On Feedforward Stock Trading Control Using a New Transaction Level Price Trend Model

In this article, we provide a new Markovian-type model for stock price trend analysis at the transaction level, and illustrate its use for trading in conjunction with a controller, which makes buy and sell decisions. Central to our formulation is a sequence of i.i.d. random variables $T_k$, which corresponds to the number of transactions between reversals in price direction. For a trader, this is an important indicator of the “duration” of a trend. For processes with “large” $T_k$, there is an incentive to try and capitalize by buying stock when a temporary trend is “up” and selling when it is “down.” The extent to which this is possible is determined by a model parameter $p_e$, called the probability of efficiency, which indicates the likelihood that the bid, ask, and current price are such that one can seamlessly enter or exit the market without slippage. The degree to which a trader can exploit trending behavior is quantified in our main result, which provides the expected value of the trading gain resulting from a strategically constructed feedforward switching controller. This article also includes an example illustrating application of the theory using historical data.