Market Influence of Portfolio Optimizers

Abstract

We study the feedback effects induced by portfolio optimizers on the underlying asset prices.Through their interaction with reference traders, who trade based on some aggregate incomes process, they are assumed to move asset prices away from the standard log-normal model. With market clearing as our main constraint, we solve analytically for the approximate dynamics of the asset price assuming that the wealth of the portfolio optimizers is small relative to the total market capitalization of the stock. We also calculate numerically the influence of portfolio optimizers when their wealth is not so small. There is good agreement between the numerical and analytical results when the wealth of the optimizers is small. We find that portfolio optimizers influence the price of the risky asset so as to decrease its volatility. The optimal allocation to the risky asset also changes as a result of the portfolio optimizers' actions. In general, it is advantageous to hold more of the risky asset, relative to the log normal Merton model.

A Feedback Model for the Financialization of Commodity Markets

“…We have checked that (34) has excellent agreement with the order ǫ asymptotic expansion derived by Nayak and Papanicolaou [28] in the small feedback regime.…”

“…In Section 4 we present the numerical solutions to the first couple of stages and quantify the induced correlation between the equity and commodity markets. In Appendix B we return to the feedback model of Nayak and Papanicolaou [28] and present an explicit solution to the first stage in the feedback sequence which greatly facilitates the model analysis. Appendix C provides a tractable but less realistic model with exponential utility, where the full fixed point problem can be reduced to solution of a system of ordinary integro-differential equations.…”

“…In a related but simpler setting, Nayak and Papanicolaou [28] studied a feedback model for the equity market in which a single stock Y is traded by reference traders (who play the role of the commodity users in Section 2 of our analysis). The reference traders have a stochastic income process I t .…”

“…This kind of demand structure in a continuous-time model is used for instance in [14,32,28]. We also assume a fixed constant supply A of the commodity available for trading at each time period.…”

An Equilibrium-Based Model of Stock-Pinning

“…Their paper showed that hedging strategies increase the volatility of the underlying asset. Nayak and Papanicolaou [11,12] extended the methods developed in that paper to the situation where portfolio optimizers cause deviation from a simple log-normal model.…”