Portfolio optimization using dynamic factor and stochastic volatility: evidence on Fat‐tailed errors and leverage

The portfolio optimization problem is investigated using a multivariate stochastic volatility model with factor dynamics, fat‐tailed errors and leverage effects. The efficient Markov chain Monte Carlo method is used to estimate model parameters, and the Rao–Blackwellized auxiliary particle filter is used to compute the likelihood and to predict conditional means and covariances. The proposed models are applied to sector indices of the Tokyo Stock Price Index (TOPIX), which consists of 33 stock market indices classified by industrial sectors. The portfolio is dynamically optimized under several expected utilities and two additional static strategies are considered as benchmarks. An extensive empirical study indicates that our proposed dynamic factor model with leverage or fat‐tailed errors significantly improves the predictions of the conditional mean and covariances, as well as various measures of portfolio performance.     

Parameter instability,stochastic volatility and estimation based on simulated likelihood: Evidence from the crude oil market

Stochastic volatility models with fixed parameters can be too restrictive for time-series analysis due to instability in the parameters that govern conditional volatility dynamics. We incorporate time-variation in the model parameters for the plain stochastic volatility model as well its extensions with: Leverage, volatility feedback effects and heavy-tailed distributed innovations. With regards to estimation, we rely on one recently discovered result, namely, that when an unbiasedly simulated estimated likelihood (available for example through a particle filter) is used inside a Metropolis-Hastings routine then the estimation error makes no difference to the equilibrium distribution of the algorithm, the posterior distribution. This in turn provides an off-the-shelf technique to estimate complex models. We examine the performance of this technique on simulated and crude oil returns from 1987 to 2016. We find that (i): There is clear evidence of time-variation in the model parameters, (ii): Time-varying parameter volatility models with leverage/Student's t-distributed innovations perform best, (iii): The timing of parameter changes align very well with events such as market turmoils and financial crises.     

AGGREGATION,HETEROGENEOUS AUTOREGRESSION AND VOLATILITY OF DAILY INTERNATIONAL TOURIST ARRIVALS AND EXCHANGE RATES*

Tourism is a major source of service receipts for many countries, including Taiwan. The two leading tourism countries for Taiwan are Japan and the USA, which are sources of short‐ and long‐haul tourism, respectively. As a strong domestic currency can have adverse effects on international tourist arrivals through the price effect, daily data from 1 January 1990 to 31 December 2008 are used to model the world price, exchange rates, and tourist arrivals from the world, the USA and Japan to Taiwan, and their associated volatility. Inclusion of the exchange rate and its volatility captures approximate daily and weekly price and price volatility effects on world, US and Japanese tourist arrivals to Taiwan. The heterogeneous autoregressive model is used to approximate the slowly decaying correlations associated with the long‐memory properties in daily and weekly exchange rates and international tourist arrivals, to test whether alternative short‐ and long‐run estimates of conditional volatility are sensitive to the long‐memory in the conditional mean, to examine asymmetry and leverage in volatility, and to examine the effects of temporal and spatial aggregation. The approximate price and price volatility effects tend to be different, with the exchange rate typically having the expected negative impact on tourist arrivals to Taiwan, whereas exchange rate volatility can have positive or negative effects on tourist arrivals to Taiwan. For policy purposes, the empirical results suggest that an arbitrary choice of data frequency or spatial aggregation will not lead to robust findings as they are generally not independent of the level of aggregation used.     

Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models

We examine and compare a large number of generalized autoregressive conditional heteroskedastic (GARCH) and stochastic volatility (SV) models using series of Bitcoin and Litecoin price returns to assess the model fit for dynamics of these cryptocurrency price returns series. The various models examined include the standard GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, t-distributed and moving average innovations. We report that the best model for Bitcoin is SV-t while it is GARCH-t for Litecoin. Overall, the t-class of models performs better than other classes for both cryptocurrencies. For Bitcoin, the SV models consistently outperform the GARCH models and the same holds true for Litecoin in most cases. Finally, the comparison of GARCH models with GARCH-GJR models reveals that the leverage effect is not significant for cryptocurrencies, suggesting that these do not behave like stock prices.     

Empirical Evidence of the Leverage Effect in a Stochastic Volatility Model: A Realized Volatility Approach

Increasing attention has been focused on the analysis of the realized volatility, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a proxy in a stochastic volatility model estimation. We estimate the leveraged stochastic volatility model using the realized volatility computed from five popular methods across six sampling-frequency transaction data (from 1-min to 60- min) based on the trust region method. Availability of the realized volatility allows us to estimate the model parameters via the MLE and thus avoids computational challenge in the high dimensional integration. Six stock indices are considered in the empirical investigation. We discover some consistent findings and interesting patterns from the empirical results. In general, the significant leverage effect is consistently detected at each sampling frequency and the volatility persistence becomes weaker at the lower sampling frequency.     

ANALYTICAL EVALUATION OF VOLATILITY FORECASTS*

Estimation and forecasting for realistic continuous‐time stochastic volatility models is hampered by the lack of closed‐form expressions for the likelihood. In response, Andersen, Bollerslev, Diebold, and Labys (Econometrica, 71 (2003), 579–625) advocate forecasting integrated volatility via reduced‐form models for the realized volatility, constructed by summing high‐frequency squared returns. Building on the eigenfunction stochastic volatility models, we present analytical expressions for the forecast efficiency associated with this reduced‐form approach as a function of sampling frequency. For popular models like GARCH, multifactor affine, and lognormal diffusions, the reduced form procedures perform remarkably well relative to the optimal (infeasible) forecasts.     

INPUT AND OUTPUT INVENTORIES IN GENERAL EQUILIBRIUM*

We build and estimate a two‐sector dynamic stochastic general equilibrium model with two types of inventories: Input inventories facilitate the production of finished goods, output inventories yield utility services. The estimated model replicates the volatility and cyclicality of inventory investment and inventory‐to‐target ratios. Although inventories are an important element of the model’s propagation mechanism, shocks to inventory efficiency are not an important source of business cycles. When the model is estimated over two subperiods (pre‐ and post‐1984), changes in the volatility of inventory shocks or in structural parameters associated with inventories play a small role in reducing the volatility of output.     

Inflation Volatility and Forecast Accuracy

We examine the statistical properties of inflation in a sample of inflation‐targeting (IT) and non‐IT countries. It is hard to distinguish in which monetary regime inflation is less volatile. Inflation became easier to forecast in both groups of countries after the introduction of IT. The improvement was greater for IT countries, but forecast errors remain smaller for non‐IT countries. Our analysis is based on a stochastic volatility model proposed by Stock and Watson and its novel modification. Forecasts from the modified model are generally superior to both simple benchmarks and the original Stock and Watson model.     

The linkages,persistence, asymmetry in the volatility,the price discovery and efficiency,and the effect of the US subprime mortgage financial crisis on the spot and the futures market’s returns: the case of India

This article examines the effects of persistence, asymmetry and the US subprime mortgage crisis on the volatility of the returns and also the price discovery, efficiency and the linkages and causality between the spot and futures volatility by using various classes of the ARCH and GARCH models, and through the Granger’s causality. We have used two indices: one for spot and the other for futures, for the daily data from 12 June 2000 to 30 September 2013 from Nifty stock indices. We have then tested for ARCH effects, and subsequently employed various models of the ARCH and GARCH conditional volatility. The GARCH(1,1) model is found to be significant, and it implies that the returns are not autocorrelated and have ‘short memory’. It supports the hypothesis of the efficiency of the markets. The negative ‘news’ has more significant effect on volatility, corroborating the ‘leverage impact’ in finance on market volatility. We have also tested the volatility spillover effects. The two methods we employed support the spillover effects and the causality is bidirectional. We also have used the dummy variable for the US subprime mortgage financial crisis and found that they are statistically significant. Indian stock market is thus integrated to the world stock markets.     

SIMULATED MAXIMUM LIKELIHOOD ESTIMATION BASED ON FIRST‐ORDER CONDITIONS*

I describe a strategy for structural estimation that uses simulated maximum likelihood (SML) to estimate the structural parameters appearing in a model's first‐order conditions (FOCs). Generalized method of moments (GMM) is often the preferred method for estimation of FOCs, as it avoids distributional assumptions on stochastic terms, provided all structural errors enter the FOCs additively, giving a single composite additive error. But SML has advantages over GMM in models where multiple structural errors enter the FOCs nonadditively. I develop new simulation algorithms required to implement SML based on FOCs, and I illustrate the method using a model of U.S. multinational corporations.     

Uncertainty and crude oil market volatility: new evidence

ABSTRACT

The main goal of this paper is to investigate the predictability of five economic uncertainty indices for oil price volatility in a changing world. We employ the standard predictive regression framework, several model combination approaches, as well as two prevailing model shrinkage methods to evaluate the performances of the uncertainty indices. The empirical results based on simple autoregression models including only one index suggest that global economic policy uncertainty (GEPU) and US equity market volatility (EMV) indices have significant predictive power for crude oil market volatility. In addition, the model combination approaches adopted in this paper can improve slightly the performances of individual autoregressive models. Lastly, the two model shrinkage methods, namely Elastin net and Lasso, outperform other individual AR-type model and combination models in most forecasting cases. Other empirical results based on alternative forecasting methods, estimation window sizes, high/low volatility and economic expansion/recession time periods further make sure the robustness of our major conclusions. The findings in this paper also have several important economic implications for oil investors.     

THE DYNAMIC RELATION BETWEEN RETURNS,TRADING VOLUME,AND VOLATILITY: LESSONS FROM SPILLOVERS BETWEEN ASIA AND THE UNITED STATES

This paper investigates the dynamic relationship between index returns, return volatility, and trading volume for eight Asian markets and the US. We find cross‐border spillovers in returns to be non‐existent, spillovers in absolute returns between Asia and the US to be strong in both directions, and spillovers in volatility to run from Asia to the US. Trading volume, especially on the Asian markets, depends on shocks in domestic and foreign returns as well as on volatility, especially those shocks originating in the US. However, only weak evidence is found for trading volume influencing other variables. In the light of the theoretical models, these results suggest sequential information arrivals, with investors being overconfident and applying positive feedback strategy. Furthermore, new information causes price volatility to rise due to differences in its interpretation among traders, but the subsequent market reaction takes the form of adjustment in price level, not volatility. Lastly, the intensity of cross‐border spillovers seems to have increased following the 1997 crisis, which we interpret as evidence of increased noisiness in prices and diversity in opinions about news originating abroad. Our findings might also help to understand the nature of financial crises, to predict their further developments and consequences.     

Business cycle fluctuations in Taiwan — A Bayesian DSGE analysis

This paper examines the Taiwanese economy in a small open economy DSGE model using Bayesian estimation. The model consists of two countries and 12 exogenous shocks with stochastic volatility to capture the fluctuations in the business cycle. The main results are: (1) shock innovations with stochastic volatility increase the model fit, (2) shocks originated from outside the country are important sources of fluctuations in the Taiwanese business cycle.     

Was the recent downturn in US real GDP predictable?

This article uses a small set of variables – real GDP, the inflation rate and the short-term interest rate – and a rich set of models – atheoretical (time series) and theoretical (structural), linear and nonlinear, as well as classical and Bayesian models – to consider whether we could have predicted the recent downturn of the US real GDP. Comparing the performance of the models to the benchmark random-walk model by root mean-square errors, the two structural (theoretical) models, especially the nonlinear model, perform well on average across all forecast horizons in our ex post, out-of-sample forecasts, although at specific forecast horizons certain nonlinear atheoretical models perform the best. The nonlinear theoretical model also dominates in our ex ante, out-of-sample forecast of the Great Recession, suggesting that developing forward-looking, microfounded, nonlinear, dynamic stochastic general equilibrium models of the economy may prove crucial in forecasting turning points.     

MODEL UNCERTAINTY AND EXCHANGE RATE VOLATILITY*

This article proposes an explanation for shifts in the volatility of exchange‐rate returns. Agents are uncertain about the true data generating model and deal with this uncertainty by making inference on the models and their parameters' approach, I call model learning. Model learning may lead agents to focus excessively on a subset of fundamental variables. Consequently, exchange‐rate volatility is determined by the dynamics of these fundamentals and changes as agents alter models. I investigate the empirical relevance of model learning and find that the change in volatility of GBP/USD in 1993 was triggered by a shift between models.     

Testing for a unit root in the presence of stochastic volatility and leverage effect

Previous studies have shown that the stationary and nonstationary time-varying volatilities have different implications on the unit root test. In this paper, we provide a Bayesian unit root test for an AR(1) model with stochastic volatility and leverage effect. Monte Carlo simulations show that the proposed Bayesian unit root test statistic achieves good finite sample properties and is robust to the stationarity of stochastic volatility.     

Comparison of Stochastic and Spline Models for Temperature‐based Derivatives in China

In this paper, we propose modelling the seasonal variation of temperature with a stochastic process to achieve normality of residuals. We conduct a heuristic comparison of the new stochastic seasonal variation model with three established empirical temperature and pricing models: the model of Alaton et al., the continuous autoregressive model and the spline model. The test criteria are residual normality, the Akaike information criterion, relative errors, and stability of price behaviour. The objective of the paper is to find the most suitable model for the application of temperature‐based derivatives in China. Therefore, 30 years of daily average temperature data from 12 cities in mainland China are applied. The results show that the stochastic seasonal variation model dominates the other three models by providing a more precise fitting of the temperature process. Furthermore, the spline model displays inconsistencies when it is applied to Chinese temperature data. This model has the smallest relative errors, but the worst results for normality of residuals.     

The structural transformation between manufacturing and services and the decline in the US GDP volatility

I construct a two-sector growth model to study the effect of the structural transformation between manufacturing and services on the decline in GDP volatility in the US. In the model, a change in the relative size of the two sectors affects the transmission mechanism that relates sectoral TFP shocks to endogenous variables. I calibrate the model to the US and show that, for given stochastic sectoral TFP processes in manufacturing and services, structural change generates a decline in the volatility of both aggregate TFP and GDP, in the volatility of each broad component of GDP (manufacturing consumption, services consumption and investment) and in the volatility of labor. Numerical results suggest that the structural transformation can account for 28% of the reduction in the US GDP volatility between the periods 1960–1983 and 1984–2005.     

Value at risk estimation by threshold stochastic volatility model

This article proposes a threshold stochastic volatility model that generates volatility forecasts specifically designed for value at risk (VaR) estimation. The method incorporates extreme downside shocks by modelling left-tail returns separately from other returns. Left-tail returns are generated with a t-distributional process based on the historically observed conditional excess kurtosis. This specification allows VaR estimates to be generated with extreme downside impacts, yet remains empirically widely applicable. This article applies the model to daily returns of seven major stock indices over a 22-year period and compares its forecasts to those of several other forecasting methods. Based on back-testing outcomes and likelihood ratio tests, the new model provides reliable estimates and outperforms others.     

Terms‐of‐Trade Shocks and Exchange Rate Regimes in a Small Open Economy*

We examine the impact of terms‐of‐trade shocks on key macroeconomic variables by numerically solving a dynamic stochastic general equilibrium model of a small open economy. The model considers nominal price rigidity under different exchange rate regimes. The numerical solutions obtained are consistent with the empirical regularities documented by Broda (2004), in which output responses to shocks are smoother in floats than in pegs; in moving from pegs to floats, the rise in nominal exchange rate volatility is coupled by the rise in real exchange rate volatility; and in both exchange rate regimes, net foreign assets is the most volatile variable.