Alex Weissensteiner

No-arbitrage conditions, scenario trees, and multi-asset financial optimization

Many numerical optimization methods use scenario trees as a discrete approximation for the true (multi-dimensional) probability distributions of the problems random variables. Realistic specifications in financial optimization models can lead to tree sizes that quickly become computationally intractable. In this paper we focus on the two main approaches proposed in the literature to deal with this problem: scenario reduction and state aggregation. We first state necessary conditions for the node structure of a tree to rule out arbitrage. However, currently available scenario reduction algorithms do not take these conditions explicitly into account. State aggregation excludes arbitrage opportunities by relying on the risk-neutral measure. This is, however, only appropriate for pricing purposes but not for optimization. Both limitations are illustrated by numerical examples. We conclude that neither of these methods is suitable to solve financial optimization models in asset-liability or portfolio management.

Cash management using multi-stage stochastic programming

We consider a cash management problem where a company with a given financial endowment and given future cash flows minimizes the Conditional Value at Risk of final wealth using a lower bound for the expected terminal wealth. We formulate the optimization problem as a multi-stage stochastic linear program (SLP). The company can choose between a riskless asset (cash), several default- and option-free bonds, and an equity investment, and rebalances the portfolio at every stage. The uncertainty faced by the company is reflected in the development of interest rates and equity returns. Our model has two new features compared to the existing literature, which uses no-arbitrage interest rate models for the scenario generation. First, we explicitly estimate a function for the market price of risk and change the underlying probability measure. Second, we simulate scenarios for equity returns with moment-matching by an extension of the interest rate scenario tree.

A stochastic programming approach for multi-period portfolio optimization

This paper extends previous work on the use of stochastic linear programming to solve life-cycle investment problems. We combine the feature of asset return predictability with practically relevant constraints arising in a life-cycle investment context. The objective is to maximize the expected utility of consumption over the lifetime and of bequest at the time of death of the investor. Asset returns and state variables follow a first-order vector auto-regression and the associated uncertainty is described by discrete scenario trees. To deal with the long time intervals involved in life-cycle problems we consider a few short-term decisions (to exploit any short-term return predictability), and incorporate a closed-form solution for the long, subsequent steady-state period to account for end effects.

A

In this paper, we consider optimal consumption and strategic asset allocation decisions of an investor with a finite planning horizon. A Q-learning approach is used to maximize the expected utility of consumption. The first part of the paper presents conceptually the implementation of Q -learning in a discrete state-action space and illustrates the relation of the technique to the dynamic programming method for a simplified setting. In the second part of the paper, different generalization methods are explored and, compared to other implementations using neural networks, a combination with self-organizing maps (SOMs) is proposed. The resulting policy is compared to alternative strategies.

Q

We investigate whether the returns of some industry portfolios predict the returns of other industry portfolios. We find a strong lead-lag structure which is statistically and economically significant. These findings suggest that information diffuses only gradually across industries. Moreover, we show that this predictability can be exploited in a mean-variance optimization framework. The calculated out-of-sample portfolio returns are attractive under different return-risk measures, and they show positive risk-adjusted

-Learning Approach to Derive Optimal Consumption and Investment Strategies

We investigate the diversification benefits of combining commodities with a traditional equity portfolio, while considering higher order statistical moments and seasonality. The literature suggests that the in-sample diversification benefits of commodities in portfolio optimization are not preserved out-of-sample. We provide an extensive in-sample and out-of-sample analysis with ten commodities and a stock index using the classical tangency mean-variance model and the maximum Omega ratio model. We show that seasonality in commodity returns should be considered, and leads to significant excess return and increase in Sharpe ratio.

Supply Chain Predictability of Returns and Portfolio Selection

The literature on the effects of parameter uncertainty on optimal portfolio choice suggests the existence of a premium for parameter uncertainty in asset returns. We use a simple extension to classical mean-variance portfolio optimization and devise a robust strategy to benefit from such a premium. Using well-known, long time series of equity returns, we show that this strategy indeed outperforms competitor strategies and yields positive and significant alphas relative to the most prominent factor models. We interpret these results to provide empirical support for the existence of a parameter uncertainty premium in equity returns.

Portfolio Optimization of Commodity Futures with Seasonal Components and Higher Moments

We derive no-arbitrage bounds for expected excess returns to generate scenarios used in financial optimization. The bounds allow to distinguish three regions: one where arbitrage opportunities will never exist, a second where arbitrage may be present, and a third, where arbitrage opportunities will always exist. No-arbitrage bounds are derived in closed form for a given covariance matrix using the least possible number of scenarios. The same setting is also used in an algorithm to generate discrete scenarios and trees. Numerical results from solving two-stage asset allocation problems indicate that even for minimal tree size very accurate results can be obtained.