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Should Stochastic Volatility Matter to the Cost‐Constrained Investor?
Author(s) -
Weiner Scott M.
Publication year - 2004
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.0960-1627.2004.00185.x
Subject(s) - transaction cost , volatility (finance) , stochastic volatility , portfolio optimization , economics , portfolio , volatility swap , econometrics , volatility risk premium , volatility smile , asset allocation , implied volatility , financial economics , microeconomics
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.