Essays in Financial Econometrics

The present doctoral thesis covers different aspects in the financial econometrics area. In particular, the research focuses on the heterogeneous agents in the market (rational and behavioural), the performance measures related to this type of agents and, more generally, the asset evaluation within a portfolio selection framework. Further, the time varying dependence among the financial markets is also considered. In general, the financial markets represent one of the main indicators for the dynamics of the business cycle as noted by Siegel (1991). Viceversa, Hamilton and Lin (1998), for example, found that economic recessions are the main factor that leads the fluctuations in the volatility of stock returns. Therefore, there is evidence for an interdependence relationship among the economic cycle and the financial markets. In this context, it is interesting to analyze the markets by looking at investors as decision makers in the asset selection process. Moreover, the time varying dependence among the financial markets could imply a change in the portfolio in term of diversification, with effects on investors' portfolios. The first chapter presents a rational learning model which considers the information coming to a HARA investor from a behavioural counterpart. The main goal is to investigate this component's effect, in terms of utility function, on asset evaluation during the allocation process. This heterogeneous framework has two types of agents with two different utility functions, a rational agent with a hyperbolic absolute risk aversion (HARA) utility function and the second with a general behavioural utility function. To compare the assets, each agent uses the concept of performance measure related to utility functions. The higher the measure, the higher the expected utility of a given asset. The HARA agent is a rational learner agent. The rational learning is defined as the process undertaken through Bayesian updating of the prior beliefs. The prior beliefs derive by the utility function of the rational agent and the updating process of beliefs takes place through the presence of the behavioural counterpart. The choice is conditioned by adopting an Herding behaviour, which is the tendency for an investor to abandon her own information to imitate the behaviour of other investors. Therefore, the rational investor is conditioning her choice towards behavioural investors to give rise to the positive feedback effect. This effect has been documented by Scharfstein and Stein (1990) on fund manager, Grinblatt et al. (1995) in mutual fund behaviour and by Devenow and Welch (1996) on forecasts made by financial analysts. The rational learner agent adopts a positive feedback strategy through herding behaviour to improve her investment. In this regard, the two components are blended in a Bayesian manner. The model is built analogously to Black-Litterman model to obtain the aggregated measure adjusted by a weighting factor. The goal in the application of the model is to check if the positive feedback effect exists. The work shows that conditioning the choice of the HARA investor towards a behavioural direction improves the selection amongst the assets. The empirical analysis is performed on all the assets present in the NASDAQ stock exchange from December 1989 to February 2012. This chapter is a solo paper. The second chapter declines with a different purpose the model developed in the first chapter. In this context, two categories of agents are considered, one rational with a risk adverse utility function and one with an S-shaped loss averse value function similar to Kahneman and Tversky (1979). Agents take investment decisions in the same way by ranking the alternative assets according to their performance measures. We assume that a type of agent is endowed with an S-shaped loss averse value function. This produces the intuitive and empirically validated prediction that the attitude of undertaking risky investments changes according to the fluctuations of the financial market. According to this assumption, in periods of (financial and economic) recession, financial agents are attracted by more risky investments that might generate, with some positive probability, returns that compensate previous (observed) losses. On the other hand, in periods of expansion, financial agents are more reluctant to undertake a risky investment that might reduce, with some positive probability, previous (observed) capital gains. In this chapter the model estimates the relative weight of the behavioural component in the financial market. The empirical analysis is based on monthly data on the components of the S&P 500 index from January 1962 to April 2012. The relative weight of the behavioural category over the rational's one has an intuitive explanation: the higher the value of the weighting factor, the higher is the weight of the behavioural component in the aggregated measure. The estimated value of the weighting factor is obtained by maximizing the cumulated return of the one hundred most performing assets of the mixture ranking. Intuitively, the weighting factor captures the extent to which the financial market should have moved from the ordering of the rational category to the ranking of the behavioural agents to maximize the return of the "best" one hundred assets. By choosing a selection of one hundred assets, we capture the systemic dimension of the financial market. The results confirm the existence of a significant behavioural component, which is more likely to emerge during recessions. A strong correlation emerges between the estimated relative weight series and the VIX index, which implies that the estimates substantially explain financial expectations. This is a joint paper with Professors Massimiliano Caporin and Luca Corazzini (University of Padova). The third chapter introduces a novel criterion for performance measure combination designed to be used as an equity screening algorithm. The combination criterion follows the general idea of linearly combining existing performance measures with positive weights. These weights are determined by means of an optimisation problem. The underlying criterion function explicitly takes into account the risk-return trade-off potentially associated with the equity screens, evaluated on a historical and rolling basis. By construction, and due to the rolling window evaluation approach, the methodology provides performance combination weights that can vary over time, thus allowing for changes in preferences across performance measures. The proposed approach is implicitly robust to the dynamic features of the returns densities, as these will affect the evaluation of performance measures that are the inputs of our screening algorithm. The final product of the linear combination of performance measure is a composite performance index, which can then be used to create asset screens. We present an empirical application that illustrates the use of the screening algorithm in a simplified portfolio allocation. This is a joint paper with Professors Monica Billio (Ca' Foscari University of Venice) and Massimiliano Caporin. The fourth chapter examines the financial contagion using a regime switching approach with vine copulas. Vine Copulas allows us to model easily a multivariate framework with the use of the pair-copula decomposition introduced by Aas et al. 2009). The marginals are modelled by the GARCH process with long memory volatility{in mean as introduced by Christensen et al. (2010). In particular, this model well captures the long{range dependence characterizing financial time series, allowing for asymmetric effects in the GARCH equation and for the news impact in the mean. Moreover, we decided to use Copula functions to model the dependence structure across variables. The final purpose is to use a long memory GARCH process to filter the marginal series and then to use a regime switching approach among different copula families to model the dependence structure. Diebold and Inoue (2001) highlight that these two approaches can lead to misleading results. In fact, long memory can easily be confused with structural changes and viceversa. In our case, we are looking at long memory and regime switching in a complementary way, since we use them on different dimensions. Vine Copula families are considered to build the multivariate dependence structure with Pair-Copula construction methodology (Aas et al., 2009). In the empirical analysis, we focus on the main European countries (Germany, France, Italy, Spain and Netherlands) to detect contagion (and financial integration). In the thesis, a preliminary version of the paper is included in which we filtered the series using the exponential GARCH process. This is a joint paper with Professor Bent Jesper Christensen (CREATES - Aarhus University).