The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

Risk aversion under preference uncertainty

We show that if an agent is uncertain about the precise form of his utility function, his actual relative risk aversion may depend on wealth even if he knows his utility function lies in the class of constant relative risk aversion (CRRA) utility functions. We illustrate the consequences of this result for optimal asset allocation: poor agents that are uncertain about their risk aversion parameter invest less in risky assets than wealthy investors with identical risk aversion uncertainty.     

Market Valuation,Pension Fund Policy and Contribution Volatility

Summary Market valuation is becoming more and more popular, both in accounting and regulation, as well as in academic circles. For pension funds and their participants, the knowledge that market-valued pension liabilities can indeed be transferred to a third party, if necessary, is a great virtue. Using a simulation model, this paper demonstrates the implicit costs and benefits of using market valuation for a typical Dutch pension fund, which offers a guaranteed average pay nominal pension with conditional indexation. The impact turns out to be fairly small, if fixed discount rates are still used for conditional rights. However, if market valuation is used for both unconditional and conditional rights, contribution volatility increases significantly. A remedy is to increase the duration of assets considerably. It is not clear, though, whether this option is available for large pension funds given the limited supply of long-term bonds. This paper benefited from discussions at seminars at DNB, PVK, ABP and CPB. We are grateful to Jan-Marc Berk, Dirk Broeders, and Peter van Els for useful suggestions and comments on a previous version of the paper. Views expressed are those of the authors and do not necessarily reflect official positions of De Nederlandsche Bank.