Portfolio Allocation Problem Research Articles

Robustness meets co-jumps: optimal consumption and portfolio choice with derivatives

In this paper, we study a robust, dynamic, continuous-time optimal consumption and portfolio allocation problem for investors with recursive preferences who have access to both stock and derivatives markets. We assume the stock price process follows a stochastic volatility model, with instantaneous precision as the unique state variable, allowing for discontinuities in all the dynamics. We obtain a closed-form approximate solution up to a system of ODEs to the optimization problem for a non-unitary value of the elasticity of intertemporal substitution of consumption, being able to derive an exact solution as a particular case. Our theoretical findings show that the optimal policies are remarkably affected by the ambiguity-aversion parameters to diffusive and jump risks. A detailed numerical analysis confirms the effectiveness of our theoretical results on real data. Finally, we prove that investors who do not believe in ambiguity may suffer considerable wealth losses.

Mean-variance Dynamic Portfolio Allocation with Transaction Costs: A Wiener Chaos Expansion Approach

This paper studies the multi-period mean-variance portfolio allocation problem with transaction costs. Many methods have been proposed these last years to challenge the famous uni-period Markowitz strategy. However, these methods cannot integrate transaction costs or become computationally heavy and hardly applicable. In this paper, we try to tackle this allocation problem by proposing an innovative approach that relies on representing the set of admissible portfolios by a finite-dimensional Wiener chaos expansion. This method can find an optimal strategy for the allocation problem subject to transaction costs. To complete the study, the link between optimal portfolios submitted to transaction costs and the underlying risk aversion is investigated. Then a competitive and compliant benchmark based on the sequential uni-period Markowitz strategy is built to highlight the efficiency of our approach.

Optimization of large portfolio allocation for new-energy stocks: Evidence from China

Investment in the fast-growing new-energy of China has gradually attracted great attention. At present, more than 100 new-energy stocks are listed on China’s stock markets. How to effectively manage the investment risk of these stocks and achieve better returns is of great interest to investors and policymakers. In finance, mean–variance portfolio (MVP) is often applied to solve portfolio allocation problems. However, when investing in numerous stocks, the classical MVP is no longer applicable. For large portfolio allocation, this study constructs a comprehensive MVP model, called an unconstrained regression model with latent factors (URELAF). It applies a factor structure with latent factors to modify the covariance matrix estimation in the classical MVP, using an unconstrained penalized regression to estimate the allocation. In addition, to more realistically simulate the investment of stock markets, transaction costs are considered. The empirical results show that URELAF model can control the risk with Sharpe ratio reaching 6 times as many as MVP model, and even improve about 26% compared with the sub-optimal portfolio model. URELAF also outperforms other portfolios with transaction costs. Finally, hypothesis tests further verify that URELAF can significantly improve portfolio performance compared with other portfolio methods for China’s new-energy market.

Commitment and partial naïveté: Early withdrawal penalties on retirement accounts

We analyze a portfolio allocation problem in a standard model of conflict within temporal selves who suffer from partial naïveté – the current self holds a deterministic but possibly wrong perception (underestimation) about the present bias of her future selves. The current self can invest in a liquid and a longer-maturity, illiquid asset; the latter offers partial commitment since the future self may prematurely liquidate it at a penalty rate. If the cost is prohibitive, no liquidation happens, and the first-best plan laid out by the current self is followed. When such costs are modest, raising them has countervailing income and substitution effects. Consequently, in a range, a strengthening of the commitment device of illiquidity is not necessarily welfare increasing for the current self.

Optimal Portfolio Using Factor Graphical Lasso

Abstract Graphical models are a powerful tool to estimate a high-dimensional inverse covariance (precision) matrix, which has been applied for a portfolio allocation problem. The assumption made by these models is a sparsity of the precision matrix. However, when stock returns are driven by common factors, such assumption does not hold. We address this limitation and develop a framework, Factor Graphical Lasso (FGL), which integrates graphical models with the factor structure in the context of portfolio allocation by decomposing a precision matrix into low-rank and sparse components. Our theoretical results and simulations show that FGL consistently estimates the portfolio weights and risk exposure and also that FGL is robust to heavy-tailed distributions which makes our method suitable for financial applications. FGL-based portfolios are shown to exhibit superior performance over several prominent competitors including equal-weighted and index portfolios in the empirical application for the S&P500 constituents.

Portfolio Selection under Systemic Risk

AbstractThis paper proposes a modified Sharpe ratio to construct optimal portfolios under systemic events. The portfolio allocation problem is solved analytically under the absence of short‐selling restrictions and numerically when short‐selling restrictions are imposed. This approach is made operational by embedding it in a multivariate dynamic setting using dynamic conditional correlation and copula models. We evaluate the out‐of‐sample performance of our portfolio empirically over the period 2007 to 2020 using ex post final wealth paths and systemic risk metrics against mean–variance, equally weighted, and global minimum variance portfolios. Our portfolio outperforms all competitors under market distress and remains competitive in noncrisis periods.

Co-jumps and recursive preferences in portfolio choices

This paper investigates a multivariate, dynamic, continuous-time optimal consumption and portfolio allocation problem when the investor faces recursive utilities. The economy we are considering is described through both diffusion and discontinuities in the dynamics. We derive an approximated closed-form solution to optimal rules by exploiting standard dynamic programming techniques. Our findings are manifold. First, we obtain dynamic optimal weights, inversely proportional to volatility. Second, we show that both co-jumps frequency and intensity play a crucial role, as they considerably limit potential losses in the investors’ wealth. Third, we prove that jumps in precision reinforce the effect of jumps in price, further reducing optimal allocation. Finally, we highlight how co-jumps may influence investors’ choices regarding intertemporal consumption.

Almost exact risk budgeting with return forecasts for portfolio allocation

We revisit the portfolio allocation problem with designated risk-budget. We generalize the problem of arbitrary risk budgets with unequal correlations to one that includes return forecasts and transaction costs while keeping the no-shorting constraint. We offer a convex second order cone formulation that scales well with the number of assets and explore solutions to problem variants - on equity-bond asset allocation problems as well as formulating portfolios using index constituents from the NASDAQ100 index, illustrating the benefits of this approach.

Dynamic portfolio allocation for financial markets: A perspective of competitive-cum-compensatory strategy

Portfolio allocation is an important research branch in the realm of financial management and financial engineering. In this paper, a dynamic portfolio allocation problem considering the competitive-cum- compensatory relationship among decision objectives is discussed. Interval type-2 fuzzy numbers that provide more flexibility for processing uncertainty are innovatively utilized to characterize asset returns. To capture the behavioral characteristics of investors’ bounded rationality, prospect theory with dynamic updating of loss aversion rate and reference wealth is introduced. The expected semi-absolute deviation and the entropy function based on the Minkowski measure are adopted to describe the risk and diversification degree of portfolio allocation, respectively. With this description, a dynamic multi-objective portfolio allocation model is formulated. Regarding the multi-dimensional characteristics of the problem, competitive-cum-compensatory strategy-based fuzzy goal programming is embedded in the whole optimization process; thus, the model is transformed into a single-objective form for the solution. Several interesting conclusions are drawn from empirical studies in two financial markets. The robustness and superiority of the proposed model are verified by multi-angle comparison and sensitivity analysis. This research not only enriches and extends the field of dynamic portfolio allocation in the fuzzy context, but also offers an effective means for the optimization of multi-objective portfolio models.

Optimal investment with correlated stochastic volatility factors

AbstractThe problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal time with only one random factor can be linearized thanks to a classical distortion transformation. In the present paper, we address the situation with several factors using a perturbation technique around the case where these factors are perfectly correlated reducing the problem to the case with a single factor. Our proposed approximation requires to solve numerically two linear equations in lower dimension instead of a fully nonlinear HJB equation. A rigorous accuracy result is derived by constructing sub‐ and super‐solutions so that their difference is at the desired order of accuracy. We illustrate our result with a particular model for which we have explicit formulas for the approximation. In order to keep the notations as explicit as possible, we treat the case with one stock and two factors and we describe an extension to the case with two stocks and two factors.

Can Deep Reinforcement Learning Solve the Portfolio Allocation Problem? (PhD Manuscript)

Can Deep Reinforcement Learning Solve the Portfolio Allocation Problem? (PhD Manuscript)

An asymmetric PROMETHEE II for cryptocurrency portfolio allocation based on return prediction

Portfolio allocation, portfolio selection, and portfolio optimization are recognized as three crucial problems in the financial field. Using different criteria in addition to return and risk in the portfolio allocation problem based on the multi-criteria decision-making (MCDM) methods makes it more practical in the real world. The emergence of new and volatile assets such as cryptocurrencies has recently increased the need to use portfolio allocation models. In order to reduce inequalities and alleviate poverty as one of the sustainable development goals, cryptocurrency portfolio construction leads to sustainable income and wealth. This paper proposes a cryptocurrency portfolio allocation model based on the asymmetric Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE II) method using eight criteria and nine cryptocurrencies. To reduce the uncertainty of the problem, the return prediction obtained from the Auto-Regressive Integrated Moving Average (ARIMA), the Long Short-Term Memory (LSTM), and the Random Forest Regression (RFR) models as return-related criteria and has been used from the SlideVaR, along with the Value at Risk (VaR) and the Conditional Value at Risk (C-VaR) as risk-related criteria to consider investor insight from the market situation. It is also proposed that an asymmetric preference function be proposed to consider gain and loss asymmetry as a behavioral phenomenon in the model. The out-of-sample performance of the proposed model in the last three months of 2021 confirms the superiority of the proposed model in terms of average return (= 0.017) and standard deviation (= 0.036) among other proposed models.

Cryptocurrency portfolio allocation using a novel hybrid and predictive big data decision support system

Establishing a cryptocurrency portfolio management and allocation decision support is vital in enabling investors to thrive in this market. More than nearly 5000 cryptocurrencies are traded daily at cryptocurrency exchanges, and one of the primary challenges is the optimal selection of the assets. While research studies considered cryptocurrency price prediction as a typical time series forecasting problem, a portfolio allocation problem can be defined as a Multiple Criteria Decision-Making (MCDM) problem. To tackle this problem and generate a response to these dynamic challenges, this study developed an analytical and predictive approach to guide investors through their decisions. Time series forecasting was conducted using the Prophet Forecasting Model (PFM) to predict the prices. For the asset allocation stage, this study extended the Cluster analysis for improving the Multiple Criteria Decision Analysis (CLUS-MCDA) algorithm by adding additional features to this large-scale decision-making technique, including Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and the Višekriterijumsko kompromisno rangiranje (meaning: multi-criteria optimization and compromise solution) (VIKOR) methods. While the concept of Parallel Decision Making (PDM) in massive structured problems was previously introduced in the CLUS-MCDA algorithm, this study also utilized a target-based normalization technique that gives the decision-makers more control over the extended CLUS-MCDA II algorithm. To validate the reliability of the method, a cryptocurrency trade experiment considering more than 70 cryptocurrencies and multiple scenarios based on decision-makers' preferences was analysed. The outcomes of this study showed that the proposed decision support system is a reliable tool for such practical and real-world big data problems.

Risk Aware Minimum Principle for Optimal Control of Stochastic Differential Equations

We present a probabilistic formulation of risk aware optimal control problems for stochastic differential equations. Risk awareness is in our framework captured by objective functions in which the risk neutral expectation is replaced by a risk function, a nonlinear functional of random variables that accounts for the controller's risk preferences. We state and prove a risk aware minimum principle that gives necessary and sufficient conditions for optimality of generalized control processes taking values on probability measures defined on a given action space. We show that going from the risk neutral to the risk aware case, the minimum principle is modified by the introduction of one additional real-valued stochastic process that acts as a risk adjustment factor. This adjustment process is explicitly given as the expectation, conditional on the filtration at the given time, of an appropriately defined functional derivative of the risk function evaluated at the random total cost. The control model we employ differs from standard relaxed controls, and we elaborate on the differences, and benefits and drawbacks, of the control types; we further give conditions under which the generalized control can be realized using a strict control process. We present an application of the results for a portfolio allocation problem and show that the risk awareness of the objective function gives rise to a risk premium term that is characterized by the risk adjustment process described above. This suggests uses of our results in e.g. pricing of risk modeled by generic risk functions in financial applications.

Economic evaluation of asset pricing models under predictability

This paper performs an out-of-sample comparison of linear factor asset pricing models from an economic perspective under predictability. I assess the economic value added of several factor models when a Bayesian investor is faced with a portfolio allocation problem whereby each model imposes cross-sectional restrictions on the parameters of a predictive stock return regression. The empirical framework explicitly accounts for investor skepticism about the model, i.e., mispricing uncertainty. Despite vast statistical work on in-sample model comparison for the new-generation asset-pricing models, their out-of-sample performance cannot beat a simple benchmark on a wide range of tests from an economic perspective. This is consistent with thus extends the conclusion for the first-generation of factor models. An exceptional case of factor models yielding significant economic gains is observed when evaluating industry portfolios at the shortest horizon (1-month). In this case, I find that the q5 model of Hou et al. (2021) and the behavioral factor model of Stambaugh and Yuan (2017) outperform the historical benchmark in several cases.

Unified discrete-time factor stochastic volatility and continuous-time Itô models for combining inference based on low-frequency and high-frequency

This paper introduces unified models for high-dimensional factor-based Itô process, which can accommodate both continuous-time Itô diffusion and discrete-time stochastic volatility (SV) models by embedding the discrete SV model in the continuous instantaneous factor volatility process. We call it the SV-Itô model. Based on the series of daily integrated factor volatility matrix estimators, we propose quasi-maximum likelihood and least squares estimation methods. Their asymptotic properties are established. We apply the proposed method to predict future vast volatility matrix whose asymptotic behaviors are studied. A simulation study is conducted to check the finite sample performance of the proposed estimation and prediction method. An empirical analysis is carried out to demonstrate the advantage of the SV-Itô model in volatility prediction and portfolio allocation problems.

Bayesian portfolio selection using VaR and CVaR

We study the optimal portfolio allocation problem from a Bayesian perspective using value at risk (VaR) and conditional value at risk (CVaR) as risk measures. By applying the posterior predictive distribution for the future portfolio return, we derive relevant quantities needed in the computations of VaR and CVaR, and express the optimal portfolio weights in terms of observed data only. This is in contrast to the conventional method where the optimal solution is based on unobserved quantities which are estimated. We also obtain the expressions for the weights of the global minimum VaR (GMVaR) and global minimum CVaR (GMCVaR) portfolios, and specify conditions for their existence. It is shown that these portfolios may not exist if the level used for the VaR or CVaR computation are too low. By using simulation and real market data, we compare the new Bayesian approach to the conventional plug-in method by studying the accuracy of the GMVaR portfolio and by analysing the estimated efficient frontiers. It is concluded that the Bayesian approach outperforms the conventional one, in particular at predicting the out-of-sample VaR.

Smart network based portfolios

In this article we deal with the problem of portfolio allocation by enhancing network theory tools. We propose the use of the correlation network dependence structure in constructing some well-known risk-based models in which the estimation of the correlation matrix is a building block in the portfolio optimization. We formulate and solve all these portfolio allocation problems using both the standard approach and the network-based approach. Moreover, in constructing the network-based portfolios we propose the use of three different estimators for the covariance matrix: the sample, the shrinkage toward constant correlation and the depth-based estimators . All the strategies under analysis are implemented on three high-dimensional portfolios having different characteristics. We find that the network-based portfolio consistently performs better and has lower risk compared to the corresponding standard portfolio in an out-of-sample perspective.

Optimal carry trade portfolio choice under regime shifts

This paper studies optimal currency allocation of the carry trade in foreign exchange (FX). A number of empirical studies have documented a phenomenon referred to as the ‘forward premium puzzle’, which states that the carry trade is profitable on average. However, the carry reversal during the 2008 global crisis periods wiped out the profits earned by the trade. To account for the regime shifts in the joint distribution of returns on the carry trade with FX market portfolios, we adopt a Markov regime switching model. We find evidence of two economic regimes: one state captures periods of the forward premium puzzle and UIP being violated, whilst the other reports high FX volatility and negative return of carry trade portfolio. Furthermore, to quantify the economic significance of regimes in returns on currency portfolios, we consider their importance in investors’ optimal portfolio allocation problem. We find strong evidence that optimal currency portfolio holdings vary significantly across regimes and across short and long investment horizons, as investors anticipate a shift out of the current state. Our results also show that the regimes partially anticipate peso events as well as the changes of funding liquidity measured by the TED spreads. A strategy that accounts for regimes, thus, generates overall stronger performance than the single-state Gaussian IID model, a carry trade procedure as well as a buy-and-hold strategy.

Multivariate Overnight GARCH-Ito Model with Applications in Large Volatility Matrix Estimation and Prediction

This paper introduces a unified multivariate overnight GARCH-It\^o model for volatility matrix estimation and prediction both in the low- and high-dimensional set-up. To account for whole-day market dynamics in the financial market, the proposed model has two different instantaneous volatility processes for the open-to-close and close-to-open periods, while each embeds the discrete-time multivariate GARCH model structure. We call it the multivariate overnight GARCH-It\^o (MOGI) model. Based on the connection between the discrete-time model structure and the continuous-time diffusion process, we propose a weighted least squares estimation procedure for estimating model parameters with open-to-close high-frequency and close-to-open low-frequency financial data, and establish its asymptotic theorems. We further discuss the prediction of future vast volatility matrices and study its asymptotic properties. A simulation study is conducted to check the finite sample performance of the proposed estimation and prediction methods. The empirical analysis is carried out to compare the performance of the proposed MOGI model with other benchmark methods in portfolio allocation problems.