Fat tails,VaR and subadditivity

Financial institutions rely heavily on Value-at-Risk (VaR) as a risk measure, even though it is not globally subadditive. First, we theoretically show that the VaR portfolio measure is subadditive in the relevant tail region if asset returns are multivariate regularly varying, thus allowing for dependent returns. Second, we note that VaR estimated from historical simulations may lead to violations of subadditivity. This upset of the theoretical VaR subadditivity in the tail arises because the coarseness of the empirical distribution can affect the apparent fatness of the tails. Finally, we document a dramatic reduction in the frequency of subadditivity violations, by using semi-parametric extreme value techniques for VaR estimation instead of historical simulations.     

变结构门限t-GARCH模型及其伪持续性研究

为了反映金融时间序列的波动集聚性、非对称性、厚尾性以及在实证研究中表现出的伪持续性，本文结合门限GARCH模型以及变结构的方法提出了变结构门限t—GARCH模型。首先用Monte Carlo模拟的方法考虑了变结构GARCH模型中存在的伪持续性问题；其次针对金融时间序列非对称性、厚尾性以及强持续性的特点提出了变结构门限t—GARCH模型，总结了关于变结构点检验的几个主要方法；最后用该模型来拟合沪市和深市两个股市的周收益率序列，得到了比GARCH模型更好的拟合结果。     

A novel two-stage method for well-diversified portfolio construction based on stock return prediction using machine learning

The performance of portfolio model can be improved by introducing stock prediction based on machine learning methods. However, the prediction error is inevitable, which may bring losses to investors. To limit the losses, a common strategy is diversification, which involves buying low-correlation stocks and spreading the funds across different assets. In this paper, a diversified portfolio selection method based on stock prediction is proposed, which includes two stages. To be specific, the purpose of the first stage is to select diversified stocks with high predicted returns, where the returns are predicted by machine learning methods, i.e. random forest (RF), support vector regression (SVR), long short-term memory networks (LSTM), extreme learning machine (ELM) and back propagation neural network (BPNN), and the diversification level is measured by Pearson correlation coefficient. In the second stage, the predictive results are incorporated into a modified mean–variance (MMV) model to determine the proportion of each asset. Using China Securities 100 Index component stocks as study sample, the empirical results demonstrate that the RF+MMV model achieves better results than similar counterparts and market index in terms of return and return–risk metrics.     

基于多标度分形理论的金融资产收益非对称性测度方法研究

基于多标度分形理论,提出了一种新的更适用于实际金融资产收益数据的非对称性测度方法——两阶段非对称性检验法（Two-step asymmetry testing,TAT）,并运用Monte Carlo模拟考察了其与传统的偏度系数检验法的非对称性判定结论差异。实证结果表明：总体来讲,本文提出的两阶段非对称性检验法在常用检验水平下取得了较偏度系数法更为准确的金融资产收益非对称性判定结论,且两阶段非对称性检验法较偏度系数法更适用于具有非独立、非正态特性数据的非对称性检验。     

Are the interdependence characteristics of the US and Canadian energy equity sectors nonlinear and asymmetric?

Nonlinear, symmetric, and asymmetric dependence characteristics in energy equity sectors matter to portfolio investors and risk managers because of the risks and diversification opportunities they entail. Specifically, nonlinear dependence dynamics between assets are harder to predict, monitor, and manage, and can make investment positions go wrong unexpectedly. In this paper, we investigate whether the dependence dynamics of US and Canadian large-capitalized energy equity portfolios are nonlinear, symmetric, or asymmetric. We draw our results by implementing a robust copula approach based on time-varying parameter copulas and vine copula methods. Both time varying parameter and vine-copula methods indicate that the Canadian energy sector portfolio is driven by nonlinear negative tail asymmetric dependence during the global financial crisis and when the full sample period is employed. On the other hand, it displays nonlinear symmetric dependence during the oil price crisis, implying the need for close monitoring and rebalancing and a more continuous assessment of long investment positions. The US energy sector portfolio is driven by positive tail asymmetric dependence, and by symmetric dependence dynamics during crisis and non-crisis periods.     

我国股市行业时变β系数研究

本文主要考察了我国股市13个行业的β系数及信息的影响。研究发现市场信息和行业信息对β系数都有影响,但影响的方向和大小因行业而异。进而对这些行业的β系数的信息非对称效应产生原因进行考察。仅有部分行业的β系数的信息非对称效应可由市场利空消息或行业利空消息解释。     

基于投资组合理论的企业多项目投资管理研究

投资行为所具有的风险和收益密切相关的特点,使投资者必须努力寻求低风险和高收益的投资策略。而投资组合则能够为企业进行分散风险和扩张经营提供强有力的保证。本文使用现代投资组合理论,为企业的多项目投资组合建立优化模型,从定量的角度说明在企业多项目投资管理中运用投资组合的合理性和有效性。     

Performance measurement and best-practice benchmarking of mutual funds: combining stochastic dominance criteria with data envelopment analysis

We propose a method for mutual fund performance measurement and best-practice benchmarking, which endogenously identifies a dominating benchmark portfolio for each evaluated mutual fund. Dominating benchmarks provide information about efficiency improvement potential as well as portfolio strategies for achieving them. Portfolio diversification possibilities are accounts for by using Data Envelopment Analysis (DEA). Portfolio risk is accounted for in terms of the full return distribution by utilizing Stochastic Dominance (SD) criteria. The approach is illustrated by an application to US based environmentally responsible mutual funds.     

基于高阶矩风险防范的银行资产负债组合优化模型研究——以A银行为例

资产负债管理能力是现代商业银行的基本能力,其核心在于风险控制和价值创造。商业银行资产负债组合优化是现代商业银行信贷管理框架中的核心内容,它对于保持银行资产流动性、安全性和赢利性的＂三性＂的最佳组合、优化配置资源、提高银行的生存能力和竞争能力,具有重要的现实意义。本文通过以贷款组合的VaR约束控制贷款组合的二阶矩,即控制了资产组合的风险;以贷款组合收益率的偏度约束控制贷款组合的三阶矩,即控制了贷款组合收益率发生总体损失的可能性;以组合收益率的峰度约束控制贷款组合的四阶矩,即减少了组合收益率发生极端损失的可能性,建立了资产分配的收益率均值-方差-偏度-峰度模型。     

Assessing skewness in financial markets

It is a matter of common observation that investors value substantial gains but are averse to heavy losses. Obvious as it may sound, this translates into an interesting preference for right-skewed return distributions, whose right tails are heavier than their left tails. Skewness is thus not only a way to describe the shape of a distribution, but also a tool for risk measurement. We review the statistical literature on skewness and provide a comprehensive framework for its assessment. Then, we present a new measure of skewness, based on the decomposition of variance in its upward and downward components. We argue that this measure fills a gap in the literature and show in a simulation study that it strikes a good balance between robustness and sensitivity.     

Lessons from naïve diversification about the risk-reward trade-off

Studies of naïve diversification show that average total portfolio risk declines asymptotically as number of stocks increases. Recent work shows that a significant amount of idiosyncratic risk remains, even for portfolios with large numbers of stocks. The corresponding shocks are non-trivial. For example, more than half of all equal-weighted portfolios with 100 stocks have better than a 16 percent chance of an annual shock at least as large as about half of the annualized mean excess return on the U.S. total stock market index over July 1963–June 2018. I perform a simulation analysis of portfolio reward-to-risk as well as the components of total portfolio risk. On average, investors do not appear to be rewarded for exposure to non-systematic risk. The cross-sectional distribution of the true Sharpe ratio rises and its dispersion shrinks significantly as the number of stocks in the portfolio increases, whereas the cross-sectional distribution of the true non-systematic risk falls and its dispersion shrinks significantly as the number of stocks in the portfolio increases. This pattern appears regardless of the true asset pricing model for generating security returns, the portfolio weighting method, or specification of security alphas.     

Fractal statistical measure and portfolio model optimization under power-law distribution

An effective portfolio selection model is constructed on the premise of measuring accurately the risk and return on assets. According to the reality that the tail of returns on assets obey power-law distribution, this paper firstly builds two fractal statistical measures, fractal expectation and fractal variance, to measure the asset returns and risks, inspired by the method of measuring curve length in the fractal theory. Then, by incorporating the fractal statistical measure into the return-risk criterion, a portfolio selection model based on fractal statistical measure is established, namely the fractal portfolio selection model, and the closed-form solution of the model is given. Finally, through empirical analysis we find that the fractal portfolio selection model is effective and can improve investment performance.     

Modeling common volatility characteristics and dynamic risk premia in European equity markets

The paper applies a Factor-GARCH model to evaluate the impact of the market portfolio, as a single common dynamic risk factor, on conditional volatility and risk premia for the returns on size-based equity portfolios of three major European markets; France, Germany and the United Kingdom. The results show that for the size-based portfolios the factor loading for the dynamic market factor is significant and positive but the association between the risk premia and the conditional market volatility is weak. However, the dynamic market factor is shown to explain common characteristics in the conditional variance such as asymmetry and persistence. This finding is consistent across markets and portfolio sizes.     

Market risks that change domestic diversification benefits

We study the options-implied market risks and correlations to identify factors that affect U.S. stock correlations during 2007–2018. We discover that U.S. stock- and bond-market uncertainty, equity tail risk, European equity risk, and global credit risk are dominant contributors to changing correlations. While correlations rise universally with rising U.S. and European stock-market uncertainty, other market risks show diverging effects on correlations in crisis and non-crisis periods. Rising equity tail risk and global credit risk raise correlations in crisis times. Our results disentangle the risks of stock and bond markets that change the domestic stock diversification benefits.     

Modeling the conditional distribution of financial returns with asymmetric tails

This paper proposes a conditional density model that allows for differing left/right tail indices and time-varying volatility based on the dynamic conditional score (DCS) approach. The asymptotic properties of the maximum likelihood estimates are presented under verifiable conditions together with simulations showing effective estimation with practical sample sizes. It is shown that tail asymmetry is prevalent in global equity index returns and can be mistaken for skewness through the center of the distribution. The importance of tail asymmetry for asset allocation and risk premia is demonstrated in-sample. Application to portfolio construction out-of-sample is then considered, with a representative investor willing to pay economically and statistically significant management fees to use the new model instead of traditional skewed models to determine their asset allocation.     

Asymmetric positive feedback trading and stock pricing in China

Defining asymmetry of feedback trading (AFC) as the difference between buying-winners and selling-losers intensities, the paper investigates if AFC impacts stock pricing. We show that buying stocks with low AFC and selling stocks with high AFC makes significant positive returns after controlling traditional pricing factors. The return mainly comes from the long leg and cannot be simply attributed to either mispricing, liquidity, or risk premium. Further study shows that the negative impact of AFC on future stock return is reinforced with an increase in past returns, maximum daily return, relative valuation level, asset growth rate, or operating profit rate. As AFC represents retail trading intensity, the results imply that the inactiveness of retail investors may make price relative underreaction to good news and thus lead to positive expected stock return.     

EVT and tail-risk modelling: Evidence from market indices and volatility series

Value-at-Risk (VaR) has become the universally accepted risk metric adopted internationally under the Basel Accords for banking industry internal control, capital adequacy and regulatory reporting. The recent extreme financial market events such as the Global Financial Crisis (GFC) commencing in 2007 and the following developments in European markets mean that there is a great deal of attention paid to risk measurement and risk hedging. In particular, to risk indices and attached derivatives as hedges for equity market risk. The techniques used to model tail risk such as VaR have attracted criticism for their inability to model extreme market conditions. In this paper we discuss tail specific distribution based Extreme Value Theory (EVT) and evaluate different methods that may be used to calculate VaR ranging from well known econometrics models of GARCH and its variants to EVT based models which focus specifically on the tails of the distribution. We apply Univariate Extreme Value Theory to model extreme market risk for the FTSE100 UK Index and S&P-500 US markets indices plus their volatility indices. We show with empirical evidence that EVT can be successfully applied to financial market return series for predicting static VaR, CVaR or Expected Shortfall (ES) and also daily VaR and ES using a GARCH(1,1) and EVT based dynamic approach to these various indices. The behaviour of these indices in their tails have implications for hedging strategies in extreme market conditions.     

Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes

Given that underlying assets in financial markets exhibit stylized facts such as leptokurtosis, asymmetry, clustering properties and heteroskedasticity effect, this paper applies the stochastic volatility models driven by tempered stable Lévy processes to construct time changed tempered stable Lévy processes (TSSV) for financial risk measurement and portfolio reversion. The TSSV model framework permits infinite activity jump behaviors of returns dynamics and time varying volatility consistently observed in financial markets by introducing time changing volatility into tempered stable processes which specially refer to normal tempered stable (NTS) distribution as well as classical tempered stable (CTS) distribution, capturing leptokurtosis, fat tailedness and asymmetry features of returns in addition to volatility clustering effect in stochastic volatility. Through employing the analytical characteristic function and fast Fourier transform (FFT) technique, the closed form formulas for probability density function (PDF) of returns, value at risk (VaR) and conditional value at risk (CVaR) can be derived. Finally, in order to forecast extreme events and volatile market, we perform empirical researches on Hangseng index to measure risks and construct portfolio based on risk adjusted reward risk stock selection criteria employing TSSV models, with the stochastic volatility normal tempered stable (NTSSV) model producing superior performances relative to others.     

Location-scale portfolio selection with factor-recentered skew normal asset returns

This paper analyzes the single period portfolio selection problem on the location-scale return family. The skew normal distribution, after recentering and reparameterization, is shown to be in this family. The recentered and reparameterized distribution, called factor-recentered skew normal, can be expressed as a skew factor model which is characterized by a location parameter and two scale parameters. Risk preference on scale parameter is non-monotonic and risk averse investors prefer larger (smaller) scale when the scale is negative (positive). The three-parameter efficient set is a part of conical surface bounded by two lines. Positive-skewness portfolios and negative-skewness portfolios do not coexist in the efficient set. Numerical cases under constant absolute risk aversion are analyzed with its closed-form certainty equivalent. An asset pricing formula which nests the CAPM is obtained.     

Stock price reactions to increases in loan-loss reserves: A broader perspective

Loan loss reserves (LLR) provide a cushion to absorb operating losses. Several studies have focused on the market's reaction to increases in LLR in response to a specific event related to the international debt crisis. This study takes a broader view of LLR by examining, over a six year period, the market's reaction to announcements of increases to LLR that are above the expected annual reserve and that are a result of factors other than the international debt crisis. We find a negative reaction in the market, indicating that the negative signal from identifying unanticipated risk in the loan portfolio appears to dominate the positive cash flow effects.