Measuring portfolio credit risk correctly: Why parameter uncertainty matters

Why should risk management systems account for parameter uncertainty? In addressing this question, the paper lets an investor in a credit portfolio face non-diversifiable uncertainty about two risk parameters – probability of default and asset-return correlation – and calibrates this uncertainty to a lower bound on estimation noise. In this context, a Bayesian inference procedure is essential for deriving and analyzing the main result, i.e. that parameter uncertainty raises substantially the tail risk perceived by the investor. Since a measure of tail risk that incorporates parameter uncertainty is computationally demanding, the paper also derives a closed-form approximation to such a measure.     

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.     

International portfolio selection with exchange rate risk: A behavioural portfolio theory perspective

This paper analyzes international portfolio selection with exchange rate risk based on behavioural portfolio theory (BPT). We characterize the conditions under which the BPT problem with a single foreign market has an optimal solution, and show that the optimal portfolio contains the traditional mean–variance efficient portfolio without consideration of exchange rate risk, and an uncorrelated component constructed to hedge against exchange rate risk. We illustrate that the optimal portfolio must be mean–variance efficient with exchange rate risk, while the same is not true from the perspective of local investors unless certain conditions are satisfied. We further establish that international portfolio selection in the BPT with multiple foreign markets consists of two sequential decisions. Investors first select the optimal BPT portfolio in each market, overlooking covariances among markets, and then allocate funds across markets according to a specific rule to achieve mean–variance efficiency or to minimize the loss in efficiency.     

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.     

Access to information and international portfolio allocation

We examine whether foreign equity holdings of portfolio investors depend on the level of information accessibility between the investors’ home and host countries. Using a comprehensive data set, alternative measures of information accessibility and robust analytical techniques, we show that differences in access to cross-country information significantly influence investors’ portfolio allocation decisions. Furthermore, the results suggest that for a given level of access to information, investors prefer to invest more in countries with a higher quality of legal/macro-institutions. Finally, the findings also confirm that the implications of information accessibility are more pronounced when markets are turbulent.     

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.     

Income hedging and portfolio decisions

We examine whether the decision to participate in the stock market and other related portfolio decisions are influenced by income hedging motives. Economic theory predicts that the market participation propensity should increase as the correlation between income growth and stock market returns decreases. Surprisingly, empirical studies find limited support for the income hedging motive. Using a rich, unique Dutch data set and the National Longitudinal Survey of the Youth (NLSY) from the United States, we show that when the income-return correlation is low, individuals exhibit a greater propensity to participate in the market and allocate a larger proportion of their wealth to risky assets. Even when the income risk is high, individuals exhibit a higher propensity to participate in the market when the hedging potential is high. These findings suggest that income hedging is an important determinant of stock market participation and asset allocation decisions.     

Nonparametric correlation models for portfolio allocation

This article proposes time-varying nonparametric and semiparametric estimators of the conditional cross-correlation matrix in the context of portfolio allocation. Simulations results show that the nonparametric and semiparametric models are best in DGPs with substantial variability or structural breaks in correlations. Only when correlations are constant does the parametric DCC model deliver the best outcome. The methodologies are illustrated by evaluating two interesting portfolios. The first portfolio consists of the equity sector SPDRs and the S&P 500, while the second one contains major currencies. Results show the nonparametric model generally dominates the others when evaluating in-sample. However, the semiparametric model is best for out-of-sample analysis.     

Global equity fund performance, portfolio concentration, and the fundamental law of active management

This paper investigates the relation between portfolio concentration and the performance of global equity funds. Concentrated funds with higher levels of tracking error display better performance than their more broadly diversified counterparts. We show that the observed relation between portfolio concentration and performance is mostly driven by the breadth of the underlying fund strategies; not just by fund managers’ willingness to take big bets. Our results indicate that when investors strive to select the best-performing funds, they should not only consider fund managers’ tracking-error levels. More important is that they take into account the extent to which fund managers carefully allocate their risk budget across multiple investment strategies and have concentrated holdings in multiple market segments simultaneously.     

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.     

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.     

Momentum strategies based on reward–risk stock selection criteria

In this paper, we analyze momentum strategies that are based on reward–risk stock selection criteria in contrast to ordinary momentum strategies based on a cumulative return criterion. Reward–risk stock selection criteria include the standard Sharpe ratio with variance as a risk measure, and alternative reward–risk ratios with the expected shortfall as a risk measure. We investigate momentum strategies using 517 stocks in the S&P 500 universe in the period 1996–2003. Although the cumulative return criterion provides the highest average monthly momentum profits of 1.3% compared to the monthly profit of 0.86% for the best alternative criterion, the alternative ratios provide better risk-adjusted returns measured on an independent risk-adjusted performance measure. We also provide evidence on unique distributional properties of extreme momentum portfolios analyzed within the framework of general non-normal stable Paretian distributions. Specifically, for every stock selection criterion, loser portfolios have the lowest tail index and tail index of winner portfolios is lower than that of middle deciles. The lower tail index is associated with a lower mean strategy. The lowest tail index is obtained for the cumulative return strategy. Given our data-set, these findings indicate that the cumulative return strategy obtains higher profits with the acceptance of higher tail risk, while strategies based on reward–risk criteria obtain better risk-adjusted performance with the acceptance of the lower tail risk.     

Country-specific equity market characteristics and foreign equity portfolio allocation

Do country-specific equity market characteristics explain variations in foreign equity portfolio allocation? We study this question using comprehensive foreign equity portfolio holdings data and different measures of country-specific equity market factors for 36 host countries. Employing panel data econometric estimations, our investigation shows that foreign investors prefer to invest more in larger and highly visible developed markets which are more liquid, exhibit a higher degree of market efficiency and have lower trading costs. The findings imply that by improving the preconditions necessary for well-functioning capital markets, policymakers should be able to attract higher levels of foreign equity portfolio investments.     

Technical analysis: An asset allocation perspective on the use of moving averages

In this paper, we analyze the usefulness of technical analysis, specifically the widely employed moving average trading rule from an asset allocation perspective. We show that, when stock returns are predictable, technical analysis adds value to commonly used allocation rules that invest fixed proportions of wealth in stocks. When uncertainty exists about predictability, which is likely in practice, the fixed allocation rules combined with technical analysis can outperform the prior-dependent optimal learning rule when the prior is not too informative. Moreover, the technical trading rules are robust to model specification, and they tend to substantially outperform the model-based optimal trading strategies when the model governing the stock price is uncertain.     

Evaluation of linear asset pricing models by implied portfolio performance

We present a theoretical perspective that motivates the use of the Generalized Least Squares R-Square, prominently advocated by Lewellen et al. [Lewellen, J., Nagel, S., Shanken, J., forthcoming. A skeptical appraisal of asset-pricing tests. Journal of Financial Economics], as an evaluation measure for multivariate linear asset pricing models. Adapting results from Shanken [Shanken, J., 1985. Multivariate tests of the zero-beta CAPM. Journal of Financial Economics 14, 327–348] and Kandel and Stambaugh [Kandel, S., Stambaugh, R.F., 1995. Portfolio inefficiency and the cross-section of expected returns. Journal of Finance 50, 157–184], we provide various interpretations and a graphical account in mean-variance space of this measure, facilitating a better understanding of its properties. We furthermore relate it to another leading evaluation metric, the HJ-distance of Hansen and Jagannathan [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 557–590]. Additionally, we present a comparison between these evaluation measures using mean-variance mathematics in risk-return space, and we provide a simple formula for calculating both model evaluation measures that involves only the parameters of the mean-variance asset and factor frontiers.     

Household portfolio choices,health status and health care systems: A cross-country analysis based on SHARE

Health risk is increasingly viewed as an important form of background risk that affects household portfolio decisions. However, its role might be mediated by the presence of a protective full-coverage national health service that could reduce households’ probability of incurring current and future out-of-pocket medical expenditures. We use SHARE data to study the influence of current health status and future health risk on the decision to hold risky assets, across ten European countries with different health systems, each offering a different degree of protection against out-of-pocket medical expenditures. We find robust empirical evidence that perceived health status matters more than objective health status and, consistent with the theory of background risk, health risk affects portfolio choices only in countries with less protective health care systems. Furthermore, portfolio decisions consistent with background risk models are observed only with respect to middle-aged and highly-educated investors.     

On portfolio optimization: Imposing the right constraints

We reassess the recent finding that no established portfolio strategy outperforms the naively diversified portfolio, 1/N, by developing a constrained minimum-variance portfolio strategy on a shrinkage theory based framework. Our results show that our constrained minimum-variance portfolio yields significantly lower out-of-sample variances than many established minimum-variance portfolio strategies. Further, we observe that our portfolio strategy achieves higher Sharpe ratios than 1/N, amounting to an average Sharpe ratio increase of 32.5% across our six empirical datasets. We find that our constrained minimum-variance strategy is the only strategy that achieves the goal of improving the Sharpe ratio of 1/N consistently and significantly. At the same time, our developed portfolio strategy achieves a comparatively low turnover and exhibits no excessive short interest.     

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.     

Non-Gaussian diversification: When size matters

Classical portfolio theory informs investors that they should have a large number of assets in their portfolios in order to diversify risk. We show that the non-Gaussian features of stock return distribution may not allow for this risk protection in times of crisis. Moreover, we demonstrate empirically that, if investors are risk-averse and consider higher order moments, they have numerous incentives not to diversify their portfolios fully. This is caused by the evolution of both large losses and asymmetry of returns when the numbers of assets in a portfolio change.