On the strategic behavior of large investors: A mean-variance portfolio approach

Abstract

One key assumption of Markowitz’s model is that all traders act as price takers. In this paper, we extend this mean-variance approach in a setting where large investors can move prices. Instead of having an individual optimization problem, we find the investors’ Nash equilibrium and redefine the efficient frontier in this new framework.We also develop a simplified application of the general model, with two assets and two investors to shed light on the potential strategic behavior of large and atomic investors. Our findings validate the claim that large investors enhance their portfolio performance in relation to perfect market conditions. Besides, we show under which conditions atomic investors can benefit in relation to the standard setting, even if they have not total influence on their eventual performance. The ‘two investors-two assets’ setting allows us to quantify performance and do sensitivity analysis regarding investors’ market power, risk tolerance and price elasticity of demand.Finally, for a group of well known ETFs, we empirically show how price variations change depending on the volume traded. We also explain how to set up and use our model with real market data.