"The success of many trading algorithms depends on the quality of the predictions of stock price movements. Predictions of the price of a single stock are generally less accurate than predictions of a portfolio of stocks. A classical strategy which makes the most of the predictability of the joint, rather than the individual, behavior of two assets is `pairs trading' where a portfolio consisting of a linear combination of two assets is traded. At the heart of the strategy is how the two assets co-move. As an example, take two assets whose spread, that is the dierence between their prices, exhibits a marked pattern and deviations from it are temporary. Pairs trading algorithms prot from betting on the empirical fact that spread deviations tend to return to their historical or predictable level.

In this paper we derive the optimal trading strategy for an agent who takes positions in n co-integrated assets. At the core of the strategy is to prot from the structural dependence in the assets' price dynamics. We assume that the drifts of the assets are co-integrated and develop an algorithmic trading strategy where the investor maximizes expected utility of wealth. We provide an explicit closed-form expression for the optimal (dynamic) investment strategy and show that it is ane in the co-integration factor. Furthermore, we use trading (ITCH) data from the Nasdaq exchange to calibrate the model and then use simulations to illustrate how the strategy performs when the investor takes positions in three assets: Google, Facebook, and Amazon.

Our paper is closest to that of Tourin and Yan (2013) who develop an optimal portfolio strategy to invest in two risky assets and the money market account. Tourin and Yan assume that log-prices are co-integrated and nd, in closed-form, the dynamic trading strategy that maximizes the investor's expected utility of wealth. In our model we generalize Tourin and Yan to allow the investor to trade in m co-integrated assets and provide an explicit closed-form solution of the dynamic trading strategy. We assume that the drift of asset returns consists of an idiosyncratic and a common drift component. The common component, which we label short-term alpha, is a zero-mean reverting process which is an essential source of prots in the trading strategy { it determines how to benet from short-lived investment opportunities in the collection of assets."

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