Portfolio selection with mental accounts and delegation

Das et al. (2010) develop an elegant framework where an investor selects portfolios within mental accounts but ends up holding an aggregate portfolio on the mean-variance frontier. This investor directly allocates the wealth in each account among available assets. In practice, however, investors often delegate the task of allocating wealth among assets to portfolio managers who seek to beat certain benchmarks. Accordingly, we extend their framework to the case where the investor allocates the wealth in each account among portfolio managers. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we present conditions under which such portfolios are not on the mean-variance frontier, and conditions under which they are. Third, we show that the aforementioned analytical characterization is also applicable within the framework of Das et al. and thus improves upon their numerical approach.     

Portfolio selection with mental accounts and background risk

Das et al. (2010) develop a model where an investor divides his or her wealth among mental accounts with motives such as retirement and bequest. Nevertheless, the investor ends up selecting portfolios within mental accounts and an aggregate portfolio that lie on the mean–variance frontier. Importantly, they assume that the investor only faces portfolio risk. In practice, however, many individuals also face background risk. Accordingly, our paper expands upon theirs by considering the case where the investor faces background risk. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we show that these portfolios lie away from the mean–variance frontier under fairly general conditions. Third, we find that the composition and location of such portfolios can differ notably from those of portfolios on the mean–variance frontier.     

Nonlinearly weighted convex risk measure and its application

We propose a new class of risk measures which satisfy convexity and monotonicity, two well-accepted axioms a reasonable and realistic risk measure should satisfy. Through a nonlinear weight function, the new measure can flexibly reflect the investor’s degree of risk aversion, and can control the fat-tail phenomenon of the loss distribution. A realistic portfolio selection model with typical market frictions taken into account is established based on the new measure. Real data from the Chinese stock markets and American stock markets are used for empirical comparison of the new risk measure with the expected shortfall risk measure. The in-sample and out-of-sample empirical results show that the new risk measure and the corresponding portfolio selection model can not only reflect the investor’s risk-averse attitude and the impact of different trading constraints, but can find robust optimal portfolios, which are superior to the corresponding optimal portfolios obtained under the expected shortfall risk measure.     

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.     

Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach

In this paper, we seek to examine the effect of the presence of long memory on the dependence structure between financial returns and on portfolio optimization. First, we focus on the dependence structure using copulas. To select the best copula, in addition to the goodness of fit tests, we employ a graphical method based on visual comparison of the fitted copula density and the smoothed copula density estimated by wavelets. Moreover, we check the stability of the copula parameter. The empirical results show that the long memory affects the dependence structure. Second, we analyze the impact of this dependence structure on the optimal portfolio. We propose a new approach based on minimizing the Conditional Value at Risk and assuming that the dependence structure is modeled by the copula parameter. The empirical results show that our approach outperforms the traditional minimizing variance approach, where the dependence structure is represented by the linear correlation coefficient.     

Portfolio selection subject to experts' judgments

Since Markowitz [Markowitz, H. M. (1952). Portfolio selection. The Journal of Finance, 7, 77-91.], mean-variance theory has assumed that risky-asset returns to be random variables. The theory deals with this uncertainty by further assuming that investors hold homogeneous beliefs regarding the probability distribution governing return uncertainty. While the theory deals with return uncertainty, it fails to address measurement imprecision. In his original work, Markowitz recognized the need to combine randomness with heterogeneous expert judgment resulting in such imprecision. The main objective contributions of the paper are (i) to explore the implications of fuzzy return indeterminacy on mean-variance optimal portfolio choice, (ii) to use bid-ask spread as a proxy measure of the indeterminacy or “fuzzy” nature of random returns, and (iii) to introduce a brief, self-contained glimpse of empirical representations to practitioners unfamiliar with the fuzzy modeling field. Exposition, such as this one, is expected to open new collaborations between other branches of fuzzy mathematics and asset-pricing theories.     

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.     

Assessing the risk-return trade-off in loan portfolios

This paper proposes a methodology to analyse the risk and return of large loan portfolios in a joint setting. I propose a tractable model to obtain the distribution of loan returns from observed interest rates and default frequencies. I follow a sectoral approach that captures the heterogeneous cyclical features of different kinds of loans and yields moments in closed form. I investigate the validity of mean–variance analysis with a value at risk constraint and study its relationship with utility maximisation. Finally, I study the efficiency of corporate and household loan portfolios in an empirical application to the Spanish banking system.     

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.     

Consumer credit-risk models via machine-learning algorithms

We apply machine-learning techniques to construct nonlinear nonparametric forecasting models of consumer credit risk. By combining customer transactions and credit bureau data from January 2005 to April 2009 for a sample of a major commercial bank’s customers, we are able to construct out-of-sample forecasts that significantly improve the classification rates of credit-card-holder delinquencies and defaults, with linear regression R²’s of forecasted/realized delinquencies of 85%. Using conservative assumptions for the costs and benefits of cutting credit lines based on machine-learning forecasts, we estimate the cost savings to range from 6% to 25% of total losses. Moreover, the time-series patterns of estimated delinquency rates from this model over the course of the recent financial crisis suggest that aggregated consumer credit-risk analytics may have important applications in forecasting systemic risk.     

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.     

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.     

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.     

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.     

Risk capital allocation for RORAC optimization

This paper considers the financial optimization problem of a firm with several sub-businesses striving for its optimal RORAC. An insightful example shows that the implementation of classical gradient capital allocation can be suboptimal if division managers are allowed to venture into all business whose marginal RORAC exceeds the firm’s RORAC. The marginal RORAC requirements are refined by adding a risk correction term that takes into account the interdependencies of the risks of different lines of business. It is shown that under certain stationarity conditions this approach can guarantee that the optimal RORAC will eventually be achieved.     

Risk factor contributions in portfolio credit risk models

Determining contributions to overall portfolio risk is an important topic in risk management. For positions (instruments and sub-portfolios), this problem has been well studied, and a significant theory built, around the calculation of marginal contributions. We consider the problem of determining the contributions to portfolio risk of risk factors. This cannot be addressed through an immediate extension of techniques for position contributions, since the portfolio loss is a nonlinear function of the risk factors. We employ the Hoeffding decomposition of the portfolio loss into a sum of terms depending on the factors. This decomposition restores linearity, but includes terms arising from joint effects of groups of factors. These cross-factor terms provide information to risk managers, since they can be viewed as best hedges of the portfolio loss involving instruments of increasing complexity. We illustrate the technique on multi-factor portfolio credit risk models, where systematic factors represent industries, geographical sectors, etc.     

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.     

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 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.     

Discrete hedging of American-type options using local risk minimization

Local risk minimization and total risk minimization discrete hedging have been extensively studied for European options [e.g., Schweizer, M., 1995. Variance-optimal hedging in discrete time. Mathematics of Operation Research 20, 1–32; Schweizer, M., 2001. A guided tour through quadratic hedging approaches. In: Jouini, E., Cvitanic, J., Musiela, M., Option pricing, interest rates and risk management, Cambridge University Press, pp. 538–574]. In practice, hedging of options with American features is more relevant. For example, equity linked variable annuities provide surrender benefits which are essentially embedded American options. In this paper we generalize both quadratic and piecewise linear local risk minimization hedging frameworks to American options. We illustrate that local risk minimization methods outperform delta hedging when the market is highly incomplete. In addition, compared to European options, distributions of the hedging costs are typically more skewed and heavy-tailed. Moreover, in contrast to quadratic local risk minimization, piecewise linear risk minimization hedging strategies can be significantly different, resulting in larger probabilities of small costs but also larger extreme cost.