Robust Positive Expectation Feedback Trading for Stock Pairs

Summary

This paper extends the Robust Positive Expectation theorem from a single stock to a pair of stocks. The original result concerns combining specially designed linear feedback controllers, one long and one short, to produce a gain-loss function with robustly positive expected value across a broad class of stochastic stock-price processes.

For the two-stock case, the theorem relies on assumptions about the stocks’ expected returns, including a price-correlation condition and bounded nonzero momentum. Given known uncertainty bounds for the parameters, the paper derives necessary and sufficient conditions on the controller’s positive feedback parameter for robust positive expectation. It states that the result encompasses the single-stock version and can be interpreted as pairs trading. The excerpt does not provide the precise conditions or empirical tests, so it does not establish performance in live markets.

Key ideas

• The theorem extends robust positive-expectation feedback trading from one stock to a pair.
• The strategy combines a long and a short linear feedback controller.
• The pair-stock result depends on assumptions about price correlation and bounded nonzero momentum.
• Parameter uncertainty bounds determine conditions for robust positive expectation.
• The paper connects its result to pairs trading but gives no empirical performance evidence here.

Tags

# A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control


# A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control









The starting point of this paper is the so-called Robust Positive Expectation (RPE) Theorem, a result which appears in literature in the context of Simultaneous Long-Short stock trading. This theorem states that using a combination of two specially-constructed linear feedback trading controllers, one long and one short, the expected value of the resulting gain-loss function is guaranteed to be robustly positive with respect to a large class of stochastic processes for the stock price. The main result of this paper is a generalization of this theorem. Whereas previous work applies to a single stock, in this paper, we consider a pair of stocks. To this end, we make two assumptions on their expected returns. The first assumption involves price correlation between the two stocks and the second involves a bounded non-zero momentum condition. With known uncertainty bounds on the parameters associated with these assumptions, our new version of the RPE Theorem provides necessary and sufficient conditions on the positive feedback parameter K of the controller under which robust positive expectation is assured. We also demonstrate that our result generalizes the one existing for the single-stock case. Finally, it is noted that our results also can be interpreted in the context of pairs trading.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.