This document presents the results of testing a time series momentum strategy on commodities futures and bonds. It describes the strategy of going long or short an asset based on the returns in a past lookback period. It shows correlation coefficients, p-values and backtest results for different lookback-holding period pairs on aluminum, copper, treasury notes and Korean bonds. Live trading results are also presented and compared to a simple moving average strategy.

1. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Trend Following
Abhishek Kulkarni
Dublin City University
6th November 2014

2. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Overview
Time Series Momentum
Testing significance of correlation between returns
Data and methodology
Backtest and Live trade results
Remarks

3. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Time Series Momentum: Definition
Definition
Past returns of a security predict future returns .
Characterized by serial correlation of returns.
If the returns over past n months were positive(negative) , it will be
positive(negative) for the next m months before a trend reversal occurs .
Direct test of random walk hypothesis .

4. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Why assets exhibit time series momentum ?
For futures, the persistence of roll returns.
The slow diffusion, analysis, and acceptance of new information.
The forced sales or purchases of assets of various type of funds.
Market manipulation by high-frequency traders.

5. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Correlation coefficient for two samples x, y is given by the well known formula
ρ(X, Y) =
Cov(X, Y)
Var(X)Var(Y)
.
In practice, we use the MATLAB routine corrcoef to obtain the p-value and the
correlation coefficient r.
The pair (X,Y) that has optimal correlation and minimum p-value is chosen as
lookback and holding period .
If the returns during lookback period were positive (negative) , long (short )
the asset for the duration specified by holding period .

6. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Data and methodology
Strategy is tested and traded on three futures and Korean Bond .
Historical data is divided into two intervals , backtest window and live
trading window.
Test statistic is calculated on backtest data and is used as yardstick for
live trading .

7. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Dividing the historical data

8. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Flowchart
Asset Data
Optimal Lookback , Holding period
Calculate returns
of lookback period
Returns positive? Short the assetLong the asset yes
no

9. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Backtest Results
Aluminium
Figure: Correlation coefficient Table. Rows represent lookback and columns represent
holding period

10. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: P Value Table. A low p value indicates that the correlation is significantly
different from zero

11. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 1 to 6 months on backtest data.

12. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 7 to 12 months on backtest data.

13. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Live Trade Result
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 1 to 6 months on live trading data..

14. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 7 to 12 months on live trading data.

15. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Copper
Figure: Correlation coefficient Table. Rows represent lookback and columns represent
holding period

16. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: P Value Table. A low p value indicates that the correlation is significantly
different from zero

17. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 1 to 6 months on backtest data.

18. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 7 to 12 months on backtest data.

19. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Live Trade Result
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 1 to 6 months on live trading data..

20. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 7 to 12 months on live trading data.

21. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Treasury Note Future
Figure: Correlation coefficient Table. Rows represent lookback and columns represent
holding period

22. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: P Value Table. A low p value indicates that the correlation is significantly
different from zero

23. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 1 to 6 months on backtest data.

24. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 7 to 12 months on backtest data.

25. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Live Trade Result
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 1 to 6 months on live trading data..

26. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 7 to 12 months on live trading data.

27. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Korean Bond
Figure: Correlation coefficient Table. Rows represent lookback and columns represent
holding period

28. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: P Value Table. A low p value indicates that the correlation is significantly
different from zero

29. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 1 to 6 months on backtest data.

30. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 7 to 12 months on backtest data.

31. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Live Trade Result
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 1 to 6 months on live trading data..

32. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Figure: Sharpe ratio , APR and cumulative returns for 1 month holding period and for
lookback periods ranging from 7 to 12 months on live trading data.

33. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Backtest Results for TSMOM
Symbol Lookback-Holding
period optimal pair
(months)
Corrleation APR Sharpe
ratio
Aluminium(LME) (5,1) 0.3358 6.39% 1.92
Copper
(LME)
(11,1) 0.50 32.02% 1.39
TU
(CBOT)
(9,1) 0.61 1.09% 2.13
Korean Bond (10,1) 0.71 0.45% 1.55

34. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Live trade Results for TSMOM
Symbol Lookback-Holding
period optimal pair
(months)
Corrleation APR Sharpe
ratio
Aluminium(LME) (5,1) 0.3358 22.69% 1.36
Copper
(LME)
(11,1) 0.50 4.9% 1.39
TU
(CBOT)
(9,1) 0.61 1.09% 1.33
Korean Bond (10,1) 0.71 -
2.10%
-1.77

35. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Moving Average
Backtest Results for Moving Average Strategy
Symbol Moving Aver-
age window
(months)
APR Sharpe ra-
tio
Maximum
drawdown
Aluminium(LME) 4 5.86% 1.88 -51.22%
Copper
(LME)
4 3.68% 0.85 -89.40 %
TU
(CBOT)
4 1.60% 1.71 -81.20
Live Trading Results for Moving Average Strategy
Symbol Moving Aver-
age window
(months)
APR Sharpe ra-
tio
Maximum
drawdown
Aluminium(LME) 4 9.57% 1.07 -84.56%
Copper
(LME)
4 5.08% 1.17 -99.99 %
TU
(CBOT)
4 -0.34% -1.49 -96.14%

36. Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks
Remarks
Higher correlation doesn’t mean higher returns .
TSMOM was successful on futures but not on Korean bond .