# Average Weighted Trend Ratio for a Portfolio

Calculating the Average Weighted Trend Ratio (AWTR) for a typical portfolio of futures contracts; Examining the relationship between AWTR and trend-following CTAs; Next, practical applications of TR, formulas, and data.

In this post, I’ll calculate the Average Weighted Trend Ratio (AWTR) for a portfolio of futures markets and see if it helps explain good and bad periods for trend-following CTA strategies.

In the previous post, I demonstrated how we can measure the quality of a price trend directly from price action. Briefly, we measure the absolute value of the net price movement over a lookback period (the profit potential) and divide it by the sum of the absolute values of all price movement during the same period (the risk). This gives us the Trend Ratio (TR), which is a risk-adjusted return ratio measuring the quality of trending markets.

### Average Weighted Trend Ratio Calculation

To represent a simplified typical portfolio of a trend-following CTA, we use the markets and weights shown below. The portfolio includes both financial and energy markets, but is heavily skewed toward financial markets, as is the case with most large trend-following CTAs. Currencies and interest rates are weighted more heavily than stock indices. Smaller markets such as softs are not included.

MarketWeightMarketWeight
British Pounds2Five-Year Notes2
Australian Dollar2Ten-Year Notes2
Euro Currency2BOBL2
Japanese Yen2Long Gilts2
Crude Oil1Euro STOXX 501
Natural Gas1E-mini NASDAQ1
Brent Crude1E-mini S&P 5001
Gasoil1FTSE1

Each day, we calculate the AWTR for the portfolio as the weighted average of the TR values for each of the markets in the portfolio.

We’re interested in the relationship between AWTR and the returns from trend-following CTAs. The AWTR measures the average trending quality of the markets in the portfolio over a lookback period of P. On a daily basis, we’ll compare the AWTR to the sum (i.e. non-compounded) of the daily returns of the SG Trend Index (SGTI) over the same lookback period.

### Time Series Comparison

Chart 1 shows both the AWTR and the SGTI for lookback P = 262 days (approximately one year) for all samples in the dataset (Jan-2005 through Mar-2017). Click on each of the charts below to see a larger version.

Chart 2 shows the same data, but focuses on the latest five-year period:

We can also look at the two series for other lookback periods. Chart 3 shows the latest five-year period for P = 131 days (approximately six months) and Chart 4 is the same except P is now 524 days (approximately two years).

### Scatter Plot Comparison

Visually comparing the two series seems to indicate there is a relationship, particularly over the last five years. Scatter plots should give us a better idea of the strength of the relationship.

Chart 5 shows the AWTR vs SGTI for lookback of P = 262 days over the entire dataset from Jan-2005 through Mar-2017. R² is 0.44.

The relationship seems particularly well defined for Average Weighted Trend Ratio values > 0.15. This seems reasonable, as we would expect a trend-quality measure to have more significance when markets are trending than when they aren’t.

Chart 6 shows the same data, but includes only AWTR values >= 0.15. The orange-colored outliers in the lower left are all values that occured in July 2009, when the outsized profits of 2008 turned into the losses of 2009. By limiting the data to AWTR >= 0.15, the value of R² rises to 0.54.

The relationship also seems stronger when only the last five years of data is considered. Chart 7 shows the scatter plot for the last five years for all values of AWTR and P = 262. In this case, R² = 0.81.

Considering other lookback periods, Chart 8 shows the last five years for P = 131. While there is still a relationship, it is somewhat weaker than when the lookback period is one year. R² = 0.63.

Chart 9 is the same except that P is changed to 524, or approximately two years. For this set of data, R² = 0.73.