we use it to further categorize trend-followers into short-term, intermediate-term, and long-term?

#### AWTR Review

In the first post in this series, I introduced the Trend Ratio (TR), a risk-adjusted measure of the “trend quality” in a market over a period of time. Conceptually, the TR should measure the ability of a trend-follower to harvest profits in a market over a specific time period.

In the second post, I showed how to calculate the AWTR for a portfolio of futures markets and then compared its values to the SG Trend Index, a benchmark for trend-following CTAs.

That was all mildly interesting, but now we get to the real question. What can we actually **do** with this thing?

#### Style Analysis with AWTR

The AWTR is supposed to be indicative of the ability of a trend-follower to make profits. If that’s true, we should be able to identify trend-followers by comparing their returns to AWTR values.

To test this idea, let’s use simple linear regression to compare the returns of two CTAs to AWTR values. The portfolio of futures markets used to create the AWTR is the same as was used in the previous post. The CTA programs are:

- Abraham Trading Company’s Diversified Program is described as using “a systematic, long-term, trend-following approach”.
- QIM’s Global Program uses “pattern recognition to predict short and medium-term price movements.”

Both CTAs have been in business for many years, and the analysis will run from Jan-2005 through Oct-2017.

#### Linear Regression Using AWTR

The linear regression will posit AWTR as the independent variable and the CTA returns as the dependent variable. Several different AWTR lookback periods will be used in an attempt to determine whether a CTA’s returns are from short-, intermediate-, or long-term trend following (or not from trend following at all).

There is a complication in this, however. Note that each data point in the AWTR time series represents the potential profit opportunities available to trend-followers over a lookback period preceding that data point. For example, using a lookback period of 262, each daily AWTR value represents the potential trend-following profitability of the previous 262 trading days (inclusive). Because of this, it would be meaningless to try to compare the AWTR directly to the daily returns of a CTA.

Additionally, we have daily time series for the AWTR but only monthly returns for the CTAs.

The solution is to calculate several CTA rolling-return time series where the rolling-return lookback period corresponds to the AWTR lookback period, and to only use the last AWTR value of each month for the comparison. So for an AWTR period of 262, the dependent variable will be the CTA’s 12-month rolling returns. Using the last daily AWTR value for each month, we can now compare the AWTR looking back one year to the CTA returns over the same one-year period.

This technique, however, prevents us from using multiple regression because we now have multiple dependent variables to analyze. It would be preferable to run a multiple regression of the CTA returns against AWTR with different lookback periods and thus create a single model of the CTA returns. If any of you have ideas on how to resolve this problem, I’d love to hear about it.

Another issue with this method is that there is now a great deal of overlap between successive values in each time series. This issue will be ignored.

#### Results

I used the Excel Data Analysis Regression function for performing the regression. Table 1 and Charts 1 – 3 show the results for the trend-following CTA vs the non-trend-following CTA and for different lookback periods.

###### Statistic

###### Trend-Following CTA

###### Pattern Recognition CTA

###### Lookback Period

###### Trend-Following CTA

###### Pattern Recognition CTA

###### Lookback Period

###### Trend-Following CTA

###### Pattern Recognition CTA

###### Lookback Period

###### Trend-Following CTA

###### Pattern Recognition CTA

###### Lookback Period

###### Trend-Following CTA

###### Pattern Recognition CTA

###### Lookback Period

###### Trend-Following CTA

###### Pattern Recognition CTA

*Chart 1 – R^2 values for simple linear regressions.*

*Chart 2 – Regression coefficients.*

*Chart 3 – P-Values*

#### Observations

- The R^2 values for the trend-following CTA for the 3-month, 6-month, and 12-month lookback periods are nearly equal at 18% and the P-values are vanishingly small. This would seem to indicate the returns are related to the AWTR values with these lookback periods, which is what we would expect.
- The regression coefficient for the trend-following CTA for a 12-month lookback is 1.87, which is more than twice as large as those at 3 months and 6 months. This indicates this CTA’s returns come more from longer-term trend-following than from shorter-term trend-following (which agrees with their marketing literature).
- For the non-trend-following CTA, with the exception mentioned below, there doesn’t seem to be any relationship to AWTR, which again is what we would expect.
- For the non-trend-following CTA, the only relationship to AWTR that seems significant is the very long term AWTR with a lookback of 24 months. Indeed, the relationship here seems very strong with a coefficient of -4.5, R^2 of 22%, and an extremely small P-value. I would not expect this to be the case. My suspicion is that that this is somehow related to the fact that there is a great deal of overlap in each successive point in both the AWTR and rolling return time series. I haven’t addressed the overlap issue here at all, and a more sophisticated analysis would need to examine this issue.

#### Summary

The AWTR is a measurement of the ability of trend-followers to profit in certain markets during specific periods. It is important to note that it is derived directly from market price action and doesn’t rely on indexing of CTA returns or simulating a trend-following system.

Style analysis is used both prior to investment as part of the portfolio construction process and after investment to monitor and detect style drift. The analysis conducted here is not intended to represent a professional level of style analysis, but rather to illustrate that the AWTR may have practical applications in that area.

The simple linear regression results correctly distinguished between the trend-following CTA and the non-trend-following CTA, and also indicated the kind of long-term trends the CTA is trying to capture.

There are several ways the style analysis might be improved:

- The overlap issue identified above should be investigated to determine whether it is indeed an issue and whether it can be reduced.
- Instead of simply performing a style analysis for the entire track record of a CTA, it would be more interesting to perform the analysis over different time windows to see how the trend-following strategy evolved. Style drift would also be tracked in this way.
- We previously saw that the relationship between AWTR and the SG Trend Index was strong at high values of AWTR and weak at low values. I suspect that performing the regression only for higher values of AWTR would improve the ability of the analysis to detect trend-following and also to better distinguish between shorter-term and longer-term trend-following.
- Because of the long lookback periods used in the AWTR, the time needed to detect style drift is likely to be considerable. This is often a problem with style drift analyses. Can we detect shorter-term style drift?
- The AWTR could be customized if the specific markets traded are known. For example, a currency-only AWTR could be constructed for style analysis of a currency manager. This would also lead to detection of market and sector style drift.

#### Data

The zip file contains two CSV files. “TRData.csv” is the raw Trend Ratio data. For each symbol, date, and lookback period, the NetExcursion, GrossExcursion, the ratio and absolute value of the ratio are shown. The other file, “Symbols.csv”, contains a key showing which futures products are indicated by the symbols.

THE DATA ARE PROVIDED AS-IS. USE AT YOUR OWN RISK. CTS ASSET MANAGEMENT LLC MAKES NO REPRESENTATION THAT THE DATA ARE CORRECT OR FIT FOR ANY PURPOSE WHATSOEVER.