This thesis is concerned with forecasting the variance covariance matrix (VCM) for a range of financial assets and investigating whether combining the elements of such forecasts result in more accurate predictions of portfolio volatility than those obtained from univariate models of aggregate volatility. There are three substantive chapters in the thesis; two introduce new methods for forecasting the VCM, while the third examines the accuracy of the techniques available for forecasting overall portfolio volatility. The first chapter introduces a model labelled the CD-MIDAS model, designed to improve the forecasting of the VCM at frequencies lower than a single day, for example we focus on predicting the VCM for a 22 day (monthly) horizon. The CD-MIDAS model uses the approach of Chiriac and Voev (2010) in forecasting the elements of the Cholesky decomposition of the VCM, rather than attempting to directly forecast elements of the matrix which are subject to restrictions ensuring that the forecast VCM is symmetric and positive definite. The elements of the Cholesky decomposition are modelled using the mixed data sampling (MIDAS) methodology introduced in Ghysels, Santa-Clara and Valkanov (2004,2006) which allows for the use of data observed at a high frequency (i.e. daily) to forecast the same variable observed at a lower frequency (i.e. monthly). The forecasting performance of this model is compared to that of other popular multivariate models and evidence is found, in both simulations and applied experiments, that the CD-MIDAS model is able to produce forecasts of the monthly VCM that are more accurate than its competitors. The second substantive chapter builds on findings in the univariate volatility forecasting literature that the level of return volatility for financial assets can be related to observations of certain economic variables. The kernel technique introduced in this chapter uses a multiplicative kernel to compare the characteristics of past periods with those at the point when the forecast of the VCM is being made. A weighting is then assigned to each point of time depending on how the historical economic and VCM characteristics compare to those at the point of forecast, the more similar the two points are, the higher the weight will be. All weights are positive and are applied to historical realizations of the VCM, thus the resulting forecast is guaranteed to be symmetric and positive definite, while the calculation method avoids the curse of dimensionality. In applied investigations it is shown that versions of the kernel technique produce the most accurate forecasts of those considered at horizons of 1, 5 and 22 days. In addition it is shown that the addition of the economic data to the kernel produces a statistically significant improvement in the accuracy of the forecasts generated. The final chapter considers which models provide the best forecasts when we are interested in forecasting overall portfolio volatility. This question can be seen as an extension of the aggregation vs. disaggregation literature in which we are essentially testing whether the aggregation error, cause by modelling an aggregate of several time series, is more or less important than the misspecification error caused by having a disaggregated model. While the latter can potentially capture idiosyncrasies of individual component series, it also may contain a larger number of misspecified representations and may suffer from increased parameter uncertainty due to the large number of parameters requiring estimation. Hence this chapter examines whether it is best to use multivariate models, using individual stock data, or univariate models, using portfolio level data, when the aim is to generate forecasts of total portfolio return volatility. An applied experiment shows that the best performing models are univariate models based on realized measures of portfolio variance. It is also apparent that any model, univariate or multivariate that does not make use of realized data, computed from high frequency returns data is significantly handicapped in terms of forecasting performance when compared to those that do. Hence the results imply that the misspecification errors in currently available multivariate models are of more concern to those wishing to forecast total portfolio return volatility than the misspecification inherent in modelling the aggregate of a number of variables.