Portfolio risk analysis : conditional estimates of value-at-risk and international volatility spillovers
In this thesis, we are concerned with the establishment of more accurate and easily implemented methods of modelling portfolio Value-at-Risk (VaR) . We establish this by taking the view that unconditional volatility estimates are inappropriate in VaR analysis. To provide the motivation and the justification for forwarding an alternative model we examine three empirical issues. The first issue is whether the traditional approach based on the use of unconditional measures of volatility and correlation matrix of returns are inappropriate. This thesis forwards the argument that unconditional (historical) variances and covariance are based on rigorous assumptions which are not efficient, given the distributional properties of speculative price changes, conditional on the information set available, and therefore are not appropriate in estimating portfolio VaR. Following this, the emphasis is placed in estimating variances and covariances as time-varying. Thereafter, we consider whether conditional time series models, of the variances and covariances of asset returns, provide a better indication of a portfolio's VaR. We then propose a "simplified" VaR approach that is based on historical returns of the current portfolio. This simplified VaR is faster to compute and offers flexibility in the econometric specification of the portfolio volatility. Once again, conditional volatility models are proposed to estimate portfolio VaR. The results indicate that the VaR estimates from the simplified model are more accurate than those obtained using time-varying correlations. "Stress" and other non-parametric analysis validate further our conclusions. Finally, we use (conditional) systematic risk estimates to search for international volatility spillovers. This affects the VaR estimates through the introduction of time-varying, possibly asynchronous components of portfolio volatility that are ignored in the original static framework of portfolio theory. Consequently, we put forward the notion that VaR estimates depends on the recent history of other markets. However, unlike previous studies, the analysis considers the effect of exchange rate movements on VaR estimates and the nature of the relationship between national stock markets. Our findings highlights the importance of considering the exchange rate in the estimation of VaR and in determining which national market plays the role of market leader. We found that VaR models using exponential smoothing techniques are not inferior to those based on the more advanced multivariate GARCH volatility estimates. Furthermore, in this thesis we proposed a VaR methodology which overcomes many limitations of the above and other VaR models, i.e. dimentionality and stability of the correlation matrix, and unlike them does not requires a specification of the probability distribution of returns used in the calculation of the VaR and worst case scenarios. Our methodology uses past (historical) returns but still maintains the multivariate properties of the data. As stress analysis has shown, the model proposed here provides more efficient and unbiased VaR estimates. Lastly, we provide a summary of the investigations along with the innovations provided in the thesis. Discussed in the conclusion are the implications of the thesis to both practitioners and academics.
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