Author:

Keywords:

Comovement, Factor models, Correlations, Liquidity, Contagion, Financial Econometrics

Abstract:

Comovement is ubiquitous in financial markets. The evolution of asset characteristics, such as price, volatility or liquidity, exhibits a high degree of correlation across assets---a phenomenon that in this thesis will generically be denoted with the term comovement. The origins of suchcomovement are legion. In their investment decisions, economic agents are not only influenced by their idiosyncrasies---a large part of investment motivations are shared over a population. Demographics or the political situation can generate constraints that are similar for a large number of people. A country's geography can greatly influence the sectors inwhich it is most productive, which implies that many people are sometimes subject to the same risk factors. Moreover, it is well known that mimesis is part of human psychology, and that people mimic their peers evenwhen taking personal decisions. For these reasons, and many more, financial markets have a very systematic character, and studying the nature and intensity of such comovement is important from a risk management point of view. This thesis studies comovement in financial markets under three dimensions: equity liquidity, equity return correlations and contagion in the sovereign bond market.From a theoretical perspective, the comovement of financial markets has already been widely considered. The mean-variance portfolio theory of Markowitz (1952) shows how the optimal portfolio allocation depends on the correlations between returns of securities: low or negative correlations have a reducing effect on the variance of a diversified portfolio. In the Capital Asset Pricing Model (henceforth CAPM), Sharpe (1964) shows that cross-sectional dispersion inequity returns should only come from cross-sectional dispersion in the covariance between the market return and the return on the stock. The reason for this result is that idiosyncratic price changes can be diversified away, but market dynamics cannot. The covariance of a stock's returnwith the market return is the contribution of that stock to total market variance and hence its only source of risk in a well diversified portfolio. The Arbitrage Pricing Theory (henceforth APT) of Roll (1976) assumes that stock returns can be driven by macroeconomic factors, such as interest rates or commodity prices. According to the APT, cross-sectional differences in stock returns should not only be explained by dispersion in covariance with respect to the market return, as it is the case for the CAPM, but also by dispersion in covariance with respect to these macroeconomic factors. Each of these factors is then associated with a risk premium. This result is very similar to the conclusions arising from theintertemporal CAPM of Merton (1973), according to which covariance withan exogenous random variable affecting the stochastic investment opportunity set, should be associated with a risk premium.From an econometric point of view, one may distinguish two main ways of dealing withcomovement: regression models and factor models. In regression models, common factors are assumed to be exogenous. They are observable and comoving series can be regressed on them. In factor models, factors are endogenous and unobservable (Factor models are also sometimes called latent factor models) and so need to be estimated themselves. This thesis particularly focuses on factor models. Although the literature on factor models goes back to Chamberlain and Rothschild (1983) and Rothschild (1983), most theoretical foundations have been laid during the last decade. Stock and Watson (2002a,b), Bai and Ng (2002) and Bai (2003) formalized the theory on static factor models. Important references for dynamic factor models, which allow a non constrained leading/lagging structure of commonness, are Forni et al. (2000,2004,2005), Forniand Lippi (2001,2011), Hallin and Liska (2007) and Forni et al. (2011).As said above, the thesis contains three chapters, each of them covering an application of factor models to financial markets. The firstchapter uses dynamic factor models to analyse comovement in equity liquidity. The second chapter disentangles comovement and idiosyncrasy in equity correlations and assesses its impact from an asset pricing perspective. The final chapter proposes a factor model framework for analysing contagion in the European sovereign bond market.In Chapter 1 (This chapter is published under Hallin M., Mathias, C., Pirotte, H., Veredas, D., 2011. Market Liquidity as Dynamic Factors. Journal of Econometrics 163, 42-50.), I study comovement of equity liquidity. From a very general perspective, the liquidity of a security denotes the ease with whichit can be converted into cash, that is, bought or sold. Liquidity is however an elusive concept and can be measured in several ways. More particularly, two popular proxies for liquidity of a security are its closingbid-ask spread (the difference between the lowest selling price and thehighest buying price at the end of the day) or its volume turnover (thenumber of shares exchanged divided by the total number of available shares). Since they both measure liquidity, spread and volume turnover are very similar---yet not identical. One may therefore wonder whether it isthe same aspect of liquidity that comes to the surface through spreads and volume turnover. I answer this question from a comovement perspective: Are market movements in bid-ask spread and in volume turnover the result of the same market liquidity dynamic, or do both measures capture a different aspect of market liquidity?I apply theory on Generalized Dynamic Factor Models to answer this question. The framework used is that of dynamic factors in the presence of block structure, of Hallin and Liska (2011). I first assess the dimension of the common space for both panels of spread and volume turnover. Then, I assess the dimension of the common space of the joint panel, to check whether both common spacesare different or coincide. When looking at S&P 500 stocks between 2004 and 2006, the conclusion is that both panels share the same one-dimensional commonspace. Moreover, I observe that long memory dynamics of both bid-ask spread and volume turnover are captured by the common components,and that idiosyncratic components do not exhibit long memory.Chapter 2 investigates the impact of correlation comovement on the equity risk-return tradeoff. The CAPM of Sharpe (1964) states that the covariance between a stock's return and the market return generates a risk premium. The correlation plays a very important role in that relation, since it measures the diversification benefit of that stock. Correlations are however not stable through time, and even exhibit comovement. One may wonder whether common changes in return correlations are associated with alarger risk premium than it is the case for idiosyncratic changes. On the one hand, this question is motivated by literature on contagion, since contagion can be measured through a common increase in correlations. Therefore, an additional risk premium linked to contagion risk could be captured by common correlation dynamics. On the other hand, Pollet and Wilson (2010) show that the equity market return reflects a premium for common correlation changes, due to the Roll (1977) critique, stating that the equity market is an imperfect proxy for the total wealth portfolio which investors truly consider in their asset valuation.I investigate this question in three steps. First, I use the DCC-GARCH of Engle (2002) to estimate conditional correlations between returns on a portfolio of stocks and on the market. Second, I use a Principal Components Analysis to decompose these conditional correlations in a static, a common dynamic and an idiosyncratic dynamic term. By multiplying these terms by the product of conditional volatilities, I obtain a decomposition for conditional covariances which, according to the CAPM, generate a risk premium. Third, I regress realized returns on the conditional covariance components and assess whether different components are associated with different risk premia. I take monthly return data between 1964 and 2010 on portfolios sorted on industry, size, book-to-market and momentum. Resultssuggest that, when looking at equity from an industry, size or momentumperspective, only common correlation dynamics generate a premium. However, when looking at book-to-market sorted portfolios, it are only idiosyncratic correlations that generate a premium. This suggests that time-varying conditional correlations are differently priced from a value perspective than from an industry, size or momentum point of view. More particularly, it suggests that, from a correlations perspective, the value premium is priced within the equity portfolio, whereas premia related to industry, size and momentum are priced between the equity portfolio and other asset classes.In Chapter 3, I study contagion in the European sovereign bond market. Since the introduction of the single currency, European sovereign bonds have exhibited a high degree of comovement---larger than what fundamentals about the creditor quality of different countries would suggest. The financial turmoil starting in 2007 however put the differences between countries on the table and part of the comovement disappeared during the crisis. Weaker countries, such as Greece, Portugal and Ireland, have exhibited a kind of decoupling compared to other EMU country bonds. The relationship between all these sovereign bonds is however very dual: on the one hand there are verybig differences between the countries, but on the other hand they remain economically interlinked and share the same currency. Therefore, one may wonder whether idiosyncratic shocks in one country have had an impacton the common European factor. I define this dynamic as common contagion, and the goal of Chapter 3 is to assess whether European sovereign bond markets have suffered from common contagion during the past years.To do this, I develop a model where the sovereign bond returns load on a common factor which is the sum of a contemporaneous common shock and of effects of previous day idiosyncratic shocks. The model is estimated using static factor models and vector autoregression. It is applied ondaily returns of ten-year sovereign bonds of 11 EMU countries, by considering rolling windows of 1-year length and a 3-quarter overlap. The data suggest that there was common contagion during 2010, when Greece was under heavy market pressure. Contagion mainly comes from safe countries, such as France, Italy, Finland and the Netherlands. I also consider a two-factor model, where factors are identified as the safe and the troubled European economy factor. I find that the contagion identified in the one-factor model corresponds to contagion from the safe economy factor tothe troubled: yesterday's shocks of the former have an impact on today's value of the latter. Hence, although government bonds of safe and troubled economies are very interlinked, one cannot conclude that the troubled economies have been contagious on the safe ones.