Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility

Realized measures employing intra-day sources of data have proven effective for dynamic volatility and tail-risk estimation and forecasting. Expected shortfall (ES) is a tail risk measure, now recommended by the Basel Committee, involving a conditional expectation that can be semi-parametrically estimated via an asymmetric sum of squares function. The conditional autoregressive expectile class of model, used to implicitly model ES, has been extended to allow the intra-day range, not just the daily return, as an input. This model class is here further extended to incorporate information on realized measures of volatility, including realized variance and realized range (RR), as well as scaled and smoothed versions of these. An asymmetric Gaussian density error formulation allows a likelihood that leads to direct estimation and one-step-ahead forecasts of quantiles and expectiles, and subsequently of ES. A Bayesian adaptive Markov chain Monte Carlo method is developed and employed for estimation and forecasting. In an empirical study forecasting daily tail risk measures in six financial market return series, over a seven-year period, models employing the RR generate the most accurate tail risk forecasts, compared to models employing other realized measures as well as to a range of well-known competitors.     

Tail risk of coal futures in China's market

This study evaluates the downside tail risk of coal futures contracts (coke, coking coal and thermal coal) traded in the Chinese market between 2011 and 2021, measured by value at risk (VaR). We examine the one-day-ahead VaR forecasting performance with a hybrid econometric and deep learning model (GARCH-LSTM), GARCH family models, extreme value theory models, quantile regression models and two naïve models (historical simulation and exponentially weighted moving average). We use four backtesting techniques and the model confidence set to identify the optimal models. The results suggest that the models focusing on tail risk or utilising long short-term memory generate more effective risk management.     

Credit portfolios: What defines risk horizons and risk measurement?

The strong autocorrelation between economic cycles demands that we analyze credit portfolio risk in a multiperiod setup. We embed a standard one-factor model in such a setup. We discuss the calibration of the model to Standard & Poor’s ratings data in detail. But because single-period risk measures cannot capture the cumulative effects of systematic shocks over several periods, we define an alternative risk measure, which we call the time-conditional expected shortfall (TES), to quantify credit portfolio risk over a multiperiod horizon.     

Bayesian realized-GARCH models for financial tail risk forecasting incorporating the two-sided Weibull distribution

The realized-GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed as the realized measure in the realized-GARCH framework. Sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. A Bayesian Markov Chain Monte Carlo (MCMC) method is adapted and employed for estimation and forecasting, while various MCMC efficiency and convergence measures are employed to assess the validity of the method. In addition, the properties of the MCMC estimator are assessed and compared with maximum likelihood, via a simulation study. Compared to a range of well-known parametric GARCH and realized-GARCH models, tail risk forecasting results across seven market indices, as well as two individual assets, clearly favour the proposed realized-GARCH model incorporating the two-sided Weibull distribution; especially those employing the sub-sampled realized variance and sub-sampled realized range.     

The Arbitrage Pricing Theory and Supershares

In a single-period model with options on the market portfolio, linear factor pricing holds if and only if the variance of the market conditional on the factors is zero. There is no need for factors other than nonlinear functions of the market. For accurate linear pricing of all payoff patterns the factors must be rotationally equivalent to Hakansson's “supershares.” In a multiperiod model, a similar set of results holds, but with consumption replacing the market payoff. The methodology of the empirical Arbitrage Pricing Theory literature is not consistent with either the single-period model or the multiperiod model.     

The Role of the Investment Horizon in Optimal Portfolio Sequencing (An Intuitive Demonstration in Discrete Time)

This paper examines the role played by the investor's investment horizon in the choice of optimal portfolios. A complete discrete-time, multiperiod, portfolio model is presented with a choice criterion that is consistent with the traditional utility approach but which is more amenable to a multiperiod environment. It is shown that investors should choose progressively less risky single-period portfolios as their investment horizons grow shorter, even if they do not become more risk averse. This result holds both in the presence and in the absence of a riskless asset. The results are consistent with empirical evidence and the financial planning practice of moving investors into progressively less risky portfolios as they grow older.     

THE STRONG CASE FOR THE GENERALIZED LOGARITHMIC UTILITY MODEL AS THE PREMIER MODEL OF FINANCIAL MARKETS

This paper begins by comparing the available well-developed micro-economic models in finance which recognize uncertainty. It is argued that models whose distinctive simplifying assumption restricts utility functions are superior to those which instead restrict probability distributions, both with respect to the realism of their assumptions and richness of their conclusions. In particular, the most successful model, based on generalized logarithmic utility (GLUM), is a multiperiod consumption/portfolio and equilibrium model in discrete-time which (1) requires decreasing absolute risk aversion; (2) tolerates increasing, constant, or decreasing proportional risk aversion; (3) assumes no exogenous specification of the contemporaneous or intertemporal stochastic process of security prices; (4) tolerates heterogeneity with respect to wealth, lifetime, time-and risk-preference and beliefs; (5) results in a complete specification of consumption/portfolio decision and sharing rules which include nontrivial multiperiod separation properties and explains demand for default-free bonds of various maturities and options; (6) leads to a solution to the aggregation problem; (7) results in a complete specification of the contemporaneous and intertemporal process of security prices which reveals necessary and sufficient conditions for an unbiased term structure and the market portfolio to follow a random walk as a natural outcome of equilibrium; (8) provides an empirically testable aggregate consumption function relating per capita consumption to per capita wealth and the present value of a perpetual default-free annuity which does not require inferences of ex ante beliefs from ex post data; (9) provides a nontrivial multiperiod extension of popular single-period security valuation models which is empirically testable; (10) yields a simple multiperiod valuation formula for an uncertain income stream even when this income is serially correlated over time.     

Capital standard,forbearance and deposit insurance pricing under GARCH

We propose a multiperiod deposit insurance pricing model that simultaneously incorporates the capital standard and the possibility of forbearance. The model employs the recently developed GARCH option pricing technique in determining the deposit insurance value. Our model offers two distinctive advantages. First, it explicitly considers the implications of the strict enforcement on capital standard as stipulated in FDIC Improvement Act of 1991. Second, the use of the GARCH model allows us to capture many robust features exhibited by financial asset returns. By the GARCH option pricing theory, the value of a contingent claim is a function of the asset risk premium. This unique feature is found to be prominent in determining the bank's deposit insurance value. We also examine the effects of capital forbearance and moral hazard behavior in this multiperiod deposit insurance setting.     

Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model

Investment and risk control are becoming increasingly important for financial institutions. Asset allocation provides a fundamental investing principle to manage the risk and return trade‐off in financial markets. This article proposes a general formulation of a first approximation of multiperiod asset allocation modeling for institutions that invest to meet the target payment structures of a long‐term liability. By addressing the shortcomings of both single‐period models and the single‐point forecast of the mean variance approach, this article derives explicit formulae for optimal asset allocations, taking into account possible future realizations in a multiperiod discrete time model.     

Multiperiod Strip Hedging of Forward Commitments

This paper empirically compares two multiperiod hedging strategies—a strip hedge and a stack-and-roll hedge—to hedge a forward commitment. The multiperiod strip hedge is found to outperform the stack-and-roll hedge when forward prices are subject to multiple sources of price uncertainty and to perform no better when only one source of uncertainty is present. Moreover, the relative superiority of the strip hedge increases with the presence of multiple sources of uncertainty. Last, the strip hedge is found to be more costly to trade than the stack-and-roll hedge; however, its cost varies directly with its superiority at reducing risk.     

Fair insurance guaranty premia in the presence of risk-based capital regulations,stochastic interest rate and catastrophe risk

A multiperiod model is developed to measure the costs posed to the guaranty fund in a setting that incorporates risk-based capital regulations, interest rate risk and the possibility of catastrophic losses. The guaranty contract is modeled as a put option on the asset of the insurance company with a stochastic strike price and an uncertain maturity. The impacts of the key factors of this model are examined numerically and shown to make material differences in the costs to the guaranty fund.     

我国金融机构尾部风险影响因素的非线性研究——来自面板平滑转换回归模型的新证据

“十三五”期间,我国防范化解金融风险攻坚战取得决定性成就,而在“十四五”规划开局之际,我国的金融风险形势面临新的挑战,防范风险仍是金融业的永恒主题。在此背景下,本文采用相对重要性分析技术方法,考察机构规模以及相关基本面因素对我国上市金融机构尾部风险的贡献程度。接着,本文结合边际效应分析技术考察机构规模对风险的异质性效应,深入分析“太大而不能倒”假说在中国的适用性。在此基础上,进一步运用前沿的面板平滑转换估计模型,研究机构规模与尾部风险的非线性关系,并分析基本面因素对该异质性效应的影响力度。研究结果表明,我国上市银行等金融机构规模的增加能够有效缓释我国金融系统的尾部风险,但该影响效应将随着特许权价值、资产质量、杠杆水平、成本水平、收入结构、贷款结构等基本面指标的变化而出现显著的非线性转变。在此基础上,对强化我国金融系统中的风险防控薄弱环节、提高金融机构的风险吸收能力提出建议,以期为我国深化金融业改革开放、推动高质量发展提供理论分析与实证检验的参考依据。     

The pricing of capital assets in a multiperiod world

This paper proposes a general framework for the pricing of capital assets in a multiperiod world. Under quite general conditions, the analysis shows that the equilibrium expected nominal return on any asset can always be expressed as the sum of the risk-free rate and various risk premiums. The first risk premium is identical to the usual risk premium in the Sharpe-Lintner-Mossin capital asset pricing model. The mathematical forms of all the remaining risk premiums are identical even though each individual risk premium may be present for a different reason.     

The Effect of Serial Dependence on Multiperiod Holding Period Return Performance

The impact of the investment time horizon on risk‐return properties of asset returns depends on the presence of serial correlation and higher order serial dependencies. We present a methodology for decomposing multiperiod holding period return covariance into serial and cross‐sectional components using a recursive multiplicative model that captures the effects of serial and cross‐sectional dependencies and their joint effects without requiring a distributional form assumption. Applying this model to historical monthly return series for commonly held financial assets and portfolios of assets, we investigate the significance of the investment time horizon, the existence and relevance of time diversification, the inflation‐hedging effectiveness of different assets, and the appropriateness of applying traditional capital market theory in a multiperiod framework.     

Integrating market and credit risk: A simulation and optimisation perspective

We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (ALM) problem and develop a multistage stochastic programming model which focuses on optimum risk decisions. These models exploit the dynamical multiperiod structure of credit risk and provide insight into the corrective recourse decisions whereby issues such as the timing risk of default is appropriately taken into consideration. We also present an index tracking model in which risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the index. In-sample as well as out-of-sample (backtesting) experiments are undertaken to validate our approach. The main benefits of backtesting, that is, ex-post analysis are that (a) we gain insight into asset allocation decisions, and (b) we are able to demonstrate the feasibility and flexibility of the chosen framework.     

A Theory of the Dynamics of Security Returns around Market Closures

Numerous empirical studies document patterns in the means and variances of security returns measured over periods that are punctuated by market closures. This article develops a multiperiod model in which closures delay the resolution of uncertainty, thereby redistributing risk across time and agents. Since agents are risk averse in the model, this redistribution affects the equilibrium price, altering risk premia, liquidity costs, and the degree of informational asymmetry. As a consequence, closures alter both the means and variances of returns. The article demonstrates that closures can generate a variety of mean and variance effects, including those that mirror the empirical phenomena.     

Trapped in diversification – another look at the risk of fund of hedge funds

Recent literature implies that despite being more diversified, fund of hedge funds (FOFs) are exposed to tail risk. We propose an explanation for this phenomenon; tail risk is a systematic risk factor for hedge funds, which by construction, explains the higher portion of the returns in the diversified portfolios. Our study suggests that not only an additional tail risk factor improves the explanatory power of the factor model, the relative importance of tail risk factor increases with the number of underlying hedge funds in an FOF portfolio. Furthermore, we demonstrate that FOFs with a short history, higher management fees, leverage and requiring shorter lockup periods are more sensitive to tail risk.     

Tail-risk protection trading strategies

Starting from well-known empirical stylized facts of financial time series, we develop dynamic portfolio protection trading strategies based on econometric methods. As a criterion for riskiness, we consider the evolution of the value-at-risk spread from a GARCH model with normal innovations relative to a GARCH model with generalized innovations. These generalized innovations may for example follow a Student t, a generalized hyperbolic, an alpha-stable or a Generalized Pareto distribution (GPD). Our results indicate that the GPD distribution provides the strongest signals for avoiding tail risks. This is not surprising as the GPD distribution arises as a limit of tail behaviour in extreme value theory and therefore is especially suited to deal with tail risks. Out-of-sample backtests on 11 years of DAX futures data, indicate that the dynamic tail-risk protection strategy effectively reduces the tail risk while outperforming traditional portfolio protection strategies. The results are further validated by calculating the statistical significance of the results obtained using bootstrap methods. A number of robustness tests including application to other assets further underline the effectiveness of the strategy. Finally, by empirically testing for second-order stochastic dominance, we find that risk averse investors would be willing to pay a positive premium to move from a static buy-and-hold investment in the DAX future to the tail-risk protection strategy.     

Stock market return predictability: A combination forecast perspective

Based on traditional macroeconomic variables, this paper mainly investigates the predictability of these variables for stock market return. The empirical results show the mean combination forecast model can achieve superior out-of-sample performance than the other forecasting models for forecasting the stock market returns. In addition, the performances of the mean combination forecast model are also robust during different forecasting windows, different market conditions, and multi-step-ahead forecasts. Importantly, the mean combination forecast consistently generates higher CER gains than other models considering different investors' risk aversion coefficients and trading costs. This paper tries to provide more evidence of combination forecast model to predict stock market returns.     

AN ANALYTICAL MODEL OF RISKY YIELD CURVES

This paper proposes a multiperiod certainty equivalent model of present valuation that takes a dynamic approach to valuation, as opposed to a recursive approach employed traditionally in financial economics. Assuming a flat basic, or riskless, yield curve and risk-averse investors, the model is used to examine the potential effects of default risk on the shape of the yield curve. The shape of the yield curve is shown to be directly related to the level and time pattern of default probabilities.