Robust Portfolio Optimization with a Hybrid Heuristic Algorithm

Estimation errors in both the expected returns and the covariance matrix hamper the constructing of reliable portfolios within the Markowitz framework. Robust techniques that incorporate the uncertainty about the unknown parameters are suggested in the literature. We propose a modification as well as an extension of such a technique and compare both with another robust approach. In order to eliminate oversimplifications of Markowitz’ portfolio theory, we generalize the optimization framework to better emulate a more realistic investment environment. Because the adjusted optimization problem is no longer solvable with standard algorithms, we employ a hybrid heuristic to tackle this problem. Our empirical analysis is conducted with a moving time window for returns of the German stock index DAX100. The results of all three robust approaches yield more stable portfolio compositions than those of the original Markowitz framework. Moreover, the out-of-sample risk of the robust approaches is lower and less volatile while their returns are not necessarily smaller.Hybrid heuristic algorithm, Markowitz, Robust optimization, Uncertainty sets.

Asset selection using Factor Model and Data Envelope Analysis - A Quantile Regression approach

With the growing number of stocks and other financial instruments in the investment market, there is always a need for profitable methods of asset selection. The Fama-French three factor model, makes the problem of asset selection easy, by narrowing down the number of parameters, but the usual technique of Ordinary Least Square (OLS), used for estimation of the coefficients of the three factors suffers from the problem of modelling using the conditional mean of the distribution, as is the case with OLS. In this paper, we use the technique of Data Envelopment Analysis (DEA) applied to the Fama-French Three Factor Model, to choose stocks from Dow Jones Industrial Index. We use a more robust technique called as Quantile Regression to estimate the coefficients for the factor model and show that the assets selected using this regression method form a higher return equally weighted portfolio.Asset Selection, Factor Model, DEA, Quantile Regression

Safety first portfolio choice based on financial and sustainability returns

This paper lays the mathematical foundations of the notion of an investment's sustainability return and investigates three different models of portfolio selection with probabilistic constraints for safety first investors caring about the financial and the sustainability consequences of their investments. The discussion of these chance-constrained programming problems for stochastic and deterministic sustainability returns includes theoretical results especially on the existence of a unique solution under certain conditions, an illustrating example, and a computational time analysis. Furthermore, we conclude that a simple convex combination of financial and sustainability returns - yielding a new univariate decision variable - is not sufficiently general.Finance; Socially Responsible Investing; Sustainability Value; Safety First Investor

Least Median of Squares Estimation by Optimization Heuristics with an Application to the CAPM and Multi Factor Models

For estimating the parameters of models for financial market data, the use of robust techniques is of particular interest. Conditional forecasts, based on the capital asset pricing model, and a factor model are considered. It is proposed to consider least median of squares estimators as one possible alternative to ordinary least squares. Given the complexity of the objective function for the least median of squares estimator, the estimates are obtained by means of optimization heuristics. The performance of two heuristics is compared, namely differential evolution and threshold accepting. It is shown that these methods are well suited to obtain least median of squares estimators for real world problems. Furthermore, it is analyzed to what extent parameter estimates and conditional forecasts differ between the two estimators. The empirical analysis considers daily and monthly data on some stocks from the Dow Jones Industrial Average Index (DJIA).LMS, CAPM, Multi Factor Model, Differential Evolution, Threshold Accepting