Portfolio selection: An extreme value approach

We show theoretically that lower tail dependence (χ), a measure of the probability that a portfolio will suffer large losses given that the market does, contains important information for risk-averse investors. We then estimate χ for a sample of DJIA stocks and show that it differs systematically from other risk measures including variance, semi-variance, skewness, kurtosis, beta, and coskewness. In out-of-sample tests, portfolios constructed to have low values of χ outperform the market index, the mean return of the stocks in our sample, and portfolios with high values of χ. Our results indicate that χ is conceptually important for risk-averse investors, differs substantially from other risk measures, and provides useful information for portfolio selection.     

Mean–variance portfolio selection with ‘at-risk’ constraints and discrete distributions

We examine the impact of adding either a VaR or a CVaR constraint to the mean–variance model when security returns are assumed to have a discrete distribution with finitely many jump points. Three main results are obtained. First, portfolios on the VaR-constrained boundary exhibit (K + 2)-fund separation, where K is the number of states for which the portfolios suffer losses equal to the VaR bound. Second, portfolios on the CVaR-constrained boundary exhibit (K + 3)-fund separation, where K is the number of states for which the portfolios suffer losses equal to their VaRs. Third, an example illustrates that while the VaR of the CVaR-constrained optimal portfolio is close to that of the VaR-constrained optimal portfolio, the CVaR of the former is notably smaller than that of the latter. This result suggests that a CVaR constraint is more effective than a VaR constraint to curtail large losses in the mean–variance model.     

Portfolio selection with commodities under conditional copulas and skew preferences

This article investigates the portfolio selection problem of an investor with three-moment preferences taking positions in commodity futures. To model the asset returns, we propose a conditional asymmetric t copula with skewed and fat-tailed marginal distributions, such that we can capture the impact on optimal portfolios of time-varying moments, state-dependent correlations, and tail and asymmetric dependence. In the empirical application with oil, gold and equity data from 1990 to 2010, the conditional t copulas portfolios achieve better performance than those based on more conventional strategies. The specification of higher moments in the marginal distributions and the type of tail dependence in the copula has significant implications for the out-of-sample portfolio performance.     

The distribution of realized variances: Marginal behaviors, asymmetric dependence and contagion effects

We examine the unconditional distribution of the realized variance of three European stock market indexes obtained from intraday transaction prices. We find that they share common distributional features: a significant mass close to zero, a sharp decrease afterwards and a significant right tail. Their important differences, however, compel us to model them non-parametrically through lognormal kernel estimators. We then move to the analysis of their dependence structure and find strong evidence of asymmetry. Hence, unlike common practice, we resort to non-exchangeable copula models. Such a characterization also allows us to assess the direction of greater contamination among stock market variances.     

基于GARCH-EVT-Copula的社保基金投资组合风险测度研究

社保基金是社会保障事业健康发展的物质基础,安全性是其投资的首要原则。文章基于GARCH-EVT-Copula方法测度了社保基金投资组合的VaR。首先,基于GARCH、EVT对投资组合中各金融资产收益的边缘分布建模,然后,采用极大似然估计法和Bootstrap方法估计尾部的分布函数,接着,基于Copula方法研究组合中金融资产间的相关结构,最后,运用Monte Carlo方法测度投资组合的VaR。Kupiec检验表明,基于GARCH-EVT-Copula模型测度社保基金投资组合的风险是合适的。     

期货投资组合交易保证金设置研究——基于Copula模型和极值理论的分析

本文以棉花、铜、天然橡胶三个期货合约为研究对象,基于t-Copula模型,利用Monte Carlo模拟法计算在一定权重下由三个品种构成的期货投资组合的VaR和ES值作为投资组合的保证金数值。Kupiec回溯测试结果表明,t-Copula模型结合极值理论计算出的期货投资组合保证金相比其他方法能够在较好覆盖极端风险的同时降低投资成本。     

Portfolio performance of linear SDF models: an out-of-sample assessment

We evaluate linear stochastic discount factor models using an ex-post portfolio metric: the realized out-of-sample Sharpe ratio of mean–variance portfolios backed by alternative linear factor models. Using a sample of monthly US portfolio returns spanning the period 1968–2016, we find evidence that multifactor linear models have better empirical properties than the CAPM, not only when the cross-section of expected returns is evaluated in-sample, but also when they are used to inform one-month ahead portfolio selection. When we compare portfolios associated to multifactor models with mean–variance decisions implied by the single-factor CAPM, we document statistically significant differences in Sharpe ratios of up to 10 percent. Linear multifactor models that provide the best in-sample fit also yield the highest realized Sharpe ratios.     

Marketing Period Risk in a Portfolio Context: Comment and Extension

This paper re-examines and extends the findings of Bond et al., Journal of Real Estate Finance and Economics, 34, 447–461, (2007) who consider the theoretical model of Lin and Vandell, Real Estate Economics, 35, 291–330, (2007) to determine the extent to which individual real estate asset return characteristics caused by marketing period risk disappear in a large, diversified real estate portfolio. The effects of marketing period risk are found to disappear in the limit with growth in the size of the portfolio, with ex ante variance approaching ex post variance, but only if the portfolio consists of nonsystematic risk alone, in which case both approach zero. The marketing period risk factor (MPRF), representing the ratio of ex ante to ex post variance, however, does not in general approach zero in the limit, in fact could increase or decrease depending upon the illiquidity characteristics of the individual assets and the magnitude and degree of correlation among individual property returns and marketing periods. The results suggest that even large institutional real estate portfolio managers must consider the illiquidity present in their portfolios and cannot assume that its effect will be diversified away.

Stock market dependence in crisis periods: Evidence from oil price shocks and the Qatar blockade

This paper examines the correlation and the dependence patterns of the Qatar stock market with other markets using copula statistical theory and exploiting new datasets covering the period August 1998 to June 2018. To examine the crisis –specific change in the average degree of dependence we decomposed the data into the time periods before and after oil price shocks and the 2017 political crisis among the Gulf Cooperation Council members (i.e. the Qatari blockade). Our findings from the static copula modelling show that the correlations between the Qatari and the other stock markets significantly change after the oil price and the blockade crisis as well. The degree of change in the correlation is time varying and differs from county-group to another. Moreover, our findings reveals that the 2008 global financial crisis has a stronger impact than the price shocks and political crisis. The findings of the paper are of interest and allow for formulating a reliable and dynamic portfolio design framework for investors and risk managers.     

Assessing dependence between financial market indexes using conditional time-varying copulas: applications to Value at Risk (VaR)

We analyse the dynamic dependence structure between broad stock market indexes from the United States (S&P500), Britain (FTSE100), Brazil (BOVESPA) and Mexico (PCMX). We employ Patton’s [Int. Econ. Rev., 2006, 2, 527–556] conditional copula setting and additionally observe the impact of different copula functions on Value at Risk (VaR) estimation. We conclude that the dependence between BOVESPA and the other indexes has intensified since the beginning of 2007. In our case the particular copula form is not crucial for VaR estimation. A goodness-of-fit test based on the parametric bootstrap is also applied. The best fits are obtained via time constant Student-t and time-varying Normal copulas.     

The generalized value at risk admissible set: constraint consistency and portfolio outcomes

Generalized value at risk (GVaR) adds a conditional value at risk or censored mean lower bound to the standard value at risk and considers portfolio optimization problems in the presence of both constraints. For normal distributions the censored mean is synonymous with the statistical hazard function, but this is not true for fat-tailed distributions. The latter turn out to imply much tighter bounds for the admissible portfolio set and indeed for the logistic, an upper bound for the portfolio variance that yields a simple portfolio choice rule. The choice theory in GVaR is in general not consistent with classic Von Neumann–Morgenstern utility functions for money. A re-specification is suggested to make it so that gives a clearer picture of the economic role of the respective constraints. This can be used analytically to explore the choice of portfolio hedges.     

Checking for asymmetric default dependence in a credit card portfolio: A copula approach

Traditional credit risk models adopt the linear correlation as a measure of dependence and assume that credit losses are normally-distributed. However some studies have shown that credit losses are seldom normal and the linear correlation does not give accurate assessment for asymmetric data. Therefore it is possible that many credit models tend to misestimate the probability of joint extreme defaults.This paper employs Copula Theory to model the dependence across default rates in a credit card portfolio of a large UK bank and to estimate the likelihood of joint high default rates. Ten copula families are used as candidates to represent the dependence structure. The empirical analysis shows that, when compared to traditional models, estimations based on asymmetric copulas usually yield results closer to the ratio of simultaneous extreme losses observed in the credit card portfolio.Copulas have been applied to evaluate the dependence among corporate debts but this research is the first paper to give evidence of the outperformance of copula estimations in portfolios of consumer loans. Moreover we test some families of copulas that are not typically considered in credit risk studies and find out that three of them are suitable for representing dependence across credit card defaults.     

Combining random forest and copula functions: A heuristic approach for selecting assets from a financial crisis perspective

In this paper we propose a heuristic strategy aimed at selecting and analysing a set of financial assets, focusing attention on their multivariate tail dependence structure. The selection, obtained through an algorithmic procedure based on data mining tools, assumes the existence of a reference asset we are specifically interested to. The procedure allows one to opt for two alternatives: to prefer those assets exhibiting either a minimum lower tail dependence or a maximum upper tail dependence. The former could be a recommendable opportunity in a financial crisis period. For the selected assets, the tail dependence coefficients are estimated by means of a proper multivariate copula function. Copyright © 2010 John Wiley & Sons, Ltd.     

Option pricing and hedging in different cyclical structures: a two-dimensional Markov-modulated model

The critical role of interest rate risk and associated regime-switching risk in pricing and hedging options is examined using a closed-form valuation model. Equity call options are valued under the proposed 2-dimensional Markov-modulated model in which asset prices and interest rates exhibit Markov regime-switching features. In addition, the relationship between cyclical structures and option prices are analyzed using a time-varying transition probability matrix. The proposed model can enhance the forecast transition probabilities in an out-sample period. The cycle-stylized effect of an economy exhibits different impacts on option prices and hedging strategies in a short- and a long-cycle economy. Our closed-form formula based on more realistic specifications with respect to business-cyclical structures in various financial markets is more appropriate for pricing and hedging options.