Presentation 4
Kunal Jain
April 7, 2010
Economics 201FS
Pairs Trading

Market Neutral Strategy looking at correlations within day-to-day
price movements of certain equities

Competitors in same sector
 Liquid Equities
 Used to Hedge sector- and market-risk.

Finds some sort of index or relative mean

Calculate Standard Deviations
 Mean Reversion

When correlation breaks, one equity trades up, while other trades
down:



Sell outperforming stock
Buy underperforming stock
Convergence Trade
HAR-RV Model Adaptation
HAR-RV Model Adaptation
HAR-RV Model Adaptation

Adapt HAR-RV Model to calculate Realized Betas between two
competitor equities within same sector to predict Betas:
Βt+1 = β0 + αD βt + αW βt-5,t + αM βt-22,t + εt+1

t=1 corresponds to daily Beta, t=5 corresponds to weekly Beta, t=22
corresponds to monthly Beta.

This model uses betas realized over a 1-day, 5-day, and 1-month time
interval to build the conditional betas.
HAR-RV Model Adaptation

Intuition: Test whether the HAR adaptation, using daily, weekly,
monthly Betas, can be implemented specifically in terms of Pairs
Trading to predict Beta and take advantage of strategy.

Negates Drift associated with Pairs Trading


Unless the relative prices return closer to their historical levels, the pair trade
will not be profitable
Take advantage of high-frequency data
 Potential better ways of calculating Beta?
HAR-RV Model Adaptation

Chose liquid competitor equities and Time Interval

Coca Cola (KO): 4/9/1997-4/14/2000
 Pepsi (PEP): 4/9/1997-4/14/2000

Calculate HAR-Beta coefficients (D,W,M)


Implemented in MatLAB
Find conditional Beta using observed data and Beta-coefficients from
model

Found using observed Betas (Alphas)

Calculate expected relative return based on conditional Beta

Calculate/Compare actual return to estimate differential
HAR-B Model





Model implemented in MatLAB
Calculate HAR-Beta coefficients (D,W,M)
 Implemented in MatLAB
 5-minute sampling
.0510
Bt-5,t
.1623
Bt-22,t
.4948
constant
.0001
Mean differential: 1.9869e-004
Calculated Autocorrelations for Equities:




Coefficient
Bt
Conditional Beta obtained
Utilized Conditional Beta to calculate expected relative return
Calculated Differential: Observed minus Expected


Bt+1
Expect Negative autocorrelation between differential of equities
Expect approximately Zero autocorrelation with log-returns of equity
with itself
Mean Autocorrelation: -0.1120
Autocorrelation with self (Pepsi): -0.0873
HAR-B Model
Bt+1
HAR-Beta Coefficients
(1-Minute)
HAR-Beta Coefficients
(7-minute)
HAR-Beta Coefficients
(10-minute)
Bt
0.0850
0.0516
0.0250
Bt-5,t
0.1342
0.0817
0.0964
Bt-22,t
0.4544
0.5951
0.5021
Constant
0.0266
0.0730
0.1075
Mean Autocorrelation
(Differentials)
-0.0957
-0.1158
-0.1179
Mean SELF Autocorrelation-Pepsi
-0.0710
-0.0939
-0.0984
Further Research





Significance Levels
More Competitor Pairs
Different Time Intervals
Autocorrelation for all returns
Calculate Strategy Returns and Profitability