David G. McMillan

Does VIX or volume improve GARCH volatility forecasts

ABSTRACT This article considers whether the inclusion of two additional variables can improve volatility forecasts over a standard GARCH-based model. We consider three alternative ways of incorporating the volatility index (VIX) and trading volume as exogenous variables within a selection of GARCH models. We are particularly interested in whether these variables have additional incremental forecast power over and above the baseline GARCH specification. Our results suggest that both the VIX and volume do provide some additional forecast power, and this is generally improved when considering both of these series jointly in the model. However, while the results may be statistically significant the gain is marginal and the coefficient values small. Moreover, in a horse race exercise VIX does not outperform the GARCH approach. In answering the question of whether VIX produces better forecasts than the GARCH model, then the answer is no, but the informational content of VIX cannot be ignored and should be incorporated into forecast regressions.

Interaction among stock prices and monetary variables in Pakistan

The interaction between stock market and monetary variables in Pakistan using monthly data for the last 20 years is examined. The Johansen co-integration approach is utilised to examine the equilibrium relationship between the stock price index, money supply, interest rates and a foreign exchange rate. An unrestricted VAR model is also used in order to analyse short-run dynamics and causality within these variables. The results report a long-run and significant relationship between these variables. In particular, the VAR model indicates that fluctuations in the KSE-100 index are significantly affected by the money supply and exchange rate but not the interest rate. Moreover, money supply has a positive relationship with the stock market and a negative relationship with interest rates and exchange rates. Interest rates have a weak and mixed relationship with all other variables. The dynamic relationships should aid policy-makers in understanding the effects of monetary policy changes.

Spillovers between output and stock prices: a wavelet approach

Purpose n n n n nThis paper seeks to examine the nature of spillovers between output and stock prices using both a long annual time series spanning 200 years and a shorter but quarterly observed data set. n n n n nDesign/methodology/approach n n n n nThe authors’ particular interest is to examine both the time-varying nature of the spillovers and spillovers across the frequency using wavelet analysis. n n n n nFindings n n n n nThe results reveal an interesting detail that is missed when considering spillovers for the raw data. Using annual long run data, spillovers in the raw data are in the order of approximately 10 per cent for stocks to output and 25 per cent for output to stocks. But this increases up to 50 per cent and above (in both directions) when considering different frequencies. Similar results are reported with the quarterly data, although the differences between the raw data and the wavelets are smaller in nature. Finally, output explains more of the variation in stocks than stocks explains in output. n n n n nOriginality/value n n n n nThe nature of these results is important for policy-makers, market participants and academics alike, while the use of wavelets provides information across different frequencies.

Stock return predictability and market integration: The role of global and local information

Abstract This paper examines the predictability of a range of international stock markets where we allow the presence of both local and global predictive factors. Recent research has argued that US returns have predictive power for international stock returns. We expand this line of research, following work on market integration, to include a more general definition of the global factor, based on principal components analysis. Results identify three global expected returns factors, one related to the major stock markets of the US, UK and Asia and one related to the other markets analysed. The third component is related to dividend growth. A single dominant realised returns factor is also noted. A forecasting exercise comparing the principal components based factors to a US return factor and local market only factors, as well as the historical mean benchmark finds supportive evidence for the former approach. It is hoped that the results from this paper will be informative on three counts. First, to academics interested in understanding the dynamics asset price movement. Second, to market participants who aim to time the market and engage in portfolio and risk management. Third, to those (policy makers and others) who are interested in linkages across international markets and the nature and degree of integration.

Time‐varying Predictability for Stock Returns, Dividend Growth and Consumption Growth

Using a state‐space model, this paper examines time variation in the predictive regressions for stock returns, dividend growth and consumption growth. Moreover, we linked time variation explicitly to movements in economic factors that can account for risk and cash flow. Results support the view that stock return predictability is enhanced when risk is high (negative growth, higher volatility and positive growth/return covariance). In contrast, dividend growth and consumption growth predictability is enhanced during economic expansions. These results are supported by subsample analysis and a vector autoregressive approach. Furthermore, these latter exercises may uncover differences in the stock return predictability relationship when viewed over different time horizons. Overall, the paper contributes to the literature by highlighting the different nature of returns predictability, which arises largely through the risk channel, and dividend and consumption growth predictability, which arise through the cash flow channel. Copyright

Editors’ foreword: Special issue of Quantitative Finance on ‘Hawkes Processes in Finance’

Since the invention of Hawkes processes in the early 1970s many researchers, including the pioneer seismologists, have studied applications over a very wide range of topics. However, these stochastic processes with a substantial modelling advantage were only noticed in finance research from 2005. Since then there has been a rapid expansion of papers applying Hawkes processes to diverse problems in finance. But there is still great scope to make them become standard financial econometric tools and we, as the panel of guest editors, felt that it would be both valuable and timely to have a special journal issue treating a variety of financial applications. Happily, when we approached the Editorsin-Chief of Quantitative Finance they were extremely supportive, and the result is this issue with a broad range of interesting papers. The issue begins with an introduction by the author of Hawkes processes, Professor Alan Hawkes. He has been excited by the idea of this issue and has provided a brief history to describe the basic properties of Hawkes processes —essentially a class of stochastic models for series of events whose occurrence generally increases the probability of occurrence of further events, often described as a contagious effect. He concludes with a review of some recently published papers. This is followed by a collection of nine papers, addressing many contemporary topics from both the theoretical and practical viewpoints. Achab, Bacry, Muzy and Rambaldi use a 12-dimensional mutually exciting process to model interactions between different kinds of events in a high-frequency single-asset order book. A non-parametric method is used to estimate the branching ratio matrix directly without considering the exact shape of the exciting kernels. The elements of this matrix measure the connectivity between event types and the process developed is extended to study interactions between two assets. As indicated above, Hawkes processes are usually positively exciting. However, Khashanah, Chen and Hawkes introduce a type of birth-death-immigration model which turns out to be a special kind of two-dimensional mutually exciting process. In it, the occurrence of some types of events can decrease the rate at which other events occur (so that these interactions are actually depressing rather than exciting). This feature can be useful in modelling the decay of activities that are usually observed in a market with bursts of events. For example, the burst of trading activities at the start of a trading day. A number of studies of jumps in asset prices have assumed that the kernel of a self-exciting model has a simple exponential shape or perhaps a linear combination of two or three exponential components. Chen, Hawkes, Scalas and Trinh carry out a simulation study to compare the ability of various information criteria: Akaike’s information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan-Quinn criterion (HQ) to decide on the best model to choose. Calcagnile, Bormetti, Treccani, Marmi and Lillo study a portfolio with a multiplicity of assets and are concerned with the number of assets that jump simultaneously (cojumps). It is suggested that a suitable mutually exciting Hawkes process could be used to model the time-clustering of jumps. The authors also provide a novel approach to fit such a complicated model using simplifying assumptions which reduce the model estimation to involve only three parameters! Remarkably, this approximation appears to fit data moderately well. Lu and Abergel attempt to model the various events of an order book using a mutually exciting Hawkes process with exponential kernels. On finding that interactions sometimes appear inhibitory rather than exciting, they replace the usual linear model by a non-linear model. Since the usual linear form can result in a negative intensity, they simply truncate the kernel at zero in this case. Gao, Zhou and Zhu consider a self-exciting Hawkes process in which the baseline intensity is time-dependent, the exciting function is a general function and the jump sizes of the intensity process are i.i.d. non-negative random variables. They obtain closed-form formulas for the Laplace transform, moments and distribution of the process. The process is then used to model the clustered arrival of trades in a dark pool and for a resting dark order they analyse various pool performance metrics including time-to-first-fill, time-to-complete-fill and the expected fill rate. Schneider, Lillo and Pelizzon use a peaks over threshold (PoT) method to identify abrupt liquidity drops in limit order book data. Both the self-excitation of extreme changes of liquidity in the same asset (illiquidity spirals) and cross-excitation across different assets (illiquidity spillovers) can be quantified. The application of their method to the Mercato dei Titoli di Stat (MTS) sovereign bond markets show that the proportion of shocks explained by illiquidity spillovers roughly doubles from 2011 to 2015.

Stock Returns, Illiquidity and Feedback Trading

This study aims to examine the relation between illiquidity, feedback trading and stock returns for several European markets, using panel regression methods, during the financial and the sovereign debt crises. The authors’ interest here lies twofold. First, the authors seek to compare the results obtained here under crisis conditions with those in the existing literature. Second, and of greater importance, the authors wish to examine the interaction between liquidity and feedback trading and their effect on stock returns.,The authors jointly model both feedback trading and illiquidity, which are typically considered in isolation. The authors use panel estimation methods to examine the relations across the European markets as a whole.,The key results suggest that in common with the literature, illiquidity has a negative impact upon contemporaneous stock returns, while supportive evidence of positive feedback trading is reported. However, in contrast to the existing literature, lagged illiquidity is not a priced risk, while negative shocks do not lead to greater feedback trading behaviour. Regarding the interaction between illiquidity and feedback trading, the study results support the view that greater illiquidity is associated with stronger positive feedback.,The study results suggest that when price changes are more observable, due to low liquidity, then feedback trading increases. Therefore, during the crisis periods that afflicted European markets, the lower levels of liquidity prevalent led to an increase in feedback trading. Thus, negative liquidity shocks that led to a fall in stock prices were exacerbated by feedback trading.

Conditional volatility nexus between stock markets and macroeconomic variables: Empirical evidence of G-7 countries

Purpose - The purpose of this paper is to analyse the relation between stock market volatility and macroeconomic fundamentals for G-7 countries using monthly data over the period from July 1985 to June 2015. Design/methodology/approach - The empirical methodology is based on two steps: in the first step, the authors obtain the conditional volatilities of stock market returns and macroeconomic variables through the GARCH family of models. The authors also incorporate the impact of early 2000s dotcom and the global financial crises. In the second step, the authors estimate multivariate vector autoregressive model to analyze the dynamic relation between stock markets return and macroeconomic variables. Findings - The overall results for G-7 countries indicate a weak volatility transmission from macroeconomic factors to stock market volatility at individual level but the collective impact of volatility transmission is highly significant. Although, the results of block exogeneity indicate a bidirectional causality except UK, but the causal linkage is quite weak from stock market to macroeconomic variables. Moreover, the local financial variables excluding interest rate are closely integrated, and the volatility of industrial production growth and oil price are identified as the most significant macroeconomic factors that could possibly influence the directions of stock markets. Originality/value - This research establishes the nature of the links between stock market and macroeconomic volatility. Research to date has been unable to satisfactorily establish the empirical nature of such links. The authors believe this paper begins to do this.

Stock return predictability: the role of inflation and threshold dynamics

Abstract This paper argues that the nature of stock return predictability varies with the level of inflation. We contend that the nature of relations between economic variables and returns differs according to the level of inflation, due to different economic risk implications. An increase in low level inflation may signal improving economic conditions and lower expected returns, while the opposite is true with an equal rise in high level inflation. Linear estimation provides contradictory coefficient values, which we argue arises from mixing coefficient values across regimes. We test for and estimate threshold models with inflation and the term structure as the threshold variable. These models reveal a change in either the sign or magnitude of the parameter values across the regimes such that the relation between stock returns and economic variables is not constant. Measures of in-sample fit and a forecast exercise support the threshold models. They produce a higher adjusted R2, lower MAE and RMSE and higher trading related measures. These results help explain the lack of consistent empirical evidence in favour of stock return predictability and should be of interest to those engaged in stock market modelling as well as trading and portfolio management.

Stock Return Predictability: The Role of Inflation and Threshold Dynamics

This paper argues that the nature of stock return predictability varies with the level of inflation. We contend that the nature of relations between economic variables and returns differs according to the level of inflation, due to different economic risk implications. An increase in low level inflation may signal improving economic conditions and lower expected returns, while the opposite is true with an equal rise in high level inflation. Linear estimation provides contradictory coefficient values, which we argue arises from mixing coefficient values across regimes. We test for and estimate threshold models with inflation and the term structure as the threshold variable. These models reveal a change in either the sign or magnitude of the parameter values across the regimes such that the relation between stock returns and economic variables is not constant. Measures of in-sample fit and a forecast exercise support the threshold models. They produce a higher adjusted R-squared, lower MAE and RMSE and higher trading related measures. These results help explain the lack of consistent empirical evidence in favour of stock return predictability and should be of interest to those engaged in stock market modelling as well as trading and portfolio management.