Therefore, even on a signal-to-noise ratio basis the stock pair (AB) does bet-
ter than stock pair (AC). Notice that having a high value for the specific
risk/variance (provided it is stationary) is highly desirable as it improves the
SNR. A higher specific variance means higher stock volatility, indicating that
a high volatility environment is conducive for pairs trading.
SUMMARY
The candidate list of potentially cointegrated stock pairs can be com-
piled by the process of identifying similar stocks.
The notion of similarity is formalized using a distance measure between
two stocks.
The distance measure is based on an APT model possibly with funda-
mental risk factors.
The candidate list of pairs is determined by choosing pairs with distance
values within a certain threshold.
The distance measure is the absolute value of the common factor corre-
lation between the two stocks.
If the common factor correlation is +1 or –1 and the integration of the
specific return series of the stocks involved are stationary, then condi-
tions for cointegration are satisfied.
It may be possible to trade pairs of stocks even though they deviate from
ideal conditions of cointegration.
The signal-to-noise ratio as defined is a measure of the deviation from
the ideal condition of cointegration.FURTHER READING MATERIAL
Cointegration Properties
Philips, P. C. B. and S. N. Durlauf. “Multiple Time Series Regression with Integrated
Processes,”Review of Economic Studies53 (1986): 473–495.
Park, J. Y. S. Oularis and B. Choi. “Spurious Regressions and Tests for Co-integra-
tion” (CAE working paper 88–07, Cornell University, Ithaca, New York
(1988).)
Near Cointegration
Haldrup, Niels and Michael Jansson. “Spurious Regression, Co-integration and
Near Co-integration: A Unifying Approach” (working papers, DK-8000, De-
partment of Economics, University of Aarhus, Denmark, 1999.)
102 STATISTICAL ARBITRAGE PAIRS