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Should Stochastic Volatility Matter to the Cost‐Constrained Investor?

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  • Scott M. Weiner

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.

Suggested Citation

  • Scott M. Weiner, 2004. "Should Stochastic Volatility Matter to the Cost‐Constrained Investor?," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 131-139, January.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:1:p:131-139
    DOI: 10.1111/j.0960-1627.2004.00185.x
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    References listed on IDEAS

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    1. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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    Cited by:

    1. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2011. "Transaction Costs, Trading Volume, and the Liquidity Premium," Papers 1108.1167, arXiv.org, revised Jan 2013.
    2. Feghhi Kashani, Mohammad & Mohebimajd, Ahmadreza, 2021. "Outperformance Testing of a Dynamic Assets Portfolio Selection Supplemented with a Continuous Paths Levy Process," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 16(2), pages 253-282, June.

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