Forecasting the return distribution using high-frequency volatility measures

The aim of this paper is to forecast (out-of-sample) the distribution of financial returns based on realized volatility measures constructed from high-frequency returns. We adopt a semi-parametric model for the distribution by assuming that the return quantiles depend on the realized measures and evaluate the distribution, quantile and interval forecasts of the quantile model in comparison to a benchmark GARCH model. The results suggest that the model outperforms an asymmetric GARCH specification when applied to the S&P 500 futures returns, in particular on the right tail of the distribution. However, the model provides similar accuracy to a GARCH (1, 1) model when the 30-year Treasury bond futures return is considered.     

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.     

A Comparison of Seasonal Adjustment Methods When Forecasting Intraday Volatility

In this article we compare volatility forecasts over a thirty‐minute horizon for the spot exchange rates of the Deutsche mark and the Japanese yen against the U.S. dollar. Explicitly modeling the intraday seasonal pattern improves the out‐of‐sample forecasting performance. We find that a seasonal estimated from the log of squared returns improves with the use of simple squared returns, and that the flexible Fourier form (FFF) is an efficient way of determining the seasonal. The two‐step approach that first estimates the seasonal using the FFF and then the parameters of the generalized autoregressive conditional heteroskedasticity (GARCH) model for the deseasonalized returns performs only marginally worse than the computationally expensive periodic GARCH model that includes the FFF.     

Modeling and forecasting stock return volatility using a random level shift model

We consider the estimation of a random level shift model for which the series of interest is the sum of a short-memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process which is 0 with some probability (1 ? α) and is a random variable with probability α. Our estimation method transforms such a model into a linear state space with mixture of normal innovations, so that an extension of Kalman filter algorithm can be applied. We apply this random level shift model to the logarithm of daily absolute returns for the S&P 500, AMEX, Dow Jones and NASDAQ stock market return indices. Our point estimates imply few level shifts for all series. But once these are taken into account, there is little evidence of serial correlation in the remaining noise and, hence, no evidence of long-memory. Once the estimated shifts are introduced to a standard GARCH model applied to the returns series, any evidence of GARCH effects disappears. We also produce rolling out-of-sample forecasts of squared returns. In most cases, our simple random level shift model clearly outperforms a standard GARCH(1,1) model and, in many cases, it also provides better forecasts than a fractionally integrated GARCH model.     

Real-Estate Risk Effects on Financial Institutions’ Stock Return Distribution: a Bivariate GARCH Analysis

This paper examines two relationships using the bivariate generalized autoregressive conditionally heteroskedastic (GARCH) methodology. First, the relationship between equity returns of commercial banks, savings and loans (S&Ls) and life insurance companies (LICs), and those of the real-estate investment trusts (REITs), a proxy for the real-estate sector performance. Second, the relationship between conditional volatilities of the stock returns of these financial intermediaries (FIs) and that of REITs. The former relationship allows the spillover of returns between the real-estate and the financial intermediation sector to be analyzed. The latter allows an investigation of the prevalence, direction and strength of inter-sectoral risk transmission to be carried out. Several interesting results are obtained. First, the equity returns of the FIs considered follow a GARCH process and should be modeled accordingly. Second, as found in the literature, returns on REITs should be modeled using the Fama-French multiple factor model. However, this model has to be extended to incorporate a GARCH error structure. Third, all FI returns considered are highly sensitive to REIT returns and the effects are both statistically and economically significant. This is an indication that shocks to REITs returns spillover to the former markets. Fourth, spillover of increased volatility in the real-estate sector to S&Ls and LICs is significant but not to commercial banks.     

Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence

The present study compares the performance of the long memory FIGARCH model, with that of the short memory GARCH specification, in the forecasting of multi-period value-at-risk (VaR) and expected shortfall (ES) across 20 stock indices worldwide. The dataset is composed of daily data covering the period from 1989 to 2009. The research addresses the question of whether or not accounting for long memory in the conditional variance specification improves the accuracy of the VaR and ES forecasts produced, particularly for longer time horizons. Accounting for fractional integration in the conditional variance model does not appear to improve the accuracy of the VaR forecasts for the 1-day-ahead, 10-day-ahead and 20-day-ahead forecasting horizons relative to the short memory GARCH specification. Additionally, the results suggest that underestimation of the true VaR figure becomes less prevalent as the forecasting horizon increases. Furthermore, the GARCH model has a lower quadratic loss between actual returns and ES forecasts, for the majority of the indices considered for the 10-day and 20-day forecasting horizons. Therefore, a long memory volatility model compared to a short memory GARCH model does not appear to improve the VaR and ES forecasting accuracy, even for longer forecasting horizons. Finally, the rolling-sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models. Hence, the parameters' time-variant characteristic cannot be entirely due to the news information arrival process of the market; a portion must be due to the FIGARCH modelling process itself.     

Forecasting hedge fund volatility: a Markov regime-switching approach

The article addresses forecasting volatility of hedge fund (HF) returns by using a non-linear Markov-Switching GARCH (MS-GARCH) framework. The in- and out-of-sample, multi-step ahead volatility forecasting performance of GARCH(1,1) and MS-GARCH(1,1) models is compared when applied to 12 global HF indices over the period of January 1990 to October 2010. The results identify different regimes with periods of high and low volatility for most HF indices. In-sample estimation results reveal a superior performance of the MS-GARCH model. The findings show that regime switching is related to structural changes in the market factor for most strategies. Out-of-sample forecasting shows that the MS-GARCH formulation provides more accurate volatility forecasts for most forecast horizons and for most HF strategies. Inclusion of MS dynamics in the GARCH specification highly improves the volatility forecasts for those strategies that are particularly sensitive to general macroeconomic conditions, such as Distressed Restructuring and Merger Arbitrage.     

Model risk of the implied GARCH-normal model

Model risk causes significant losses in financial derivative pricing and hedging. Investors may undertake relatively risky investments due to insufficient hedging or overpaying implied by flawed models. The GARCH model with normal innovations (GARCH-normal) has been adopted to depict the dynamics of the returns in many applications. The implied GARCH-normal model is the one minimizing the mean square error between the market option values and the GARCH-normal option prices. In this study, we investigate the model risk of the implied GARCH-normal model fitted to conditional leptokurtic returns, an important feature of financial data. The risk-neutral GARCH model with conditional leptokurtic innovations is derived by the extended Girsanov principle. The option prices and hedging positions of the conditional leptokurtic GARCH models are obtained by extending the dynamic semiparametric approach of Huang and Guo [Statist. Sin., 2009, 19, 1037–1054]. In the simulation study we find significant model risk of the implied GARCH-normal model in pricing and hedging barrier and lookback options when the underlying dynamics follow a GARCH-t model.     

Higher Moments and Exchange Rate Behavior

This paper uses 15‐minute exchange rate returns data for the six most liquid currencies (i.e., the Australian dollar, British pound, Canadian dollar, Euro, Japanese yen, and Swiss franc) vis‐à‐vis the United States dollar to examine whether a GARCH model augmented with higher moments (HM‐GARCH) performs better than a traditional GARCH (TG) model. Two findings are unraveled. First, the inclusion of odd/even moments in modeling the return/variance improves the statistical performance of the HM‐GARCH model. Second, trading strategies that extract buy and sell trading signals based on exchange rate forecasts from HM‐GARCH models are more profitable than those that depend on TG models.     

An economic evaluation of stock–bond return comovements with copula-based GARCH models

Owing to their importance in asset allocation strategies, the comovements between the stock and bond markets have become an increasingly popular issue in financial economics. Moreover, the copula theory can be utilized to construct a flexible joint distribution that allows for skewness in the distribution of asset returns as well as asymmetry in the dependence structure between asset returns. Therefore, this paper proposes three classes of copula-based GARCH models to describe the time-varying dependence structure of stock–bond returns, and then examines the economic value of copula-based GARCH models in the asset allocation strategy. We compare their out-of-sample performance with other models, including the passive, the constant conditional correlation (CCC) GARCH and the dynamic conditional correlation (DCC) GARCH models. From the empirical results, we find that a dynamic strategy based on the GJR-GARCH model with Student-t copula yields larger economic gains than passive and other dynamic strategies. Moreover, a less risk-averse investor will pay higher performance fees to switch from a passive strategy to a dynamic strategy based on copula-based GARCH models.     

A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility

We show that, for three common SARV models, fitting a minimummean square linear filter is equivalent to fitting a GARCH model.This suggests that GARCH models may be useful for filtering,forecasting, and parameter estimation in stochastic volatilitysettings. To investigate, we use simulations to evaluate howthe three SARV models and their associated GARCH filters performunder controlled conditions and then we use daily currency andequity index returns to evaluate how the models perform in arisk management application. Although the GARCH models produceless precise forecasts than the SARV models in the simulations,it is not clear that the performance differences are large enoughto be economically meaningful. Consistent with this view, wefind that the GARCH and SARV models perform comparably in testsof conditional value-at-risk estimates using the actual data.     

Forecasting daily variability of the S&P 100 stock index using historical,realised and implied volatility measurements

The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper, we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First, we consider unobserved components (UC-RV) and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility (SV) models and generalised autoregressive conditional heteroskedasticity (GARCH) models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard & Poor's 100 (S&P 100) stock index series for which trading data (tick by tick) of almost 7 years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts.     

Announcement Effects and Asymmetric Volatility in Industry Stock Returns: Evidence from Taiwan

This study employs financial econometric models to examine the asymmetric volatility of equity returns in response to monetary policy announcements in the Taiwanese stock market. The meetings of the board of directors at the Central Bank of the Republic of China (Taiwan) are considered for testing the announcement effects. The asymmetric generalized autoregressive conditional heteroskedasticity (GARCH) model and the smooth transition autoregression with GARCH model are used to measure equity returns' asymmetric volatility. We conclude that the asymmetric volatility of countercyclical equity returns can be identified. Our findings support the leverage effect of stock price changes for most industry equity returns in Taiwan.     

Commodity volatility breaks

Volatility is a key determinant of derivative prices and optimal hedge ratios. This paper examines whether there are structural breaks in commodity spot return volatility using an iterative cumulative sum of squares procedure and then uses GARCH (1,1) to model volatility during each regime.The main empirical finding is the very limited evidence of commodity volatility breaks during the recent financial crisis. This suggests commodity return volatility was not exceptionally high during the recent financial crisis compared to the 1985–2010 sample period as a whole. For many commodities there are multiple idiosyncratic breaks in volatility; this suggests commodity specific supply or demand factors are important determinants of volatility. The empirical results overall are consistent with the view that commodities are too diverse to be considered as an asset class. Finally, we find commodity volatility persistence remains very high for many commodity returns even after structural breaks are accounted for.     

Follow the money: The monetary roots of bubbles and crashes

A reduced form model for the join dynamics of liquidity and asset prices is proposed. The self-reinforcing feedback between credit creation and the market value of the financial assets employed as collateral in the bank loans (the so called financial accelerator) is modeled by a coupled non-linear stochastic process. We show that such non-linear interaction produces explosive dynamics in the financial variables announcing a regime change in finite time in the form of a market crash which can also be modeled by the same coupled non-linear stochastic process with inverted signs. Casting the financial accelerator dynamics into a highly stylized macroeconomic model, we study its macro-dynamics implications for real economy and for monetary policy interventions. Finally, by exploiting the implications of the proposed model on the dynamics of financial asset returns, we introduce an extension of the GARCH process, that can provide an early warning identification of bubbles.     

Evaluating density forecasts from models of stock market returns

Density forecasts have become important in finance and play a key role in modern risk management. Using a flexible density forecast evaluation framework that extends the Berkowitz likelihood ratio test this paper evaluates in- and out-of-sample density forecasts of daily returns on the DAX, ATX and S&P 500 stock market indices from models of financial returns that are currently widely used in the financial industry. The results indicate that GARCH-t models produce good in-sample forecasts. No model considered in this study delivers fully acceptable out-of-sample forecasts. The empirical findings emphasize that proper distributional assumptions combined with an adequate specification of relevant conditional higher moments are necessary to obtain good density forecasts.     

Intraday Return Volatility Process: Evidence from NASDAQ Stocks

This paper presents a comprehensive analysis of the distributional and time-series properties of intraday returns. The purpose is to determine whether a GARCH model that allows for time varying variance in a process can adequately represent intraday return volatility. Our primary data set consists of 5-minute returns, trading volumes, and bid-ask spreads during the period January 1, 1999 through March 31, 1999, for a subset of thirty stocks from the NASDAQ 100 Index. Our results indicate that the GARCH(1,1) model best describes the volatility of intraday returns. Current volatility can be explained by past volatility that tends to persist over time. These results are consistent with those of Akgiray (1989) who estimates volatility using the various ARCH and GARCH specifications and finds the GARCH(1,1) model performs the best. We add volume as an additional explanatory variable in the GARCH model to examine if volume can capture the GARCH effects. Consistent with results of Najand and Yung (1991) and Foster (1995) and contrary to those of Lamoureux and Lastrapes (1990), our results show that the persistence in volatility remains in intraday return series even after volume is included in the model as an explanatory variable. We then substitute bid-ask spread for volume in the conditional volatility equation to examine if the latter can capture the GARCH effects. The results show that the GARCH effects remain strongly significant for many of the securities after the introduction of bid-ask spread. Consistent with results of Antoniou, Homes and Priestley (1998), intraday returns also exhibit significant asymmetric responses of volatility to flow of information into the market.     

Predicting Long‐Term Financial Returns: VAR versus DSGE Model—A Horse Race

This paper considers a U.S. institutional investor who is implementing a long‐term portfolio allocation using forecasts of financial returns. We compare the predictive performance of two competing macrofinance models—an unrestricted vector autoRegression (VAR) and a fully‐structural dynamic stochastic general equilibrium (DSGE) model—for horizons up to 15 years. Although the performances are similar for short horizons, the DSGE model outperforms the VAR at forecasting financial returns in the long term. This model also generates substantially higher Sharpe ratios. Although it contains fewer unknown parameters, it benefits from economically grounded restrictions that help anchor financial returns in the long term.     

剩余收益模型与股票未来回报

本文采用Hou et al.(2012)公司基本面盈余预测模型并结合剩余收益模型对上市公司的内在价值进行估计,并分析内在价值与市价比率(V/P)与股票未来回报之间的关系。我们发现基于V/P分组的投资组合,在未来一至三年规模调整的持有超额回报套利分别达到15.2%、37.9%和55.9%;在控制了市账比等因素以后,V/P对股票未来回报仍然具有显著的预测作用。本文的研究克服了以往文献中运用证券分析师盈余预测进行剩余收益模型估值的内在局限,并提供了我国资本市场背景下切实可行的基于剩余收益模型估值的投资组合策略。     

Basis variations and regime shifts in the oil futures market

The conditional volatility of crude oil futures returns is modelled as a regime switching process. The model features transition probabilities that are functions of the basis. Consistent with the theory of storage, in volatile periods, an increase in backwardation is associated with an increase in the likellihood of switching to or remaining in the high-volatility state. Conditional on regimes, GARCH persistence is significantly reduced. Out-of-sample tests show that incorporating regime shifts improves the accuracy of short-term volatility forecasts.