Journal of Forecasting, J. Forecast. 34, 507–522 (2015) Published online 9 June 2015 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/for.2357 On the Benefits of Equicorrelation for Portfolio Allocation ADAM CLEMENTS, AYESHA SCOTT  AND ANNASTIINA SILVENNOINEN School of Economics and Finance, Queensland University of Technology, Brisbane, Australia ABSTRACT The importance of modelling correlation has long been recognised in the field of portfolio management, with large- dimensional multivariate problems increasingly becoming the focus of research. This paper provides a straightforward and commonsense approach toward investigating a number of models used to generate forecasts of the correlation matrix for large-dimensional problems. We find evidence in favour of assuming equicorrelation across various portfolio sizes, particularly during times of crisis. During periods of market calm, however, the suitability of the constant conditional correlation model cannot be discounted, especially for large portfolios. A portfolio allocation problem is used to compare forecasting methods. The global minimum variance portfolio and Model Confidence Set are used to compare methods, while portfolio weight stability and relative economic value are also considered. Copyright © 2015 John Wiley & Sons, Ltd. KEY WORDS volatility; multivariate GARCH; portfolio allocation INTRODUCTION AND MOTIVATION The importance of modelling the volatility of asset returns for the purpose of portfolio allocation has been the subject of extensive research. Despite this significant body of work, less is understood about the most appropriate method of handling large portfolios and subsequently generating useful volatility forecasts. Increasingly, portfolios of hundreds or thousands of assets are becoming the focus of research, and many methods have been proposed to aid in dealing with the issue of dimensionality. Surveys of the multivariate generalised autoregressive conditional heteroskedasticity (MGARCH) literature include Bauwens et al. (2006) and Silvennoinen and Teräsvirta (2009). This paper considers the performance of a number of models to generate forecasts of the correlation matrix across a number of portfolio sizes, and evaluates the economic value of using these models in the context of asset allocation. The main methods used to generate forecasts of the correlation matrix of interest here are the Dynamic Equicor- relation (DECO) model of Engle and Kelly (2012), the consistent Dynamic Conditional Correlation (cDCC) model of Aielli (2013) and Constant Conditional Correlation (CCC) model of Bollerslev (1990), as well as semi-parametric models. DECO assumes pairwise correlations to be equal at a point in time, while changing over time. This method is based upon the cDCC model; however, it is tractable for large dimensions through a simplified likelihood spec- ification. Another notable advantage of equicorrelation is reduced estimation error due to its use of the history of all assets in the portfolio for each element of the correlation matrix, in stark contrast to cDCC, where the history of only a given pair of assets is used to forecast the element of the correlation matrix pertaining to that particular pair. This advantage is highlighted in the analysis presented later in the paper. As alluded to above, the cDCC likelihood equation can be burdensome to estimate in large dimensions; however, the composite likelihood approach of Engle et al. (2008) is used here to make the cDCC model suitable for large portfolios. In this paper an empirical portfolio allocation exercise is used to compare various correlation forecasting tech- niques. Minimum variance portfolios are formed and the out-of-sample performance of the methods compared, using the Model Confidence Set (MCS) of Hansen et al. (2003). Out-of-sample periods are divided into subsamples based on the relative level of volatility, and performance again compared as before. The benefits of the choice of the MCS as an evaluation tool are twofold: it does not require a benchmark model to be specified; and it is a statistical test of equivalence of a given set of forecasting methods with respect to a particular loss function. In this case, the loss func- tion will be the variance of returns from the global minimum variance portfolios based on each of the forecasts. In terms of the out-of-sample period, investigation of the forecasting performance of models under differing volatility conditions is becoming more popular in the literature (see Luciani and Veredas, 2015, for a recent example) and is of great interest here given the market turbulence of recent years. In addition, the economic value of the methods is discussed, including the stability of the resulting portfolio and the incremental value of switching from one particu- lar method to another. The various models are again compared across a number of portfolio sizes and for both a full out-of-sample application as well as periods of relatively high and low levels of market volatility.  Correspondence to: Ayesha Scott,School of Economics and Finance, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia. E-mail: ayesha.scott@qut.edu.au Copyright © 2015 John Wiley & Sons, Ltd