CONDITIONALLY HETEROSKEDASTIC FACTOR MODELS WITH SKEWNESS AND LEVERAGE EFFECTS

Conditional heteroskedasticity, skewness and leverage effects are well‐known features of financial returns. The literature on factor models has often made assumptions that preclude the three effects to occur simultaneously. In this paper I propose a conditionally heteroskedastic factor model that takes into account the presence of both the conditional skewness and leverage effects. This model is specified in terms of conditional moment restrictions and unconditional moment conditions are proposed allowing inference by the generalized method of moments (GMM). The model is also shown to be closed under temporal aggregation. An application to daily excess returns on sectorial indices from the UK stock market provides strong evidence for dynamic conditional skewness and leverage with a sharp efficiency gain resulting from accounting for both effects. The estimated volatilitypersistence from the proposed model is lower than that estimated from models that rule out such effects. I also find that the longer the returns' horizon, the fewer conditionally heteroskedastic factors may be required for suitable modeling and the less strong is the evidence for dynamic leverage. Some of these results are in line with the main findings of Harvey and Siddique ( 1999 ) and Jondeau and Rockinger ( 2003 ), namely that accounting for conditional skewness impacts the persistence in the conditional variance of the return process. Copyright © 2012 John Wiley & Sons, Ltd.     

Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall

We estimate several GARCH- and Extreme Value Theory (EVT)-based models to forecast intraday Value-at-Risk (VaR) and Expected Shortfall (ES) for S&P 500 stock index futures returns for both long and short positions. Among the GARCH-based models we consider is the so-called Autoregressive Conditional Density (ARCD) model, which allows time-variation in higher-order conditional moments. ARCD model with time-varying conditional skewness parameter has the best in-sample fit among the GARCH-based models. The EVT-based model and the GARCH-based models which take conditional skewness and kurtosis (time-varying or otherwise) into account provide accurate VaR forecasts. ARCD model with time-varying conditional skewness parameter seems to provide the most accurate ES forecasts.     

Modeling time-varying higher-order conditional moments: A survey

Since the introduction of the Autoregressive Conditional Heteroscedasticity (ARCH) model, the literature on modeling the time-varying second-order conditional moment has become increasingly popular in the last four decades. Its popularity is partly due to its success in capturing volatility in financial time series, which is useful for modeling and predicting risk for financial assets. A natural extension of this is to model time variation in higher-order conditional moments, such as the third and fourth moments, which are related to skewness and kurtosis (tail risk). This leads to an emerging literature on time-varying higher-order conditional moments in the last two decades. This paper outlines recent developments in modeling time-varying higher-order conditional moments in the economics and finance literature. Using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) framework as a foundation, this paper provides an overview of the two most common approaches for modeling time-varying higher-order conditional moments: autoregressive conditional density (ARCD) and autoregressive conditional moment (ARCM). The discussion covers both the theoretical and empirical aspects of the literature. This includes the identification of the associated skewness–kurtosis domain by using the solutions to the classical moment problems, the structural and statistical properties of the models used to model the higher-order conditional moments and the computational challenges in estimating these models. We also advocate the use of a maximum entropy density (MED) as an alternative method, which circumvents some of the issues prevalent in these common approaches.     

Forecasting in GARCH models with polynomially modified innovations

Orthogonal polynomials can be used to modify the moments of the distribution of a random variable. In this paper, polynomially adjusted distributions are employed to model the skewness and kurtosis of the conditional distributions of GARCH models. To flexibly capture the skewness and kurtosis of data, the distributions of the innovations that are polynomially reshaped include, besides the Gaussian, also leptokurtic laws such as the logistic and the hyperbolic secant. Modeling GARCH innovations with polynomially adjusted distributions can effectively improve the precision of the forecasts. This strategy is analyzed in GARCH models with different specifications for the conditional variance, such as the APARCH, the EGARCH, the Realized GARCH, and APARCH with time-varying skewness and kurtosis. An empirical application on different types of asset returns shows the good performance of these models in providing accurate forecasts according to several criteria based on density forecasting, downside risk, and volatility prediction.     

Are regulations the answer for emerging stock markets? Evidence from the Czech Republic and Poland

Does the emergence of a stock market require a well-developed legal and/or regulatory system? Although historical work by Neal and Davis [Neal, L., & Davis, L. (2005). The evolution of the rules and regulations of the first emerging markets: The London, New York, and Paris stock exchanges, 1792–1914. Quarterly Review of Economics and Finance, 45, 296–311] and Stringham [Stringham, E. (2003). The extralegal development of securities trading in seventeenth century Amsterdam. Quarterly Review of Economics and Finance, 43, 321–344] suggests that securities markets have successfully developed with little government oversight, numerous authors [including Black, B. (2001). The legal and institutional preconditions for strong securities markets. University of California Law Angeles Law Review, 48, 781–855; Coffee, J. (1999). Privatization and corporate governance: The lessons from securities market failure. Journal of Corporation Law, 25, 1–39; Frye, T. (2000). Brokers and bureaucrats: Building market institutions in Russia. Ann Arbor: University of Michigan Press; Glaeser, E., Johnson, S., & Shleifer, A. (2001). Coase versus the Coasians. Quarterly Journal of Economics, 116, 853–899; Mlčoch, L. (2000). Restructuring of property rights: An institutional view. In L. Mlčoch et al. (Eds.), Economic and Social Changes in Czech Society After 1989. Prague: The Karolinum Press; Pistor, K. (2001). Law as a determinant for equity market development – the experience of transition economies. In Peter Murrell (Ed.), The Value of Law in Transition Economies (pp. 249–287). Ann Arbor: Michigan University Press; Stiglitz, J. (1999). Whither reform. Ten years of the transition. Keynote Address, Annual Bank Conference on Development Economics, Washington, DC, April 28–30, 1999; Zhang, X. (2006). Financial market governance in developing countries: Getting the political underpinnings right. Journal of Developing Societies, 2, 169–196] argue that the Czech Republic and other Eastern European governments need more regulation for their newly created stock markets. They maintain that the Warsaw Stock Exchange, which is seen as more regulated, has outperformed the Prague Stock Exchange which is seen as largely unregulated. Thus increased regulations are a key to increased performance. This article, however, maintains that the evidence from the Czech experience has been misinterpreted. This article provides an in depth case study of the Czech stock market and finds that (a) Czech capital markets have been hindered by government intervention from their beginning, (b) that the evidence on Poland's superior performance is not as strong as suggested, and (c) that Czech regulators seem to be unqualified, lack the proper incentives, and are unlikely to benefit the market. Under these circumstances it appears that Neal and Davis (2005:311) are correct that increased government involvement is unlikely to improve the situation.     

A dynamic CAPM with supply effect: Theory and empirical results

Breeden [Breeden, D. T. (1979). An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics 7, 265–196] and Grinols [Grinols, E. L. (1984). Production and risk leveling in the intertemporal capital asset pricing model. The Journal of Finance 39, 5, 1571–1595] and Cox et al. [Cox, J. C., Ingersoll, J. E., Jr., & Ross, S. A. (1985). An intertemporal general equilibrium model of asset prices. Econometrica 53, 363–384] have described the importance of supply side for the capital asset pricing. Black [Black, S. W. (1976). Rational response to shocks in a dynamic model of capital asset pricing. American Economic Review 66, 767–779] derives a dynamic, multiperiod CAPM, integrating endogenous demand and supply. However, Black's theoretically elegant model has never been empirically tested for its implications in dynamic asset pricing. We first theoretically extend Black's CAPM. Then we use price, dividend per share and earnings per share to test the existence of supply effect with U.S. equity data. We find the supply effect is important in U.S. domestic stock markets. This finding holds as we break the companies listed in the S&P 500 into ten portfolios by different level of payout ratio. It also holds consistently if we use individual stock data.     

Price support and spreads in the IPO aftermarket: An empirical microstructure study

Using the inventory components of spreads as a measure of inventory holding-risk, we test the hypothesis of Hanley et al. [Hanley, K. W., Kumar, A., & Seguin, P. J. (1993). Price stabilization in the market for new issues. Journal of Financial Economics, 34, 177–197] that price supports reduce market makers’ inventory holding-risk in the aftermarket of initial public offerings (IPOs). We find that both spreads and their inventory components are significantly smaller in the earlier periods of the IPO aftermarket than those in the later periods. More importantly, the inventory components of spreads are significantly smaller for stocks without over-allotment options (OAOs) exercised, and for stocks with lower or negative initial returns which are more likely to have price supports. The results are consistent with the price support hypothesis.     

The persistence of the small firm/January effect: Is it consistent with investors’ learning and arbitrage efforts?

Using improved methodology and an expanded research design, we examine whether the small firm/January effect (Keim, D. B. (1983). Size-related anomalies and stock return seasonality: further empirical evidence. Journal of Financial Economics 12:13–32), is declining over time due to market efficiency. First, we find that January returns are smaller after 1963–1979, but have simply reverted to levels that existed before that time. Second, we show that the January effect is not limited to mature markets but also appears in firms trading on the relatively new NASDAQ exchange in the 1970s. Third, trading volume for small firms in December and January is not different from other months, implying that traders are not actively arbitraging the anomaly. Together, our results suggest that this anomaly continues to defy rational explanation in an efficient market.     

Forecasting cryptocurrency volatility

This paper studies the behavior of cryptocurrencies’ financial time series, of which Bitcoin is the most prominent example. The dynamics of these series are quite complex, displaying extreme observations, asymmetries, and several nonlinear characteristics that are difficult to model and forecast. We develop a new dynamic model that is able to account for long memory and asymmetries in the volatility process, as well as for the presence of time-varying skewness and kurtosis. The empirical application, carried out on 606 cryptocurrencies, indicates that a robust filter for the volatility of cryptocurrencies is strongly required. Forecasting results show that the inclusion of time-varying skewness systematically improves volatility, density, and quantile predictions at different horizons.     

Improving variance forecasts: The role of Realized Variance features

In this paper, we effectively extend the Realized-EGARCH (R-EGARCH) framework by allowing the conditional variance process to incorporate exogenous variates related to different observable features of Realized Variance (RV). The choice of these features is well motivated by recent studies on the Heterogeneous Autoregressive (HAR) class of models. We examine several specifications nested within our augmented R-EGARCH representation, and we find that they perform significantly better than the standard R-EGARCH model. These specifications incorporate realized semi-variances, heterogeneous long-memory effects of RV, and jump variation. We also show that the performance of our framework further improves if we allow for skewness and excess kurtosis for asset return innovations, instead of assuming normality. This can better filter the true distribution of the return innovations, and thus can more accurately estimate their effects on the variance process. This is also supported by a Monte Carlo simulation exercise executed in the paper.     

Order imbalance and stock returns: Evidence from China

We investigate the relation between daily order imbalance and return in the Chinese stock markets of Shenzhen and Shanghai. Prior studies have found that daily order imbalance is predictive of subsequent returns. On the two Chinese exchanges we find the autocorrelation in order imbalances is similar to that of the New York Stock Exchange as reported by Chordia and Subrahmanyam [Chordia, T., & Subrahmanyam, A. (2004). Order imbalance and individual stock returns: Theory and evidence. Journal of Financial Economics, 72, 485–518]. We also find a strong contemporaneous relation between daily order imbalances and returns. However, we do not find evidence that order imbalances predict subsequent returns. We attribute the difference in predicative power to differences in trading mechanisms on the two exchanges and to differences in the share turnover rates.     

Unbounded exchange economies with satiation: How far can we go?

We unify and generalize the existence results in Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55 (6), 1403–1418], Dana et al. [Dana, R.-A., Le Van, C., Magnien, F., 1999. On the different notions of arbitrage and existence of equilibrium. Journal of Economic Theory 87 (1), 169–193], Allouch et al. [Allouch, N., Le Van, C., Page Jr., F.H., 2006. Arbitrage and equilibrium in unbounded exchange economies with satiation. Journal of Mathematical Economics 42 (6), 661–674], Allouch and Le Van [Allouch, N., Le Van, C., 2008. Erratum to “Walras and dividends equilibrium with possibly satiated consumers”. Journal of Mathematical Economics 45 (3–4), 320–328]. We also show that, in terms of weakening the set of assumptions, we cannot go too far.     

Forecasting ultimate resource recovery

This paper considers Hubbert's model for forecasting ultimate resource recovery and its extensions by Kaufmann (1991, Resources and Energy 13, 111–127) and Cleveland and Kaufmann (1991, Energy Journal 12, 17–46). The emphasis of the paper is on econometric and forecasting issues, and it discusses alternative methods of estimating Hubbert's model. Using data on oil production in the U.S. lower 48 states, the paper reports the results of estimating the various specifications of the model and its extensions by the maximum-likelihood method, and provides the implied estimates for ultimate resource recovery and their associated standard errors. When economic factors are taken into account the estimates of ultimate resource recovery become state-dependent, and we find that in this case the estimates are higher than those obtained from the various specifications of Hubbert's original model. Although the accuracy of the estimates of ultimate recoverable reserves cannot be evaluated before oil reserves are actually exhausted, we examine how the various models estimated over the periods 1926–1985 and 1948–1985 perform in predicting oil production over the 1986–1990 period.     

Do components of smooth tests of fit have diagnostic properties?

Smooth goodness of fit tests were introduced by Neyman (1937). They can be regarded as a compromise between globally consistent (“omnibus”) tests of fit and procedures having high power in the direction of a specific alternative. It is commonly believed that components of smooth tests like, e.g., skewness and kurtosis measures in the context of testing for normality, have special diagnostic properties in case of rejection of a hypothesisH ₀ in the sense that they constitute direct measures of the kind of departure fromH ₀. Recent years, however, have witnessed a complete change of attitude towards the diagnostic capabilities of skewness and kurtosis measures in connection with normality testing. In this paper, we argue that any component of any smooth test of fit is strictly non-diagnostic when used conventionally. However, a proper rescaling of components does indeed achieve the desired “directed diagnosis”.     

Whittle estimation of EGARCH and other exponential volatility models

The strong consistency and asymptotic normality of the Whittle estimate of the parameters in a class of exponential volatility processes are established. Our main focus here are the EGARCH model of [Nelson, D. 1991. Conditional heteroscedasticity in asset pricing: A new approach. Econometrica 59, 347–370] and other one-shock models such as the GJR model of [Glosten, L., Jaganathan, R., Runkle, D., 1993. On the relation between the expected value and the volatility of the nominal excess returns on stocks. Journal of Finance, 48, 1779–1801], but two-shock models, such as the SV model of [Taylor, S. 1986. Modelling Financial Time Series. Wiley, Chichester, UK], are also comprised by our assumptions. The variable of interest might not have finite fractional moment of any order and so, in particular, finite variance is not imposed. We allow for a wide range of degrees of persistence of shocks to conditional variance, allowing for both short and long memory.     

Econometric analysis of structural systems with permanent and transitory shocks

This paper considers the implications of the permanent/transitory decomposition of shocks for identification of structural models in the general case where the model might contain more than one permanent structural shock. It provides a simple and intuitive generalization of the influential work of Blanchard and Quah [1989. The dynamic effects of aggregate demand and supply disturbances. The American Economic Review 79, 655–673], and shows that structural equations with known permanent shocks cannot contain error correction terms, thereby freeing up the latter to be used as instruments in estimating their parameters. The approach is illustrated by a re-examination of the identification schemes used by Wickens and Motto [2001. Estimating shocks and impulse response functions. Journal of Applied Econometrics 16, 371–387], Shapiro and Watson [1988. Sources of business cycle fluctuations. NBER Macroeconomics Annual 3, 111–148], King et al. [1991. Stochastic trends and economic fluctuations. American Economic Review 81, 819–840], Gali [1992. How well does the ISLM model fit postwar US data? Quarterly Journal of Economics 107, 709–735; 1999. Technology, employment, and the business cycle: Do technology shocks explain aggregate fluctuations? American Economic Review 89, 249–271] and Fisher [2006. The dynamic effects of neutral and investment-specific technology shocks. Journal of Political Economy 114, 413–451].     

Normal mixture GARCH(1,1): applications to exchange rate modelling

Some recent specifications for GARCH error processes explicitly assume a conditional variance that is generated by a mixture of normal components, albeit with some parameter restrictions. This paper analyses the general normal mixture GARCH(1,1) model which can capture time variation in both conditional skewness and kurtosis. A main focus of the paper is to provide evidence that, for modelling exchange rates, generalized two‐component normal mixture GARCH(1,1) models perform better than those with three or more components, and better than symmetric and skewed Student's t‐GARCH models. In addition to the extensive empirical results based on simulation and on historical data on three US dollar foreign exchange rates (British pound, euro and Japanese yen), we derive: expressions for the conditional and unconditional moments of all models; parameter conditions to ensure that the second and fourth conditional and unconditional moments are positive and finite; and analytic derivatives for the maximum likelihood estimation of the model parameters and standard errors of the estimates. Copyright © 2006 John Wiley & Sons, Ltd.     

Restricted houseswapping games

Restricted houseswapping games (RHGs) are a generalization of ‘one-sided matching games’, in which we specify a class II* of ‘allowable’ simple trading cycles. The cores of such games may be empty. Given II*, all possible closed RHGs have non-empty cores of II* is ‘strongly balanced’. Examples include the one-sided matching markets (^{Shapley and Scarf. Journal of Mathematical Economics 1974. 1. 23–37}. ^{Tijs et al., OR Spektrum 1984, 6, 119–123}; ^{Quinzii, International Journal of Game Theory 1984, 13, 41–60}) and the two-sided matching markets (^{Gale and Shapley. American Mathematical Monthly 1962. 69, 9–16}; ^{Shapley and Shubik, International Journal of Game Theory 1972, 1, 111–130}: and ^{Demange and Gale Econometrica 1985, 53, 873–888}).We then consider the subclass of RHGs in which there is no transferable resource. In this case, a weaker condition on II*, called ‘weak balancedness’, is sufficient to guarantee core non-emptiness. In addition, if II* is not weakly balanced, then there exists a preference profile such that the strict core of the resultant game is empty.Several other examples are given of II* that are (a) strongly balanced: (b) weakly balanced but not strongly balanced: and (c) not even weakly balanced.Finally, we discuss the issues of equilibrium definition, existence, and core-equilibrium allocation equivalence in RHGs.     

Housing capital-gains taxation and homeowner mobility: Evidence from the Taxpayer Relief Act of 1997

We provide new evidence on the impact of housing capital-gains taxation on homeowner behavior by examining residential mobility before and after the Taxpayer Relief Act of 1997 (TRA97), which generated the most sweeping reform of capital-gains taxation in the last two decades. In addition to lowering marginal tax rates on long-term capital gains for all assets, TRA97 also eliminated any differential treatment of housing gains above and below age 55, allowing all homeowners to qualify for capital-gains exclusions. Utilizing data drawn from the Current Population Survey (CPS) on either side of the law change (1996 and 1998) on homeowners just above (56–58 year olds) and below (52–54 year olds) the age-55 threshold and a reduced-form, difference-in-difference empirical approach, our estimates suggest that the repeal of the differential capital-gains tax treatment by age embodied in TRA97 had an economically important and statistically significant impact on the residential mobility of under-55 homeowners. Across a variety of specifications, the repeal raised the mobility rate by around 1–1.4 percentage points, which, for a mean mobility rate of 4 percentage points, represented an increase in the mobility rate of homeowners in their early 50s by 22–31%. Furthermore, the bulk of this effect was concentrated among highly mobile homeowners who a priori were more likely to have wanted to trade down (e.g., divorced, empty nesters), those facing higher capital gains tax rates, and those living in states that had experienced higher rates of nominal appreciation.     

Gold and platinum: Toward solving the price puzzle

Gold and platinum prices are positively correlated over 1985–2006. Yet, over shorter sample periods the correlation changes from positive to negative (1996–2001) and back. The objective of this paper is to determine whether this shift is the result, at least in part, of the rapid increase in forward sales by gold producers, which had the effect of substantially lowering gold prices in the second half of the 1990s (Kearney, A. & Lombra, L. (2008). The non-neutral short run effects of derivatives on gold prices. Applied Financial Economics, 18, 985–994). The results show declining gold prices are associated with large net increases in forward sales, while rising gold prices are associated with declining forward sales or producer dehedging.