This paper considers the worst-case Conditional Value-at-Risk (CVaR) in the situation where only partial information on the underlying probability distribution is available. The minimization of the worst-case CVaR under mixture distribution uncertainty, box uncertainty, and ellipsoidal uncertainty are investigated. The application of the worst-case CVaR to robust portfolio optimization is proposed, and the corresponding problems are cast as linear programs and second-order cone programs that can be solved efficiently. Market data simulation and Monte Carlo simulation examples are presented to illustrate the proposed approach.

Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management

Incentive or performance fees for money managers are frequently accompanied by high-water mark provisions which condition the payment of the performance fee upon exceeding the maximum achieved share value. In this paper, we show that hedge fund performance fees are valuable to money managers, and conversely represent a claim on a significant proportion of investor wealth. The high-water mark provisions in these contracts limit the value of the performance fees. We provide a closed-form solution to the high-water mark

High-Water Marks and Hedge Fund Management Contracts

https://www.maths.univ-evry.fr/pages_perso/jeanblanc/pubs/bejm.pdf

Optimal investment decisions when time-horizon is uncertain

http://www-optima.amp.i.kyoto-u.ac.jp/~fuku/papers/WCVaR-template.pdf

Portfolio selection with uncertain exit time: A robust CVaR approach

We examine the use of second-order stochastic dominance as both a technique for constructing portfolios and also as a way to measure performance As a preference-free technique second-order stochastic dominance will suit any risk-averse investor, and it does not require normally distributed returns Using in-sample data, we construct portfolios such that their second-order stochastic dominance over a benchmark is most probable The empirical results based on 21 years of daily data suggest that this portfolio choice technique significantly outperforms the benchmark out-of-sample Moreover, its performance is typically better - and frequently much better - than several alternative portfolio-choice approaches using equal weights, mean-variance optimization, or minimum-variance methods

/pdf/improved-portfolio-choice-using-second-order-stochastic-74ivtgje2q.pdf

Improved Portfolio Choice Using Second-Order Stochastic Dominance

We generalize Markowitz analysis to the situations involving an uncertain exit time. Our approach preserves the form of the original problem in that an investor minimizes portfolio variance for a given level of the expected return. However, inputs are now given by the generalized expressions for mean and variance-covariance matrix involving moments of the random exit time in addition to the conditional moments of asset returns. Although efficient frontiers in the generalized and the standard Markowitz case may coincide under certain conditions, we demonstrate that, by means of an example, in general that is not true. In particular, portfolios efficient in the standard Markowitz sense can be inefficient in the generalized sense and vice versa. As a result, an investor facing an uncertain time horizon and investing as if her time of exit is certain would in general make suboptimal portfolio allocation decisions. Numerical simulations show that a significant efficiency loss can be induced by an improper use of standard mean-variance analysis when time horizon is uncertain.

Branko Uroevi

Papers

Static Mean-Variance Analysis with Uncertain Time Horizon