Stefano Herzel

A Quadratically Convergent Method for Linear Programming

Abstract A new method to solve linear programming problems is introduced. This method follows a path defined by a system of o.d.e., and for nondegenerate problem is quadratically convergent.

The Cost of Sustainability in Optimal Portfolio Decisions

We examined the impact of including sustainability-related constraints in optimal portfolio decision-making. Our analysis covered an investment set containing the components of the S&P500 index from 1993 to 2008. Optimizations were performed according to the classic mean–variance approach, while sustainability constraints were introduced by eliminating, from the investment pool, those assets that do not comply with the given social responsibility criteria (screening). We compared the efficient frontiers with and without screening. The analysis focused on the three main dimensions of sustainability, namely the environmental, social and governance ones. We found that socially responsible screening gives rise to a small loss in terms of the Sharpe ratio even though it has a great impact on the market capitalization of the optimal portfolio. The spanning test showed that the ex-post differences between the two frontiers, when short selling is not allowed, are significant only in the case of environmental screening.

Consistent Initial Curves for Interest Rate Models

It was a significant step forward in modeling the term structure of interest rates to require the model to be arbitrage-free, in the sense that applying the model’s dynamics to the current market yield curve did not produce any arbitrage opportunities, and therefore, internal inconsistency. The Heath-Jarrow-Morton (HJM) class of interest rate models leads to a large family of arbitrage-free term structure processes. Fitting HJM models empirically requires estimating a continuous forward rate curve from the discrete set of bond prices observed in the market. But, as the authors point out, unless this is done with care, the function that is fitted to market rates may not be consistent with the HJM dynamics for the forward curve. That is, current forward rates would be fitted to a functional form that cannot evolve to another forward curve of the same type in the next period under the assumed HJM model specification. This problem is generally overlooked in practice, since the forward rate curve is refitted every period anyway, but it may well show up in the form of parameter instability in the model. In this article, Angelini and Herzel examine this issue both theoretically and empirically, and show that requiring the forward curve to be fitted to a functional form that is consistent with the interest rate process can make a substantial difference in model performance and in parameter stability.

Evaluating discrete dynamic strategies in affine models

We consider the problem of measuring the performance of a dynamic strategy, re-balanced at a discrete set of dates, with the objective of hedging a claim in an incomplete market driven by a general multi-dimensional affine process. The main purpose of the paper is to propose a method to efficiently compute the expected value and variance of the hedging error of the strategy. Representing the payoff of the claim as an inverse Laplace transform, we are able to obtain semi-explicit formulas for strategies satisfying a certain property. The result is quite general and can be applied to a very rich class of models and strategies, including Delta hedging. We provide illustrations for the case of the Heston stochastic volatility model.

Portfolio management with benchmark related incentives under mean reverting processes

We study the problem of a fund manager whose compensation depends on the relative performance with respect to a benchmark index. In particular, the fund manager’s risk-taking incentives are induced by an increasing and convex relationship of fund flows to relative performance. We consider a dynamically complete market with N risky assets and the money market account, where the dynamics of the risky assets exhibit mean reversions, either in the drift or in the volatility. The manager optimizes the expected utility of the final wealth, with an objective function that is non-concave. The optimal solution is found by using the martingale approach and a concavification method. The optimal wealth and the optimal strategy are determined by solving a system of Riccati equations. We provide a semi-closed solution based on the Fourier transform.

Delegated portfolio management with socially responsible investment constraints

We consider the problem of how to establish compensation for a portfolio manager who is required to restrict the investment set, for example, because of socially responsible screening. This is a problem of delegated portfolio management, where the reduction of investment opportunities to the subset of sustainable assets involves a loss in expected earnings for the portfolio manager, compensated by the investor through an extra bonus on the realized return. Under simple assumptions on the investor, manager and market, we compute the optimal bonus as a function of the managers risk aversion and expertise, and of the impact of portfolio restriction on the mean-variance efficient frontier.

Delegated portfolio management under ambiguity aversion

We examine the problem of setting optimal incentives for a portfolio manager hired by an investor who wants to induce ambiguity-robust portfolio choices with respect to estimation errors in expected returns. Adopting a worst-case max-min approach we obtain the optimal compensation in various cases where the investor and the manager, adopt or relinquish an ambiguity averse attitude. We also provide examples of applications to real market data.

A Socially Responsible Portfolio Selection Strategy

We propose a new methodology to integrate Socially Responsible (SR) standards in the process of investment decisions. We use SR scores of companies in the S&P500 and in the Domini Social Index (DSI) to define the level of SR of a portfolio. We model this as a linear combination of the SR scores of the single stocks with coefficients given by the portfolio’s weights. We form portfolios that minimize the tracking error from the DSI while improving the SR level. The analysis of the performances of the portfolios show that the improvement of the SR is usually possible at a small cost in terms of tracking error, and that the improved portfolios produced, in most of the cases, better financial performances than the benchmark.

An Agent-Based Model to Study the Impact of Convex Incentives on Financial Markets

We investigate by means of agent-based simulations the influence of convex incentives, e.g. option-like compensation, on financial markets. We propose an agent based model already developed in Fabretti et al (2015), where the model was build with the aim of studying convex contract effect using the results of a laboratory experiment performed by Holmen et al. (2014) as benchmark. Here we replicate their results studying prices dynamics, volatility, volumes and risk preference effect. We show that convex incentives produces higher prices, lower liquidity and higher volatility when agents are risk averse, while, differently from Fabretti et al (2015), their effect is less evident if agents are risk lovers. This appears related to the fact that prices in the long run converge more likely to the equilibrium when agents are risk averse.

Convex Incentives in Financial Markets: An Agent-Based Analysis

This paper uses agent-based simulation to analyze how financial markets are affected by market participants with convex incentives, e.g. option-like compensation. We document that convex incentives are associated with (i) higher prices, (ii) larger variations of prices, and (iii) larger bid-ask spreads. We conclude that convex incentives may lead to decreased stability of financial markets. Our analysis suggests that the decreased stability is driven by the fact that convex incentives pushes agents towards more extreme decisions. Furthermore, while risk preferences affect agent behavior if they have linear incentives, the effect of risk preferences vanishes with convex incentives.