Volatility Forecasting and Asset Allocation In Portfolio Management

Volatility is a fundamental concept in finance. Referring to the conditional standard deviation of asset returns, volatility represents an important measure of risk and, as such, it has applications in almost all areas of finance. Therefore, it is difficult to overstate the importance of accurate measurement and forecasting of volatility for academics, practitioners and policy makers. The main aim of this thesis is to compare alternative ways of forecasting volatility and to evaluate their performance. This thesis is tackling this research topic in 4 main research questions.

First, Chapter 3 examines how different models can produce efficient forecasts of future volatility. Various approaches are used from simple non-parametric to parametric GARCH models and Realized Volatility (RV) models. Then, the produced forecasts are combined and the extent to which combinations can improve the forecasting accuracy is evaluated. To explore the robustness of the results, single, pairwise and multiple comparisons are considered. The purpose of this study is not just to identify the optimal specification but most importantly it tries to provide an insight interpretation of the models' performance. We use daily data for stock indices returns and 5-min realized variance for the period 2000-2017. Our main finding are that TGARCH and log HAR specifications and the simple mean combination outperform the rest. Our results are robust to various loss functions, stock index, and sample size. Then, we continue working on univariate volatility forecasting but we move one step further. Chapter 4 aims to evaluate the performance of several GARCH models and forecast combinations for the direction of future volatility. Several alternative forecast combinations are considered based on i) a hierarchical encompassing-MSE procedure; ii) a weighted average scheme based on directional change and iii) weighted schemes based on directional accuracy, along with measures of directional accuracy (DA) and direction forecast value (DV). The empirical analysis is conducted using daily data for the S&P 500 index over the period 2000-2017 and the realized variance is used as a proxy for the true unobservable volatility. Our findings indicate that forecast combinations, in particular those based on directional accuracy and the hierarchical MSE procedure, perform as well as the best single model, thus alleviating uncertainty over the choice of a single predictive model. Further, a multivariate approach is considered as assets' volatilities have been found to move together.

Multivariate volatility models can arise as a direct generalization of univariate GARCH-type models. Alternative approaches include linear and nonlinear combinations of univariate GARCH models, such as generalized orthogonal models, latent factor models, constant and dynamic conditional correlation models (CCC, DCC), the general dynamic covariance model and copula-GARCH models. This study is not another "horse-race" but it is focused on how multivariate models can be used in a portfolio framework, using alternative assets such as Hedge Funds (HF). Since classical portfolio allocation has received a lot of criticism, this study is focusing on the risk-based approach, called Risk Parity (RP).

This study aims at constructing a RP portfolio consisting of hedge funds which is competing against the Hedge Funds Research (HFR) RP Indices in an attempt to outperform them. Our empirical results suggest that for both volatility targets (10% and 12%) at least one of the our constructed portfolios (alpha and Sharpe-Ratio based) outperform the HFR Indices in the out-of-sample period. Finally, given the lack of agreement in the literature as to which approach is superior; volatility forecasts from historical univariate models or forward looking volatility implied from option prices, a comparison of those two is performed. Chapter 6 examines under what circumstances option-Implied Volatility models provide more accurate density forecasts compared to historical volatility. What is more, since densities implied by option prices produce unrealistic risk-neutral densities (RND) calibrated real-world densities (RWD) are also calculated. Future densities are evaluated using Goodness of-Fit tests. We use options written on European indices for the years 2006-2016. We found that historical densities outperform RND and RWD forecasts. Overall, the intention is to significantly contribute to the literature by providing methodological solutions and new empirical evidence to important open questions on volatility forecasting. Successfully tackling these issues will result in producing more effective ways of measuring and, importantly, anticipating risk.