Empirical Studies on the Conditional CAPM and Equity Premium Prediction

Abstract

This thesis consists of three self-contained essays that analyse two important subjects in Empirical Finance: the Conditional Capital Asset Pricing Model (CCAPM) and out-of-sample equity premium prediction. The first two essays concern the CCAPM model and analyse the choice of variables used to capture the time variation in the risk loadings. The lack of a theory to guide the choice of conditioning variables, and the rather large pool of potential variables that have been identified in the CCAPM literature, creates an empirical dilemma over how to optimally parameterise the model. The first essay considers a dynamic model selection (DMS) approach where the choice of conditioning variables, selected from a large pool of state variables, is allowed to vary through time rather than remaining fixed. We find that estimating the CCAPM using the DMS method can improve the performance in some asset pricing tests, however, it still fails to explain the value and momentum anomalies. Using bootstrap methods to quantify the model uncertainty and instability, we find that the DMS selection of conditioning variables is subject to considerable estimation error. This provides strong motivation for our second essay, where we consider alternative forecasting approaches which try to address this variable-selection uncertainty (VSU). We implement combination of forecasts (CF), and combination of information (CI) approaches to capture the beta dynamics. CF combines forecasts generated from simple models, each incorporating a part of the whole information set, while CI brings the entire or selected information set into one single model to generate an ultimate forecast. Our findings suggest that CF approaches dominate the CI approaches in explaining the cross-section of assets returns. However, we also demonstrate that further improvements in results are possible by combining the CI and CF methods. The topic of the third essay concerns the predictability, or otherwise, of the equity premium. In this essay, we use some of the techniques developed in earlier chapters of the thesis, such as CF and CI methods, in order to select the best conditioning variables for predicting market excess returns. In particular, we focus on the issue of parameter instability (PI) in predictive models caused by abrupt changes in financial market conditions which result in structural breaks in the underlying relationship between the variables in the model. Since standard forecasting models assume that the relationship between these variables remains constant over the entire period, any parameter instability, therefore, can lead to poor out-of-sample performance (e.g., Rapach and Wohar, 2006; Paye and Timmermann, 2006; Rapach et al., 2010). Here, we introduce a novel approach to predicting returns which uses a combining forecasts (CF) approach with a variance-covariance (VC) method that addresses PI and VSU. The essay has two main findings: i) by taking into account the correlation structure among forecast errors through our VC approach, the forecasting accuracy of univariate prediction of the equity premium significantly improves, and ii) by addressing PI and VSU simultaneously the VC approach can substantially improve the forecasting accuracy compared to existing approaches in equity premium such as CF (Rapach et al., 2010), CI approaches such as dimension reduction methods (Neely et al., 2014 and Kelly and Pruitt, 2013) and shrinkage methods such as Least Absolute Shrinkage and Selection Operator (LASSO), (Tibshirani, 1996), adaptive LASSO (Zou, 2006), and Elastic Net (Zou and Hastie, 2005).

Date of Award	24 May 2021
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Ian Garrett (Supervisor) & Alex Taylor (Supervisor)