Investigation of Portfolio Choice that Tracks a Continuously Moving Target

Abstract

We investigate the problem of tracking a moving target, specifically a given continuously compounded, deterministic growth rate by using linear quadratic control theory. We first present some preliminaries and then derive and solve the corresponding Riccati equations for our problem. We then implement our findings in MATLAB by using one stock from the FTSE100 and a risk-less
asset and analyze the results. Furthermore, we focus on situations when the performance of our tracking is not the expected and highlight when this can happen and what the risks involved are. We also present situations when we would need to borrow or short sell, like in the case of aggressively tracking a target. We then briefly present the extension to multi asset portfolios. Finally, we discuss the case of tracking a market index.