Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix

The estimation of the inverse covariance matrix plays a crucial role in optimal portfolio choice. We propose a new estimation framework that focuses on enhancing portfolio performance. The framework applies the statistical methodology of shrinkage directly to the inverse covariance matrix using two non-parametric methods. The first minimises the out-of-sample portfolio variance while the second aims to increase out-of-sample risk-adjusted returns. We apply the resulting estimators to compute the minimum variance portfolio weights and obtain a set of new portfolio strategies. These strategies have an intuitive form which allows us to extend our framework to account for short-sale constraints, transaction costs and singular covariance matrices. A comparative empirical analysis against several strategies from the literature shows that the new strategies often offer higher risk-adjusted returns and lower levels of risk.     

Generalized DEA model of fundamental analysis and its application to portfolio optimization

Fundamental analysis is used in asset selection for equity portfolio management. In this paper, a generalized data envelopment analysis (DEA) model is developed to analyze a firm’s financial statements over time in order to determine a relative financial strength indicator (RFSI) that is predictive of firm’s stock price returns. RFSI is based on maximizing the correlation between the DEA-based score of financial strength and the stock market performance. This maximization involves a difficult binary nonlinear program that requires iterative re-configuration of parameters of financial statements as inputs and outputs. We utilize a two-step heuristic algorithm that combines random sampling and local search optimization. The proposed approach is tested with 230 firms from various US technology-industries to determine optimized RFSI indicators for stock selection. Then, those selected stocks are used within portfolio optimization models to demonstrate the usefulness of the scheme for portfolio risk management.     

Omega performance measure and portfolio insurance

We analyze the performance of the two main portfolio insurance methods, the OBPI and CPPI strategies, using downside risk measures. For this purpose, we introduce Kappa performance measures and especially the Omega measure. These measures take account of the entire return distribution. We show that the CPPI method performs better than the OBPI. As a-by-product, we determine the set of threshold values for these risk/reward performance measures.     

Regime switching based portfolio selection for pension funds

This paper shows how a mean variance criterion can be applied to a multi period setting in order to obtain efficient portfolios in an asset and liability context. The optimization model allows for rebalancing activities, transaction costs, stochastic volatilities for both assets and liabilities. Furthermore, a general framework for the projection of pension fund liabilities as well as for the generation of asset returns is given. In a further step the dynamics of the liability maturity structure is modeled as customized index, whose volatility and correlation with asset returns become integral components of the applied regime switching approach. The numerical results illustrate the diversification of the assets and its risk return pattern in dependency of the liability dynamics.     

Nonlinear portfolio selection using approximate parametric Value-at-Risk

As the skewed return distribution is a prominent feature in nonlinear portfolio selection problems which involve derivative assets with nonlinear payoff structures, Value-at-Risk (VaR) is particularly suitable to serve as a risk measure in nonlinear portfolio selection. Unfortunately, the nonlinear portfolio selection formulation using VaR risk measure is in general a computationally intractable optimization problem. We investigate in this paper nonlinear portfolio selection models using approximate parametric Value-at-Risk. More specifically, we use first-order and second-order approximations of VaR for constructing portfolio selection models, and show that the portfolio selection models based on Delta-only, Delta–Gamma-normal and worst-case Delta–Gamma VaR approximations can be reformulated as second-order cone programs, which are polynomially solvable using interior-point methods. Our simulation and empirical results suggest that the model using Delta–Gamma-normal VaR approximation performs the best in terms of a balance between approximation accuracy and computational efficiency.     

Dynamic hedge fund portfolio construction: A semi-parametric approach

In this article, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. We compare the standard mean–variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semi-parametric methodology, which is based on extreme value theory, copula and Monte Carlo simulation. We compare the semi-parametric approach with the standard, non-parametric approach, used to compute CVaR, CDaR and Omega, and the benchmark parametric approach, based on both static and dynamic mean–variance optimization. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the parametric mean–variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.     

New strategies and a new paradigm for Shariah-compliant portfolio optimization

In this paper we analyze the effects of different strategies to construct Shariah compatible financial portfolios. The difference between conventional and current Shariah portfolio management is the application of sector screens and financial screens by which the asset universe is reduced. Yet, here different schools of scholars define different screening rules leading to significant differences with respect to compliance, but also with respect to performance. After analyzing this discrepancy we propose several new strategies to apply the inconsistent rule systems and a new paradigm for defining Shariah-compliance. Under this new paradigm compliance is attributed to the portfolio and not to the individual assets of the universe. We report results of an empirical study analyzing the potentials of these strategies and of the paradigm. We can show that under the proposed concepts Shariah-compliant portfolios can be realized which have return and risk profiles comparable to the conventional non-constrained portfolios.     

Characteristic-based mean-variance portfolio choice

We study empirical mean-variance optimization when the portfolio weights are restricted to be direct functions of underlying stock characteristics such as value and momentum. The closed-form solution to the portfolio weights estimator shows that the portfolio problem in this case reduces to a mean-variance analysis of assets with returns given by single-characteristic strategies (e.g., momentum or value). In an empirical application to international stock return indexes, we show that the direct approach to estimating portfolio weights clearly beats a naive regression-based approach that models the conditional mean. However, a portfolio based on equal weights of the single-characteristic strategies performs about as well, and sometimes better, than the direct estimation approach, highlighting again the difficulties in beating the equal-weighted case in mean-variance analysis. The empirical results also highlight the potential for ‘stock-picking’ in international indexes using characteristics such as value and momentum with the characteristic-based portfolios obtaining Sharpe ratios approximately three times larger than the world market.     

Noise sensitivity of portfolio selection under various risk measures

We study the sensitivity to estimation error of portfolios optimized under various risk measures, including variance, absolute deviation, expected shortfall and maximal loss. We introduce a measure of portfolio sensitivity and test the various risk measures by considering simulated portfolios of varying sizes N and for different lengths T of the time series. We find that the effect of noise is very strong in all the investigated cases, asymptotically it only depends on the ratio N/T, and diverges (goes to infinity) at a critical value of N/T, that depends on the risk measure in question. This divergence is the manifestation of a phase transition, analogous to the algorithmic phase transitions recently discovered in a number of hard computational problems. The transition is accompanied by a number of critical phenomena, including the divergent sample to sample fluctuations of portfolio weights. While the optimization under variance and mean absolute deviation is always feasible below the critical value of N/T, expected shortfall and maximal loss display a probabilistic feasibility problem, in that they can become unbounded from below already for small values of the ratio N/T, and then no solution exists to the optimization problem under these risk measures. Although powerful filtering techniques exist for the mitigation of the above instability in the case of variance, our findings point to the necessity of developing similar filtering procedures adapted to the other risk measures where they are much less developed or non-existent. Another important message of this study is that the requirement of robustness (noise-tolerance) should be given special attention when considering the theoretical and practical criteria to be imposed on a risk measure.     

Asset-liability management under time-varying investment opportunities

Stochastic linear programming is a suitable numerical approach for solving practical asset-liability management problems. In this paper, we consider a multi-stage setting under time-varying investment opportunities and propose a decomposition of the benefits in dynamic re-allocation and predictability effects. We use a first-order unrestricted vector autoregressive process to model asset returns and state variables and include, in addition to equity returns and dividend-price ratios, Nelson/Siegel parameters to account for the evolution of the yield curve. The objective is to minimize the Conditional Value at Risk of shareholder value, i.e., the difference between the mark-to-market value of (financial) assets and the present value of future liabilities.     

A robust optimization approach to asset-liability management under time-varying investment opportunities

This paper presents an asset liability management model based on robust optimization techniques. The model explicitly takes into consideration the time-varying aspect of investment opportunities. The emphasis of the proposed approach is on computational tractability and practical appeal. Computational studies with real market data study the performance of robust-optimization-based strategies, and compare it to the performance of the classical stochastic programming approach.     

A comparison of MAD and CVaR models with real features

In this paper we consider two different mixed integer linear programming models for solving the single period portfolio selection problem when integer stock units, transaction costs and a cardinality constraint are taken into account. The first model has been formulated by using the maximization of the worst conditional expectation as objective function. The second model is based on the maximization of the safety measure corresponding to the mean absolute deviation. Extensive computational results are provided to compare the financial characteristics of the optimal portfolios selected by the two models on real data from European stock exchange markets. Some simple heuristics are also introduced that provide efficient and effective solutions when an optimal integer solution cannot be found in a reasonable amount of time.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

A conditional asset-pricing model with the optimal orthogonal portfolio

This paper employs a conditional asset-pricing model based on the optimal orthogonal portfolio approach to construct a factor portfolio that embodies all the latent factors important for pricing a given set of test assets. The advantage of this portfolio to the anomaly related mimicking portfolios is its ability to separate out the components of average return that are not related to the return covariation. The performance of this portfolio is evaluated against several conventional factors, using both cross-sectional and time-series regression approaches, as well as the Hansen and Jagannathan (1997) distance measure. Its strong out-of-sample results indicate that our suggested methodology may have important applications in risk management, portfolio selection and performance evaluation.     

Combining equilibrium,resampling, and analyst’s views in portfolio optimization

This paper proposes the use of a portfolio optimization methodology which combines features of equilibrium models and investor’s views as in Black and Litterman (1992), and also deals with estimation risk as in Michaud (1998). In this way, our combined methodology is able to meet the needs of practitioners for stable and diversified portfolio allocations, while it is theoretically grounded on an equilibrium framework. We empirically test the methodology using a comprehensive sample of developed countries fixed income and equity indices, as well as sub-samples stratified by geographical region, time period, asset class and risk level. In general, our proposed combined methodology generates very competitive portfolios when compared to other methodologies, considering three evaluation dimensions: financial efficiency, diversification, and allocation stability. By generating financially efficient, stable, and diversified portfolio allocations, our methodology is suitable for long-term investors such as Central Banks and Sovereign Wealth Funds.     

Mutual fund portfolio trading and investor flow

I estimate the extent to which mutual fund portfolio trading of securities is triggered by investor flows into and out of the funds, and find that this liquidity-induced portfolio trading activity is smaller than previously estimated by Edelen (1999). I obtain estimates from a much larger and broader sample of funds than Edelen’s (1999) sample. Portfolio managers of international funds trade a smaller fraction of investor flow than do those of domestic funds. Index funds invest a larger fraction. A funds’ usage of futures contracts does not have a statistically significant effect on how it trades in response to investor flows, but the unpredictability of investor flow weakly affects the trading response to flow.     

A model for tax advantages of portfolios with many assets

Taxable portfolios present challenges for optimization models with even a limited number of assets. Holding many assets, however, has a distinct tax advantage over holding few assets. In this paper, we develop a model that takes an extreme view of a portfolio as a continuum of assets to gain the broadest possible advantage from holding many assets. We find the optimal strategy for trading in this portfolio in the absence of transaction costs and develop bounding approximations on the optimal value. We compare the results in a simulation study to a portfolio consisting only of a market index and show that the multi-asset portfolio’s tax advantage can lead either to significant consumption or bequest increases.     

A statistical model of speculative bubbles,with applications to the stock markets of the United States,Japan, and China

It is common knowledge that the more prices deviate from fundamentals, the more likely it is for prices to reverse. Taking this into account, we propose a simple statistical model to identify speculative bubbles in financial markets. Through the estimates of the time varying parameters, including transition probabilities, we can identify when and how newly born bubbles grow and burst over time. The model can be estimated by recursive computations, which require a huge storage capacity for standard computers. For this reason, we introduce an approximation in the computation, maintaining the recursive nature of our estimation technique. We then apply this model to the stock markets of the United States, Japan, and China, estimate its parameters and the probabilities of a bubble crash, and obtain several interesting results: the time series data of the stock price bubble show an inherently non-stationary development and the probability of a bubble crash indeed increases as the stock price becomes too high or too low.     

Mutual fund performance evaluation with active peer benchmarks

We propose a simple approach to account for commonalities in mutual fund strategies that relies solely on information on fund returns and investment objectives. Our approach augments commonly used factor models with an additional benchmark that represents an equal investment in all same-category funds, which we call an active peer benchmark (APB). We find that APBs substantially reduce the average time series correlation of residuals between individual funds within a group when added to a four-factor equity model (or to a seven-factor fixed-income model). Importantly, adding this APB significantly improves the selection of funds with future outperformance.     

Detecting time-variation in corporate bond index returns: A smooth transition regression model

This paper investigates the time-varying corporate bond index returns in a multi-factor smooth transition regression model. We find that expected index returns vary between weak and strong economic regimes, where the transition from one regime to the other is governed by the 3-quartered growth of industrial production. Weak economic regimes are characterized by low growth of industrial production, vice versa for strong economic regimes. Further, risk factor sensitivities are generally more negative in strong economic regimes than in weak regimes, implying that index returns are low when economic conditions are good and high when economic conditions are poor.