Seminar: Optimal Portfolios under Worst Case Scenarios

Time: 10:30am – 11:30am, March 5th 2012

Location: Wang Dao Han Conference Room, Lingnan (University) College

Reporter: Carole Bernard (University of Waterloo)

Dr Carole Bernard joined the University of Waterloo in 2007 as an Assistant Professor in the Department of Statistics and Actuarial Science where she had previously been a postdoctoral fellow. In 2005, she obtained her PhD in Finance from the University of Lyon in France on the subject of “Valuation of Guarantees in Insurance and in Finance using the Option Theory”. It received the award for the best PhD in Finance (2005) in France. Since then, Dr. Bernard has published in many journals in actuarial science, mathematics, economics and finance. She was recently awarded the EGRIE Young Economist Best Paper Award for the paper "Financial bounds for Insurance Claims" with Steven Vanduffel.

Seminar Introduction:
Standard portfolio theories such as Expected Utility Theory, Yaari's Dual Theory, Cumulative Prospect Theory and Mean-Variance optimization all assume that investors only look at the distributional properties of strategies and do not care about the states of the world in which the cash-flows are received. In a very interesting paper Dybvig (1988a, 1988b) essentially showed that in these instances optimal portfolios are decreasing in the state price density, also pointing indirectly to the important role of diversified portfolios. In this seminar we first observe that the worst outcomes for optimal strategies then exactly occur when the market declines (i.e. during a financial crisis), but this is at odds with the aspirations and requirements of many investors. Hence we depart from the traditional behavioral setting and study optimal strategies for investors who do not only care about the distribution of wealth but, additionally, also impose constraints on its interaction with the (stressed) financial market. Preferences become state-dependent and we are able to assess the impact of these on trading decisions. We construct optimal strategies explicitly and show how they outperform traditional diversification strategies under worst case scenarios.