Chair: Milos Kopa, Charles University in Prague, MFF, Czech Republic
Portfolio efficiency testing with respect to stochastic dominance criteria - representative sets of utility functions
Milos Kopa (firstname.lastname@example.org), Thierry Post (email@example.com)
We present linear formulations of stochastic dominance relations for testing whether a given portfolio is efficient with respect to all portfolios which can be created from the considered set of assets. The formulations are derived for several different types of stochastic dominance (N-th order stochastic dominance, decreasing absolute risk aversion stochastic dominance, increasing relative risk aversion stochastic dominance). Our approach is based on the theory of representative utility functions. Application to historical stock market data suggests that a passive stock market portfolio is inefficient relative to concentrated portfolios of small-cap stocks.
Keywords: stochastic dominance, portfolio efficiency, risk aversion
A Comparison of Surrogate Relaxations for a Capital Budgeting Model
Anabela Costa (firstname.lastname@example.org), José Paixão (email@example.com)
Contingent claims analysis can be used for project evaluation when the project develops stochastically over time and the decision to invest into this project can be postponed. In that perspective, a scenario based capital budgeting model that captures risk uncertainty and managerial flexibility, maximizing the time-varying of a portfolio of investment options has been presented in the literature. With that linear integer programming model, one determines the project value but, also, one discerns when to exercise the option to invest. Specifically, the option to postpone an investment is exercised if such decision yields a value larger than the value of immediate exercise. Since the value of each project is estimated by the binomial option pricing approach, the number of variables of the corresponding linear integer program is straightforwardly related to the number of states in the binomial tree which grows exponentially with the number of projects and the number of periods. According to our experience, the linear integer problem turns out to be computationally quite intractable even for a small number of projects or a reduced number of periods. Hence, we present and discuss surrogate constraint relaxation approaches for the problem that lead to the determination of upper bounds for the optimal value of the problem. In each surrogate relaxation, a surrogate constraint represents a weighted nonnegative linear combination of the constraints of the original model. We derive and computationally test several of rules for initializing and updating the constraint weights associated to the surrogating process. In order to determine lower bounds for the optimal value of the problem, the optimal solution of the surrogate relaxation is used to guiding a greedy-type heuristic procedure for building up a feasible solution for the problem. For comparing the surrogate relaxation approaches, computational experience is carried out for a set of test instances previously considered in the literature.
Keywords: Real options, Capital budgeting, Surrogate Relaxation
Portfolio Optimisation with Second-Order Stochastic Dominance Criteria
Nonthachote Chatsanga (firstname.lastname@example.org), Andrew J. Parkes (email@example.com )
The typical mean-variance portfolio optimisation model fails to capture some characteristics of financial assets which eventually results in misestimating risk and could subsequently lead to falsely optimistic solutions. Specifically, uncertainty lies in return and risk estimation which should be included properly into the optimisation model. We estimate the joint distribution of a portfolio using Markov Chain Monte Carlo (MCMC) simulation where dependence structure of assets in the portfolio is modeled by a copula. Then we solve for optimal allocation under second-order stochastic dominance (SSD) criteria where the objective function can be formulated by Conditional Value at Risk (CVaR). In terms of portfolio performance, we observe the portfolio returns over some specific out-of-sample periods. We apply the SSD optimisation framework as a portfolio rebalancing policy over the out-of-sample periods in which the portfolio allocation in the next period is either the reoptimised allocation based on updated information of asset returns or the carried-over allocation from the last period. The test results show that our portfolio outperforms other portfolios with various rebalancing policies such as buy-and-hold or continuously rebalancing.
Keywords: Second-Order Stochastic Dominance, Markov Chain Monte Carlo simulation, Copula