# 14-039/III (2014-03-20)

Lukasz Gatarek, Erasmus University Rotterdam; Lennart Hoogerheide, VU University Amsterdam; Herman K. van Dijk, VU University Amsterdam, Erasmus University Rotterdam
Bayesian analysis; cointegration; linear normalization; orthogonal normalization; pairs trading; statistical arbitrage
JEL codes:
C11, C15, C32, C58, G17

We investigate the direct connection between the uncertainty related to estimated stable ratios of stock prices and risk and return of two pairs trading strategies: a conditional statistical arbitrage method and an implicit arbitrage one. A simulation-based Bayesian procedure is introduced for predicting stable stock price ratios, defined in a cointegration model. Using this class of models and the proposed inferential technique, we are able to connect estimation and model uncertainty with risk and return of stock trading. In terms of methodology, we show the effect that using an encompassing prior, which is shown to be equivalent to a Jeffreys’ prior, has under an orthogonal normalization for the selection of pairs of cointegrated stock prices and further, its effect for the estimation and prediction of the spread between cointegrated stock prices. We distinguish between models with a normal and Student t distribution since the latter typically provides a better description of daily changes of prices on financial markets. As an empirical application, stocks are used that are ingredients of the Dow Jones Composite Average index. The results show that normalization has little effect on the selection of pairs of cointegrated stocks on the basis of Bayes factors. However, the results stress the importance of the orthogonal normalization for the estimation and prediction of the spread — the deviation from the equilibrium relationship — which leads to better results in terms of profit per capital engagement and risk than using a standard linear normalization.