Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks

Trend Following

Abhishek Kulkarni

Dublin City University

6th November 2014

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

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 bepositive(negative) for the next m months before a trend reversal occurs .

Direct test of random walk hypothesis .

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.

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 thecorrelation coefficient r.

The pair (X,Y) that has optimal correlation and minimum p-value is chosen aslookback and holding period .

If the returns during lookback period were positive (negative) , long (short )the asset for the duration specified by holding period .

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 livetrading window.

Test statistic is calculated on backtest data and is used as yardstick forlive trading .

Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks

Figure: Dividing the historical data

Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks

Flowchart

Asset Data

Optimal Lookback , Holding period

Calculate returnsof lookback period

Returns positive? Short the assetLong the asset yes no

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 representholding period

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 significantlydifferent from zero

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 forlookback periods ranging from 1 to 6 months on backtest data.

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 forlookback periods ranging from 7 to 12 months on backtest data.

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 forlookback periods ranging from 1 to 6 months on live trading data..

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 forlookback periods ranging from 7 to 12 months on live trading data.

Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks

Copper

Figure: Correlation coefficient Table. Rows represent lookback and columns representholding period

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 significantlydifferent from zero

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 forlookback periods ranging from 1 to 6 months on backtest data.

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 forlookback periods ranging from 7 to 12 months on backtest data.

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 forlookback periods ranging from 1 to 6 months on live trading data..

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 forlookback periods ranging from 7 to 12 months on live trading data.

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 representholding period

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 significantlydifferent from zero

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 forlookback periods ranging from 1 to 6 months on backtest data.

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 forlookback periods ranging from 7 to 12 months on backtest data.

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 forlookback periods ranging from 1 to 6 months on live trading data..

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 forlookback periods ranging from 7 to 12 months on live trading data.

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 representholding period

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 significantlydifferent from zero

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 forlookback periods ranging from 1 to 6 months on backtest data.

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 forlookback periods ranging from 7 to 12 months on backtest data.

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 forlookback periods ranging from 1 to 6 months on live trading data..

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 forlookback periods ranging from 7 to 12 months on live trading data.

Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks

Backtest Results for TSMOMSymbol Lookback-Holding

period optimal pair(months)

Corrleation APR Sharperatio

Maximumdrawdown

Aluminium(LME) (5,1) 0.3358 6.39% 1.92 -51.22%Copper(LME)

(11,1) 0.50 32.02% 1.39 -81.91%

TU(CBOT)

(9,1) 0.61 1.09% 2.13 -46.89

Korean Bond (10,1) 0.71 0.45% 1.55 -89.86

Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks

Live trade Results for TSMOMSymbol Lookback-Holding

period optimal pair(months)

Corrleation APR Sharperatio

Maximumdrawdown

Aluminium(LME) (5,1) 0.3358 22.69% 1.36 -61.89%Copper(LME)

(11,1) 0.50 4.9% 1.39 -81.91%

TU(CBOT)

(9,1) 0.61 1.09% 1.33 -78.29

Korean Bond (10,1) 0.71 -2.10%

-1.77 NaN

Introduction Time Series Momentum Tests for Correlation Data and Methodology Flowchart Backtest Results Remarks

Moving Average

Backtest Results for Moving Average StrategySymbol Moving Aver-

age window(months)

APR Sharpe ra-tio

Maximumdrawdown

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 StrategySymbol Moving Aver-

age window(months)

APR Sharpe ra-tio

Maximumdrawdown

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%

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 .