Measuring and Optimizing Portfolio Credit Risk: A Copula‐based Approach*

In this work, we present a methodology for measuring and optimizing the credit risk of a loan portfolio taking into account the non‐normality of the credit loss distribution. In particular, we aim at modelling accurately joint default events for credit assets. In order to achieve this goal, we build the loss distribution of the loan portfolio by Monte Carlo simulation. The times until default of each obligor in portfolio are simulated following a copula‐based approach. In particular, we study four different types of dependence structure for the credit assets in portfolio: the Gaussian copula, the Student's t‐copula, the grouped t‐copula and the Clayton n‐copula (or Cook–Johnson copula). Our aim is to assess the impact of each type of copula on the value of different portfolio risk measures, such as expected loss, maximum loss, credit value at risk and expected shortfall. In addition, we want to verify whether and how the optimal portfolio composition may change utilizing various types of copula for describing the default dependence structure. In order to optimize portfolio credit risk, we minimize the conditional value at risk, a risk measure both relevant and tractable, by solving a simple linear programming problem subject to the traditional constraints of balance, portfolio expected return and trading. The outcomes, in terms of optimal portfolio compositions, obtained assuming different default dependence structures are compared with each other. The solution of the risk minimization problem may suggest us how to restructure the inefficient loan portfolios in order to obtain their best risk/return profile. In the absence of a developed secondary market for loans, we may follow the investment strategies indicated by the solution vector by utilizing credit default swaps.     

Multi-objective private wealth allocation without subportfolios

As opposed to institutional investors, individual investors typically have several investment objectives in mind. The traditional utility maximization approach is not only oversimplified but also may not be suitable for real world application. Behavioral asset allocation divides a portfolio into subportfolios, which can cause potential problems. This paper follows the Modern Portfolio Theory and introduces the practical idea of treating some goals as constraints. How this works in practice is illustrated by an example of an individual having three different objectives. This article follows the idea of Chen et al. (2006) and includes life insurance. Consumption is modeled into three parts and accommodates a reasonable basis for calculating life insurance requirements and generally integrates consumption into the investment decision. As a whole, the model provides a customized solution for the environment and complex investment goals of an individual.     

Illiquidity, position limits, and optimal investment for mutual funds

We study the optimal trading strategy of mutual funds that face both position limits and differential illiquidity. We provide explicit characterization of the optimal trading strategy and conduct an extensive analytical and numerical analysis of the optimal trading strategy. We show that the optimal trading boundaries are increasing in both the lower and the upper position limits. We find that position limits can affect current trading strategy even when they are not currently binding and other seemingly intuitive trading strategies can be costly. We also examine the optimal choice of position limits.     

International portfolio reallocation: Diversification benefits and European monetary union

We investigate the determinants of bilateral international equity and bond portfolio reallocation across a large cross-section of countries spanning over two sample periods: 1997-2001 and 1997-2005. We find that the strongest drivers are the marginal diversification benefits arising from the pure asset component and the initial degree of underweight. This evidence suggests that global portfolio reallocations over the asset boom and bust period were determined by optimal diversification considerations. We also find that due to economic and monetary union (EMU) the weight assigned by euro area investors to investment in euro area countries increased significantly in equity and fixed income portfolios, with a trade diverting effect against the British bond market.     

Non-addictive habits: optimal consumption-portfolio policies

We formulate a model of preferences with non-addictive habits, where consumption is required to be non-negative at all times, but can fall below a “standard of living” index that aggregates past consumption. We study the consumption-portfolio problem taking account of the non-negativity constraint on consumption, and provide a constructive proof for the existence of an optimal policy on a finite time-horizon [0,T]. We show that the consumption constraint binds up to an endogenous stopping time τ∗∈[0,T], after which it remains slack until T. A decomposition of constrained consumption involving an Asian average-strike capped call-option is demonstrated.     

Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium

I analyze the optimal intertemporal portfolio problem of an investor who worries about model misspecification and insists on robust decision rules when facing a mean-reverting risk premium. The desire for robustness lowers the total equity share, but increases the proportion of the intertemporal hedging demand. I present a methodology for calculation of detection-error probabilities, which is based on Fourier inversion of the conditional characteristic functions of the Radon-Nikodym derivatives. The quantitative effect of robustness is more modest than in i.i.d. settings, because model discrimination between the benchmark and the worst-case alternative model is easier, as indicated by the detection-error probabilities.     

International portfolio diversification and endogenous labor supply choice

This paper presents a multi-country general equilibrium model driven by productivity shocks, where labor supply and consumption are chosen endogenously. We use this framework to study the effect of labor supply for optimal international diversification. We find that the model's ability to help explain home-bias depends crucially on the level of substitutability between consumption and non-working time. Quantitatively, the non-separability in the preferences helps in a nonnegligible way, but it cannot entirely explain the extreme degree of home-bias in U.S. portfolios.     

On the impact of leverage constraints on asset prices and trading volume

Abstract. Researchers have used stylized facts on asset prices and trading volume in stock markets (in particular, the mean reversion of asset returns and the correlations between trading volume, price changes and price levels) to support theories where agents are not rational expected utility maximizers. This paper shows that this empirical evidence is in fact consistent with a standard infinite horizon – perfect information – expected utility economy where some agents face leverage constraints similar to those found in todays financial markets. In addition, and in sharp contrast to the theories above, we explain some qualitative differences that are observed in the price-volume relation on stock and on futures markets. We consider a continuous-time economy where agents maximize the integral of their discounted utility from consumption under both budget and leverage constraints. Building on the work by Vila and Zariphopoulou (1997), we find a closed form solution, up to a negative constant, for the equilibrium prices and demands in the region of the state space where the constraint is non-binding. We show that, at the equilibrium, stock holdings volatility as well as its ratio to stock price volatility are increasing functions of the stock price and interpret this finding in terms of the price-volume relation. We would like to thank the editor and two anonimous referees for valuable substantive comments. Our gratitude also to Franklin Allen, Kerry Back, Domenico Cuoco, Xavier Freixas, Sanford Grossman, Michel Habib, Lutz Hendricks, Richard Kihlstrom, Fernando Restoy, Mary Thomson, Jean-Luc Vila, participants to seminars at Birkbeck College, Carnegie-Mellon, Columbia, ESSEC, HEC, IAE, INSEAD, London Business School, London School of Economics, McGill, Michigan, National University of Singapore, Pompeu Fabra, North Carolina, Washington-St-Louis, Wharton, the Jornadas de Economía Financiera BBV, and the Meetings of the Society for Economic Dynamics and Control and the American Finance Association. Special thanks are due to Süleyman Basak for his enthusiastic support and many helpful suggestions. The usual disclaimer applies. We gratefully acknowledge the support of the BBV and Caja de Madrid Foundations and CREF (both authors) and of the Spanish Ministry of Education under DGICYT grant no. PB93-0388 (first author).     

A structural dynamic microsimulation model of household savings and labour supply

A structural model of the household is described that represents current best-practice in the analysis of savings and labour supply responses to the policy environment. Care has been taken in specifying the model so that it represents an appropriate basis for the analysis of incentive effects to policy change, and for exploring the empirical support for alternative structural assumptions. Matching the model to survey data for the UK reveals some interesting puzzles in relation to the timing of retirement.     

Moving costs, nondurable consumption and portfolio choice

The substantial adjustment cost for housing affects nondurable consumption and portfolio allocations, as well as the frequency of housing transactions. A simple theoretical model, roughly calibrated, is used to assess the quantitative impact of adjustment costs on those decisions. The impact on portfolios is found to be significant, suggesting that housing wealth should be useful in empirical studies of portfolio choice. The welfare loss from the transaction cost is also substantial. The effect on nondurable consumption is small, however, so adjustment costs can explain only a small part of the equity premium puzzle.     

Empirical analysis of jump dynamics, heavy-tails and skewness on value-at-risk estimation

This study provides a comprehensive analysis of the possible influences of jump dynamics, heavy-tails, and skewness with regard to VaR estimates through the assessment of both accuracy and efficiency. To this end, the ARJI model, and its degenerative GARCH model with normal, GED, and skewed normal (SN) distributions were adopted to capture the properties of time-varying volatility, time-varying jump intensity, heavy-tails and skewness, for a range of stock indices across international stock markets during the period of the U.S. subprime mortgage crisis. Empirical results show that, with regard to the evaluation of accuracy, the role of jump dynamics is more substantial than heavy-tails or skewness as it pertains to VaR accuracy at the 90% and 95% levels, while heavy-tails become more important at the 99% level for a long position. However, the influence of the abovementioned properties on VaR estimation does not appear substantial for a short position. In addition, the properties of jump dynamics and skewness appear to be beneficial for the improvement of efficiency.     

A new estimator for trade costs and its small sample properties

This paper discusses the estimation of parameters of a traditional transportation model, as it is typically present in so-called Takayama–Judge type spatial price equilibrium models. In contrast to previously used estimation methods, observations of regional prices as well as of trade costs are used in a direct estimation of the first order conditions. The proposed method uses bi-level programming techniques to minimize a weighted least squares criterion under the restriction that the estimated parameters satisfy the Kuhn–Tucker conditions for an optimal solution of the transport model. A penalty function and a smooth reformulation are used to iteratively approximate the complementary slackness conditions. Monte-Carlo simulations are used to trace out some properties of the estimator and compare it with a traditional calibration method. The analysis shows that the proposed technique estimates prices as well as trade costs more precisely than the traditional calibration method. It is suggested to apply the same method to a range of linear and quadratic models.     

Currency substitution, portfolio diversification, and money demand

Abstract .  We extend the Thomas (1985) dynamic optimizing model of money demand and currency substitution to the case in which the individual has restricted or no access to foreign currency denominated bonds. In this case currency substitution decisions and asset substitution decisions are not separable. The results obtained suggest that the significance of an expected exchange rate depreciation term in the demand for domestic money provides a valid test for the presence of currency substitution. Applying this approach to six Latin-American countries, we find evidence of currency substitution in Colombia, Dominican Republic, and Venezuela, but not in Brazil and Chile.     

Portfolio choice and pricing in illiquid markets

This paper studies portfolio choice and pricing in markets in which immediate trading may be impossible. It departs from the literature by removing restrictions on asset holdings, and finds that optimal positions depend significantly and naturally on liquidity: When expected future liquidity is high, agents take more extreme positions, given that they do not have to hold those positions for long when they become undesirable. Consequently, larger trades should be observed in markets with more frequent trading. Liquidity need not affect the price significantly, however, because liquidity has offsetting impacts on different agents' demands. This result highlights the importance of unrestricted portfolio choice. The paper draws parallels with the transaction-cost literature and clarifies the relationship between the price level and the realized trading frequency in this literature.     

A portfolio choice model with utility from anticipation of future consumption and stock market mean reversion

This paper studies a consumption and portfolio choice problem of a long-lived investor who derives pleasure not only from current consumption, but also from the contemplation of future consumption. The model assumes that all effects of future consumption on current well being are assumed to enter through a single variable—namely, the “stock of future consumption”—analogously to habit-formation models. The main implications of the model concern the incentives for savings, and the fundamental sources of risk in financial markets. It is shown that, when the stock market exhibits mean reversion, deriving utility from anticipation of future consumption has a tremendous effect on portfolio choice. In particular, mean allocation to stocks is much lower under the proposed preferences relative to the standard preferences, especially for high risk averse investors.     

Saving rates and portfolio choice with subsistence consumption

We analytically show that a common across rich/poor individuals Stone-Geary utility function with subsistence consumption in the context of a simple two-asset portfolio-choice model is capable of qualitatively and quantitatively explaining: (i) the higher saving rates of the rich, (ii) the higher fraction of personal wealth held in risky assets by the rich, and (iii) the higher volatility of consumption of the wealthier. On the contrary, time-variant “keeping-up-with-the-Joneses” weighted average consumption which plays the role of moving benchmark subsistence consumption gives the same portfolio composition and saving rates across the rich and the poor, failing to reconcile the model with what micro data say.     

Equilibrium portfolios in the neoclassical growth model

This paper studies equilibrium portfolios in the standard neoclassical growth model under uncertainty with heterogeneous agents and dynamically complete markets. Preferences are purposely restricted to be quasi-homothetic. The main source of heterogeneity across agents is due to different endowments of shares of the representative firm at date 0. Fixing portfolios is the optimal equilibrium strategy in stationary endowment economies with dynamically complete markets. However, when the environment displays changing degrees of heterogeneity across agents, the trading strategy of fixed portfolios cannot be optimal in equilibrium. Very importantly, our framework can generate changing heterogeneity if and only if either minimum consumption requirements are not zero or labor income is not zero and the value of human and non-human wealth are linearly independent.