Essays on portfolio optimization and estimation risk

This thesis is a collection of essays that study the issue of estimation risk in portfolio optimization. Each essay investigates the usage of a probability estimator or optimization approach which addresses estimation risks in portfolio selection under lower-partial moments and stochastic dominance. The three approaches use option-implied data, robust optimization, and sparse multivariate copula models, respectively. The considered empirical applications show robust evidence of enhanced portfolio performance in an out-of-sample setting. The first essay uses an eclectic financial modelling approach to equity sector rotation using sector Exchange Traded Funds. The approach combines stochastic dominance ordering with the use of option-implied probabilities and copulas. We find that the performance of the monthly reweighted long-only portfolio can be improved using an option-implied probability distribution. We further find that option-implied probabilities estimated using the Heston pricing model provide the best portfolio performance. The portfolio outperforms the S&P 500 index, an equally-weighted portfolio and strategies based on historical time series, even after accounting for transaction costs. The superior performance is more pronounced during bad economic times proxied by bear market and high volatility states. No significant performance gains are evident for portfolios formed when we account for non-linear dependence (R-Vine copula) relative to traditional linear dependence (Gaussian copula). The second essay provides an empirical analysis of the out-of-sample performance of robust portfolios, where uncertainty exists in the underlying probability distribution. This study proposes an alternative specification of the uncertainty set allowing for joint uncertainty in both probability and threshold levels for three portfolio selection approaches (expected shortfall, semi-variance and the Omega ratio). There are two cases considered where the uncertainty sets are dependent or independent. The empirical results show that joint uncertainty with dependent sets yields superior results to other portfolios. Furthermore, portfolios constructed using joint uncertainty also have the additional benefit of significant protection against market crashes for portfolios. Robust portfolios have a different correlation with common risk factors compared to non-robust portfolios. In particular, joint uncertainty with dependent sets yields portfolios with significant exposure to the momentum factor, that is, betting on stocks that were past winners. The performance of the robust Omega ratio portfolios can be attributed to the combination of value and momentum factors. The third essay studies the use of high-dimensional Regular-vine copula models in estimating asset interdependence for portfolios with varying sizes. For a large portfolio, the copula parameters outnumber the assets and observations, giving rise to estimation errors. This estimation risk leads to suboptimal portfolio selection and consequently poor out-of-sample performance. In this context, sparse vine models, in which independence pair-copulas prevail, provide significantly improved results for large portfolios across various performance measures. The improvement of portfolio performance is more pronounced in low market volatility periods. The truncated vine copulas, a sub-class of sparse copulas, yield more stable weights for large portfolios and significantly reduce transaction costs.