Efficient Frontier for Robust Higher-order Moment Portfolio Selection

This article proposes a non-parametric portfolio selection criterion for the static asset allocation problem in a robust higher-moment framework. Adopting the Shortage Function approach, we generalize the multi-objective optimization technique in a four-dimensional space using L-moments, and focus on various illustrations of a four-dimensional set of the first four L-moment primal efficient portfolios. our empirical findings, using a large European stock database, mainly rediscover the earlier works by Jean (1973) and Ingersoll (1975), regarding the shape of the extended higher-order moment efficient frontier, and confirm the seminal prediction by Levy and Markowitz (1979) about the accuracy of the mean-variance criterion.Efficient frontier, portfolio selection, robust higher L-moments, shortage function, goal attainment application.

Investment, income, incompleteness

The utility-maximizing consumption and investment strategy of an individual investor receiving an unspanned labor income stream seems impossible to find in closed form and very dificult to find using numerical solution techniques. We suggest an easy procedure for finding a specific, simple, and admissible consumption and investment strategy, which is near-optimal in the sense that the wealthequivalent loss compared to the unknown optimal strategy is very small. We first explain and implement the strategy in a simple setting with constant interest rates, a single risky asset, and an exogenously given income stream, but we also show that the success of the strategy is robust to changes in parameter values, to the introduction of stochastic interest rates, and to endogenous labor supply decisions

OSQP: An Operator Splitting Solver for Quadratic Programs

We present a general-purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the same coefficient matrix at almost every iteration. Our algorithm is very robust, placing no requirements on the problem data such as positive definiteness of the objective function or linear independence of the constraint functions. It can be configured to be division-free once an initial matrix factorization is carried out, making it suitable for real-time applications in embedded systems. In addition, our technique is the first operator splitting method for quadratic programs able to reliably detect primal and dual infeasible problems from the algorithm iterates. The method also supports factorization caching and warm starting, making it particularly efficient when solving parametrized problems arising in finance, control, and machine learning. Our open-source C implementation OSQP has a small footprint, is library-free, and has been extensively tested on many problem instances from a wide variety of application areas. It is typically ten times faster than competing interior-point methods, and sometimes much more when factorization caching or warm start is used. OSQP has already shown a large impact with tens of thousands of users both in academia and in large corporations

Asset Location in Tax-Deferred and Conventional Savings Accounts

The optimal allocation of assets among different asset classes (such as stocks and bonds) has received considerable attention in financial theory and practice. On the other hand, investors have not been given much guidance about which assets should be located in tax-deferred retirement accounts and which in conventional savings accounts. This paper derives optimal asset allocations (which assets to hold) and asset locations (where to hold them) for a risk-averse investor saving for retirement. Locating assets optimally can significantly improve the risk-adjusted performance of retirement savings.

Portfolio optimisation models and properties of return distributions

Mean-risk models have been widely used in portfolio optimisation. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is nondominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed into a single objective problem by using the reference point method, in which target levels, known as aspiration points, are specified for the objective function values. A model is proposed in which the aspiration points relate to ordered return outcomes of the portfolio return. The model is extended by additionally specifying reservation points, which act pre-emptively in the optimisation. The theoretical properties of the models are studied. The performance of the models on real data drawn from the Hang Seng index is also investigated

Utility-Based Hedging of Stochastic Income

In this dissertation, we study and examine utility-based hedging of the optimal portfolio choice problem in stochastic income. By assuming that the investor has a preference governed by negative exponential utility, we a derive a closed-form solution for the indifference price through the pricing methodology based on utility maximization criteria. We perform asymptotic analysis on this closed form solution to develop the analytic approximation for the indifference price and the optimal hedging strategy as a power series expansion involving the risk aversion and the correlation between the income and a traded asset. This gives a fast computation route to assess these quantities and perform our analysis. We implemented the model to perform simulations for the optimal hedging policy and produce the distributions of the hedging error at terminal time over many sample paths histories. In turn, we analyze the performance of the utility-based hedging strategy together with the strategy which arises from employing the traded asset as a substitute for the stochastic income

Portfolio choice and optimal hedging with general risk functions: a simplex-like algorithm.

The minimization of general risk functions is becoming more and more important in portfolio choice theory and optimal hedging. There are two major reasons. Firstly, heavy tails and the lack of symmetry in the returns of many assets provokes that the classical optimization of the standard deviation may lead to dominated strategies, from the point of view of the second order stochastic dominance. Secondly, but not less important, many institutional investors must respect legal capital requirements, which may be more easily studied if one deals with a risk measure related to capital losses. This paper proposes a new method to simultaneously minimize several general risk or dispersion measures. The representation theorems of risk functions are applied to transform the general risk minimization problem in a minimax problem, and later in a linear programming problem between infinite-dimensional Banach spaces. Then, new necessary and sufficient optimality conditions are stated and a simplex-like algorithm is developed. The algorithm solves the dual problem and provides both optimal portfolios and their sensitivities. The approach is general enough and does not depend on any particular risk measure, but some of the most important cases are specially analyzed. A final real data numerical example illustrates the practical performance of the proposed methodology.Risk measures; Deviation measure; Portfolio selection; Infinite dimensional linear programming; Simplex like method;