This research investigates various issues relating to the level and volatility of returns on ordinary shares. In particular, we have looked at the relation over time between volatility and risk premia, both at a univariate and multivariate levels. We also look at the links between stock markets over the world, and whether they are integrated. We evaluate the role of measurable economic variables in explaining asset price (co-)movements over time. Our model combines an APT factor pricing approach with a GARCH-type parameterisation of the volatility of the factors. These can be "observable" (i.e. related to economic variables), "unobservable" and country-specific. Estimates of these factors and their time-varying variances are obtained using a Kalman Filter-based Full Information Maximum Likelihood method. Using monthly data on sixteen markets it is found that idiosyncratic risk is significantly priced, and that the "price of risk" is not common across countries, which rejects the null of global capital market integration. Another empirical finding is that most of the correlation between markets is accounted for by the "unobservables". The econometric background to the conditionally heteroskedastic factor model employed is also analysed. We find that the matrix of factor loadings is unique under orthogonal transformations, and as a result, that it is possible to evaluate the separate contribution of the different factors to the risk premia if time-variation in the volatility of the factors is recognised. We also obtain a full characterisation of this model under the assumption that the conditional distribution is multivariate t, (the normal being a special case), and GARCH formulations for the conditional variances. A fundamental question in Finance is whether the stock market satisfies the Efficient Market Hypothesis. In this regard, we explore whether lagged variables that help predict stock returns are merely proxying for mis-measured risk. Three different ways of measuring risk are employed (i.e. semi-parametric, GARCH and lagged squared returns). In an application to Japanese data, four key predictor economic variables are shown to have non-trivial additional forecasting power irrespective of how risk is measured. Interestingly, unlike the US, the level of the lagged dividend yield is not positively correlated with returns in either Japan or South Korea. Moreover, there is no consistent relationship between expected volatility and excess returns. Another interesting topic is the hypothesis that the degree of autocorrelation shown by high frequency stock returns may change with volatility. This may result from non-trading effects, feedback trading strategies or variable risk aversion. Results using a century of daily data suggest that when volatility is low there tends to be positive autocorrelation in returns, but this serial correlation can become negative during very volatile episodes. Our results also suggest that returns are more likely to exhibit negative serial correlation after price declines. Finally, a new Quadratic ARCH model for the conditional variance of a time series is introduced, and interpreted as the quadratic projection of the square innovations on information. Since it nests the original ARCH model and several of its extensions, its statistical properties are very similar, while avoiding some of their criticisms. In an application to a century of daily US stock returns, QARCH models provide a better representation of the data by capturing the leverage effect (i.e. volatility is higher following price declines than after rises). QARCH models are also able to capture this asymmetry in a multivariate context: in a factor model for monthly excess returns on 26 industrial UK sectors, the common factor (which is highly correlated with the FTA500) also shows a significant leverage effect.
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