Should Stochastic Volatility Matter to the Cost‐Constrained Investor?

Abstract

Significant strides have been made in the development of continuous‐time portfolio optimization models since Merton (1969). Two independent advances have been the incorporation of transaction costs and time‐varying volatility into the investor's optimization problem. Transaction costs generally inhibit investors from trading too often. Time‐varying volatility, on the other hand, encourages trading activity, as it can result in an evolving optimal allocation of resources. We examine the two‐asset portfolio optimization problem when both elements are present. We show that a transaction cost framework can be extended to include a stochastic volatility process. We then specify a transaction cost model with stochastic volatility and show that when the risk premium is linear in variance, the optimal strategy for the investor is independent of the level of volatility in the risky asset. We call this the Variance Invariance Principle.