RESEAR CH
Historical Analysis of CTA Performance in Q4 Relating returns to trends ROBERT ROTELLA, JAGDEESH PRAKASAM & JOHN HARPER, ROTELLA CAPITAL MANAGEMENT
O
ne issue faced by fund managers is developing expectations for the future returns of their products. This task for
CTAs is made more complicated by the fact that many strategies are designed to be uncorrelated to conventional market indices, benchmarks and indicators. An approach to generating such a forecast
Fig.1 SNR = 0.077 104
is to relate strategy returns to bespoke factors that pertain to the known characteristics of the strategy (e.g., trend following or mean reversion). If some of these factors can themselves be predicted with accuracy, then in principal that prediction can be extrapolated to the returns of the strategy.
103
While CTA returns tend to be uncorrelated to commonly used factors (such as Fama-French factors), it is possible to follow this approach and define custom indicators that have explanatory value. An example of this is a market trend index: if markets exhibit strong, persisting trends, one would expect trend following CTAs to perform well. If trends are weak or nonexistent, trend following CTAs ought to have flat or negative performance. This effect can be measured quantitatively.
102 101 100
2468 10 TIME
SNR = 0.4 104
103 102 101
100 99
24 6 810 TIME
SNR = 1 108 0.10
SNR index PL
106 Jun 2000 Dec 2001 Dec 2003 Dec 2004 Jun 2006 Dec 2007 Jun 2009 Dec 2010 Jun 2012 Dec 2013 Mar 2015 104 102 Sector 100
2468 10 TIME
Table 1 p-values for Q4 sector SNR when compared to Q1-Q3 Less than Q1-Q3
Commodity Currency Equity Interest Rate
95.72% 50.14% 63.12% 36.98%
4.28% 49.86% 36.88% 63.02%
There are many ways to define the concept of “trend.” A market trend index is one possible approach, which happens to be a useful explanatory factor for CTA (as defined by the Newedge CTA index) performance. The first step in computing the market trend index is to calculate a signal to noise ratio (SNR) for asset prices over a given lookback period. The SNR is simply the absolute price change over the lookback period divided by the sum of the absolute daily price changes. The lookback period may vary depending on the length of trends of interest, but two months or longer tends to relate sufficiently closely to CTA returns in terms of linear correlation to a benchmark index. The closer the
price path is to a straight line, the higher the SNR. A perfectly straight line will have an SNR of 1, while a completely flat path will have an SNR of 0. In Fig.1 are some examples with generated data.
In the second step to computing the market trend index, the SNR for individual futures is aggregated into an index by taking the relevant average. For example, the equity sector trend index is the average of the SNR for equity futures such as the Dow Jones Industrial Average, S&P 500 E-Mini, Eurex DAX 30 and the FTSE 100. An overall trend index would be the average among all tradable markets.
Because this market trend index is a measure of how “trendy” futures prices are, we expect it to correlate with CTA trend follower performance over comparable time frames. In Fig.2 is a plot of the Newedge CTA index quarterly returns (blue) alongside the SNR trend index (red) computed for the same period.
The correlation between these two series is 62%. Fig.3 the same data are depicted in scatterplot form.
Notice the clustering of points around the regression line.
Given this quantitative definition of the level of trend, statistical tests can be performed to examine
Fig.2 NewEdge Rolling Quarterly PL vs. Market Trend Index
0.20 0.15
0.20 0.15 0.10 0.05 0.00 -0.05 -0.10
Greater than Q1-Q3
Not Equal to Q1-Q3
8.57% 99.72% 73.76% 73.97%
16
PRICE
PRICE
PRICE
TREND INDEX
PL
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