Copula Conditional Probabilities for Pairs Trading
Summary
This note explains a long-short pairs strategy that uses a copula to model the dependence between two stocks. After selecting a pair, for example with a cointegration test, the method fits the copula and each stock’s empirical distribution on a formation sample. Prices in the trading sample are mapped to quantiles, from which conditional probabilities estimate whether one stock looks unusually cheap or expensive relative to the other.
The strategy opens a long spread when one conditional probability is sufficiently low and the other sufficiently high, and reverses the signal for a short spread. It exits when probabilities return across the median boundary; the note discusses both requiring both probabilities to cross and exiting when either one does. It also specifies how its implementation resolves overlapping signals. The examples and cited research illustrate the method, but provide no general evidence of profitability. Results depend on pair selection, fitted dependence, thresholds, formation data, and exit rules.
Key ideas
- The strategy fits a copula and marginal distributions on a formation period, then evaluates conditional probabilities during trading.
- Extreme conditional probabilities indicate that one member of the pair may be under- or overvalued relative to the other.
- Opposing extreme signals open long or short spread positions, with the spread convention defined by the stock ordering.
- Exits can require both conditional probabilities to cross the midpoint or allow either one to trigger an exit.
- Pair choice, model fit, thresholds, and exit logic can materially affect the strategy, and the document gives no broad profitability evidence.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.