Hedging crash risk in optimal portfolio selection

We study a problem of optimal consumption and portfolio selection in a market where the logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve pure-jump Levy processes as driving noise instead of Brownian motion like in the Black and Scholes model. The state constrained optimization problem involves the notion of local substitution and is of singular type. The associated Hamilton-Jacobi-Bellman equation is a nonlinear first order integro-differential equation subject to gradient and state constraints. We characterize the value function of the singular stochastic control problem as the unique constrained viscosity solution of the associated Hamilton-Jacobi-Bellman equation. This characterization is obtained in two main steps. First, we prove that the value function is a constrained viscosity solution of an integro-differential variational inequality. Second, to ensure that the characterization of the value function is unique, we prove a new comparison (uniqueness) result for the state constraint problem for a class of integro-differential variational inequalities. In the case of HARA utility, it is possible to determine an explicit solution of our portfolio-consumption problem when the Levy process posseses only negative jumps. This is, however, the topic of a companion paper [7].

Portfolio is the set of assets either real or financial owned by investor. One asset used by investor is stock because the stock has various price along the period time. Nowadays, stock investments have been done by investors. Stock price can be either profit or loss so that it is required portfolio selection. From the various price of stock, we can compute the return, expected return, and the risk of stock. In this research, we will make the optimal portfolio which can result maximum return and minimum risk of stock with the available investation. Goal programming is the mathematical programming techniques to solve the objectives subject to some constraints where the there are priorities for each objective. An application of goal programming is portfolio selection. Portfolio selection is determining some stocks optimizing maximum return and minimum risk of stock with the available investation. The novelty of this research is Goal Programming as portfolio selection method will be optimized by Particle Swarm Optimization (PSO) so that it is called Particle Swarm Optimization-Goal Programming (PSOGP). In PSO, there is initialization of particle i.e. proportion of investation on each stock as decision variable. Particle must be constructed so that it can satisfy the constraint investation of all stocks. In optimization process, the new particle is also modified so that satisfying the constraints. In multiobjective optimization, sort the fitness on the value of the first priority objective. If first fitness have the same value of the objective, then sort them on the second priority objective, and so forth. Based on simulation, PSOGP can be applied on the portfolio selection and can optimize priority of some objectives.

Extreme return spillovers and connectedness between crude oil and precious metals futures markets: Implications for portfolio management

Value-At Risk(VaR) measures the worst expected loss under normal market conditions over a specific time interval at a given confidence level. VaR answers the question: “How much can I lose with x% probability over a pre-set horizon?” Another way of expressing this, is that VaR is the lowest quantile of the potential losses that can occur within a given portfolio during a specified time period. In the risk management perspective of VaR, suppose that a portfolio manager has a daily VaR equal to $1 million at %1. This means that there is only one chance in 100 that a daily loss bigger than $1 million occurs under normal market conditions. In this article the emphasis is on the market risk of a small, fixed-income portfolios in commercial banks. Data from Turkey were used and the effect of the recent sharp devaluation in the TL was investigated in this context, with the exponential volatility measurement method.

Using the volatility spillover index method based on the quantile vector autoregression (QVAR) model, this paper systematically examines structural changes and corresponding spillover effects within 20 major stock markets under both extreme and normal market conditions, using data spanning from January 2005 to January 2023. The results show that, compared to the traditional volatility spillover index method, which focuses mainly on average spillover effects, the QVAR model-based spillover index better captures spillover effects under extreme and various market conditions among global stock markets. The connections between stock markets are closer in extreme market conditions. The total spillover index of major global stock markets significantly increases in extreme conditions compared to normal conditions. In extreme market conditions, inflow indices show varying degrees of increase, with emerging economy stock markets displaying more significant increases. The outflow indices exhibit heterogeneity; emerging economies show consistent increases, while developed economies show mixed changes.

PurposeDespite the growing recognition of the complex interplay between macroeconomic shock indexes and stock market dynamics, there is a significant research gap concerning their interconnectedness and return spillovers in the context of the African stock market. This leaves much to be desired, given that the financial market in Africa is arguably one of the most preferred destinations for hedge and portfolio diversification (Alagidede, 2008; Anyikwa and Le Roux, 2020). Further, like other financial markets across the globe, the increased capital flow, coupled with declining information asymmetry in Africa, has deepened intra and inter-sectoral integration within and across national borders. This has, thus, increased the susceptibility of financial markets in Africa to spillover of shocks from other sectors and jurisdictions. Additionally, while previous studies have investigated these factors individually (Asafo-Adjei et al., 2020), with much emphasis on developed markets, an all-encompassing examination of spillovers and the connectedness between the aforementioned macroeconomic shock indexes and stock market returns remains largely unexplored. This study happens to be the first to consider the impact of each of the indexes on stock returns in Africa, with evidence spanning from May 2007 to April 2023, covering notable global crisis episodes such as the Global Financial Crisis (GFC), the COVID-19 pandemic and the Russia–Ukraine war.Design/methodology/approachThis study employs the novel quantile vector autoregression (QVAR) model, making it the first of its kind in literature. By applying the QVAR, the study captures the potential nonlinear and asymmetric relationship between stock returns and the factors of interest across different quantiles, i.e. bearish, normal and bullish market conditions. Thus, the approach allows for a more accurate and nuanced examination of the tail dependence and extreme events, providing insights into the behaviour of the variables under extreme events.FindingsThe study revealed that connectedness and spillovers intensified under bearish and bullish market conditions. It was also observed that, among the macroeconomic shock indicators, FSI exerted the highest influence on stock returns in Africa in both bullish and normal market conditions. Across the various market regimes, the Egyptian Exchange (EGX) and the Nairobi Stock Exchange (NSE) were net receiver of shocks.Originality/valueThis study happens to be the first to consider the impact of each of the indexes on stock returns in Africa, with evidence spanning from May 2007 to April 2023, covering notable global crisis episodes such as the GFC, the COVID-19 pandemic and the Russia–Ukraine war. On the methodology front, this study employs the novel QVAR model, making it one of the few studies in recent literature to apply the said method.

Volatility Contagion: New Evidence from Market Pricing of Volatility Risk

Marginal risk that represents the risk contribution of an individual asset is an important criterion in portfolio selection and risk management. In the literature, however, the measure of marginal risk has been only employed in ex post analysis of a portfolio policy, and the control of marginal risk is achieved usually via position diversification that simply imposes upper bounds on the portfolio position without considering the effect of correlations of asset returns in risk diversification. We investigate in this paper a new optimal portfolio selection problem with direct (relative) marginal risk control in the mean-variance framework, accounting for the correlations of asset returns. The resulting optimization model, however, is a notorious non-convex quadratically constrained quadratic programming problem. By exploiting the special structure of the problems, we propose an efficient branch-and-bound solution method to achieve a global optimality in which convex quadratic relaxation subproblems with second-order cone constraints are formulated to generate a tight lower bound. Empirical study shows that the model with marginal risk control is a suitable analytical tool for active portfolio risk management and demonstrates several preferable features of this new model to the traditional mean-variance model in risk management. The method is tested and compared with the commercial global optimization solver BARON for portfolio optimization problems with up to hundreds of assets and tens of marginal risk constraints.

We present convincing empirical results on the application of Randomized Signature Methods for non-linear, non-parametric drift estimation for a multi-variate financial market. Even though drift estimation is notoriously inaccurate due to small signal to noise ratio, one can still try to learn optimal non-linear maps from past data to conditional expectations of future returns for the purposes of portfolio optimization. Randomized Signatures, in contrast to classical signatures, allow for high dimensional markets and provide features on the same scale. We do not contribute to the theory of Randomized Signatures here, but rather present our empirical findings on portfolio selection in real world settings including real market data and transaction costs.

Optimal portfolio selection using a simple double-shrinkage selection rule

In a typical capital rationing problem, a project portfolio is selected to maximize expected return on investment while adhering to the capital budget constraint. Sometimes projects may be delayed and they have to be funded beyond their planned completion time. This type of ‘unplanned carryovers’ represents a financial obligation to the company. If future years' capital budgets cannot be expanded to cover such obligations, future projects may be cancelled or postponed to fund the unplanned carryover. In this paper, we develop a methodology based on multi-attribute utility theory and chance-constrained programming to optimize portfolio selection subject to the constraints that the selected portfolio does not exceed the available budget and that the carryover of the unspent funds to the next fiscal year does not exceed predetermined limits. We use this technique to select an optimal project portfolio for Lockheed Martin Space Systems' infrastructure investments.

The optimal portfolio selection is one of the most investigated problem in Investment Theory. When randomness is introduced in return rates, one has to take into account the risk associated to each investment. The set of admissible portofolio becomes a two dimensional set and utility function has to be modified introducing risk which, in a rational market, is directly proportional to return. When it is possible to find a line of efficient portfolios the investor uses subjective preference to choose a particular point on it. The tools to tackle uncertain situation span from mathematical programming to stochastic optimal control, referring in any case to uniqueness of the decision maker. Aim of this paper is to imbed portfolio selection in a dynamic cooperative game framework and qualify the choice of an optimal portfolio as the corresponding bargaining solution.KeywordsOptimal PortfolioPortfolio SelectionExpected ReturnEfficient FrontierBargaining SolutionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We show an isomorphism between optimal portfolio selection or competitive equilibrium models with utilities incorporating linear habit formation, and corresponding models without habit formation. The isomorphism can be used to mechanically transform known solutions not involving habit formation to corresponding solutions with habit formation. For example, the Constantinides (1990) and Ingersoll (1992) solutions are mechanically obtained from the familiar Merton solutions for the additive utility case, without recourse to a Bellman equation or first-order conditions. More generally, recent solutions to portfolio selection problems with recursive utility and a stochastic investment opportunity set are readily transformed to novel solutions of corresponding problems with utility that combines recursivity with habit formation. The methodology also applies in the context of Hindy–Huang–Kreps (1992) preferences, where our isomorphism shows that the solution obtained by Hindy and Huang (1993) can be mechanically transformed to Dybvig’s (1995) solution to the optimal consumption-investment problem with consumption ratcheting.

This paper introduces a multiperiod model for the optimal selection of a financial portfolio of options linked to a single index. The objective of the model is to maximize the expected return of the portfolio under constraints limiting its Value-at-Risk. We rely on scenarios to represent future security prices. The model contains several interesting features, like the consideration of transaction costs, bid-ask spreads, arbitrage-free option pricing, and the possibility to rebalance the portfolio with options introduced at the start of each period. The resulting mixed integer programming model is applied to realistic test instances involving options on the S&P500 index. In spite of the large size and of the numerical difficulty of this model, near-optimal solutions can be computed by a standard branch-and-cut solver or by a specialized heuristic. The structure and the financial features of the selected portfolios are also investigated.

Dividends, taxes, and normative portfolio theory