Optimal Portfolio Choice and Stochastic Volatility

Anne Gron, Bjørn N. Jørgensen, Nicholas G. Polson*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


In this paper we examine the effect of stochastic volatility on optimal portfolio choice in both partial and general equilibrium settings. In a partial equilibrium setting we derive an analog of the classic Samuelson–Merton optimal portfolio result and define volatility-adjusted risk aversion as the effective risk aversion of an individual investing in an asset with stochastic volatility. We extend prior research which shows that effective risk aversion is greater with stochastic volatility than without for investors without wealth effects by providing further comparative static results on changes in effective risk aversion due to changes in the distribution of volatility. We demonstrate that effective risk aversion is increasing in the constant absolute risk aversion and the variance of the volatility distribution for investors without wealth effects. We further show that for these investors a first-order stochastic dominant shift in the volatility distribution does not necessarily increase effective risk aversion, whereas a second-order stochastic dominant shift in the volatility does increase effective risk aversion. Finally, we examine the effect of stochastic volatility on equilibrium asset prices. We derive an explicit capital asset pricing relationship that illustrates how stochastic volatility alters equilibrium asset prices in a setting with multiple risky assets, where returns have a market factor and asset-specific random components and multiple investor types.
Original languageEnglish
JournalApplied Stochastic Models in Business and Industry
Issue number1
Pages (from-to)1-15
Number of pages15
Publication statusPublished - 2012
Externally publishedYes


  • Portfolio choice
  • Stochastic volatility
  • Risk aversion
  • CAPM
  • Stein's lemma

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