Chapter 2: FAQs 67
What is Cointegration?
Short Answer
Two time series are cointegrated if a linear combination
has constant mean and standard deviation. In other
words, the two series never stray too far from one
another. Cointegration is a useful technique for studying
relationships in multivariate time series, and provides
a sound methodology for modelling both long-run and
short-run dynamics in a financial system.
Example
Suppose you have two stocksS 1 andS 2 and you find
thatS 1 − 3 S 2 is stationary, so that this combination
never strays too far from its mean. If one day this
‘spread’ is particularly large then you would have sound
statistical reasons for thinking the spread might shortly
reduce, giving you a possible source of statistical
arbitrage profit. This can be the basis forpairs trading.
Long Answer
The correlations between financial quantities are noto-
riously unstable. Nevertheless correlations are regularly
used in almost all multivariate financial problems. An
alternative statistical measure to correlation is cointe-
gration. This is probably a more robust measure of the
linkage between two financial quantities but as yet there
is little derivatives theory based on the concept.
Two stocks may be perfectly correlated over short
timescales yet diverge in the long run, with one grow-
ing and the other decaying. Conversely, two stocks may
follow each other, never being more than a certain dis-
tance apart, but with any correlation, positive, negative
or varying. If we are delta hedging then maybe the short
timescale correlation matters, but not if we are hold-
ing stocks for a long time in an unhedged portfolio. To
