Measuring downside risk of stock returns with time-dependent volatility (Downside-Risikomessung für Aktien mit zeitabhängigen Volatilitäten)

Transcription

1 Topic 1: Measuring downside risk of stock returns with time-dependent volatility (Downside-Risikomessung für Aktien mit zeitabhängigen Volatilitäten) One of the principal objectives of financial risk management is to determine the amount of capital needed to protect a financial institution against future losses in order to satisfy regulatory requirements and ensure its solvency. The two risk measures typically used in industry are Value-at-Risk and Expected Shortfall. In order to estimate those risk measures, one can rely on the unconditional loss distribution assuming that the return data is generated by a stationary process. An alternative approach is to treat the data as a realization of a time series process where the conditional distribution of the returns is assumed to follow a model that can describe empirical stylized properties of financial data, such as volatility clustering. The aim of the thesis is to compare the RiskMetrics technique of forecasting volatility based on the exponentially weighted moving-average (EWMA) model with models from the GARCH family. The focus is to evaluate the accuracy of risk estimates for a set of equity indices and to provide a recommendation of a specific volatility form and the innovation distribution. The candidate should be willing to acquire basic knowledge of MATLAB (licenses will be provided). Albrecht, P., M. Huggenberger (2015): Finanzrisikomanagement, Stuttgart: Schäffer- Poeschel, Abschnitt 3. Master Thesis Topics

2 Topic 2: Risk measurement using skewed distributions (Risikomessung mit schiefen Verteilungen) The measurement of the tail risk of a financial position using Value-at-Risk or Expected Shortfall requires the specification of a loss distribution function, which is equal to the probability that the loss does not exceed a certain value. In case of the normal distribution, this probability is a function of the mean and the standard deviation of the loss variable and ignores the presence of asymmetries. This implies that risk estimates based on the assumption of normally distributed loss variables can be inaccurate, for example when the data exhibit nonzero skewness. The aim of the thesis is to present different models that are able to describe asymmetric probability densities. After fitting the models to a set of financial asset returns and testing for their goodness-of-fit, Value-at-Risk and Expected Shortfall estimates are computed using simulated return samples. The accuracy of risk forecasts is backtested providing a comparison to results for elliptical distributions such as the normal or student-tdistribution. Eling, M. (2014): Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models? Insurance: Mathematics and Economics (59), p Master Thesis Topics

3 Topic 3: Financial market contagion (Contagion auf Finanzmärkten) Many financial applications such as portfolio optimization or capital allocation involve the modeling of the simultaneous behavior of multiple sources of risk, such as equity risk, interest rate risk or real estate risk. A multivariate distribution model consists of probability models for the behavior of each risk factor and their correlation structure. During the last two decades, the dependence structure was observed to change across the states of the economy. In this context, contagion refers to an increase in cross-market linkages during periods of crises. The problem in providing evidence on the existence of contagion is that simply comparing correlation coefficients conditioned on realizations of market returns can lead to biased conclusions. The aim of the thesis is to present a multivariate distribution model that can account for asymmetries in state-dependent conditional correlations. The candidate should review methods used for analyzing contagion and to perform an empirical illustration of the relationships between different asset classes based on a bivariate regime-switching model. MATLAB code for fitting the model is available in the references. Chan, K.F.; Treepongkaruna, S.; Brooks, R.; Gray, S. (2011), Asset market linkages: Evidence from financial, commodity and real estate assets, Journal of Banking & Finance, 35(6), p Perlin, M. (2015), MS Regress - The MATLAB Package for Markov Regime Switching Models, Available at SSRN Master Thesis Topics

4 Topic 4: Hedging energy price risk (Hedging von Energiepreisrisiken) Offsetting the price risk of a given spot position in energy commodities can be aspired by minimizing the variation of the return on a portfolio of spot and appropriately chosen futures instruments. The computation of a minimum-variance futures hedge ratio requires the specification of the multivariate distribution of spot and futures returns. Regime- Switching models are well suited to capture non-gaussian features of univariate return series such as skewness and kurtosis and were found to provide a good approximation of the dependence structure between economic, financial and commodity risk factors. The aim of the thesis is to compare the optimal hedge ratios across different models and to run dynamic hedging strategies for a set of energy commodities. The hedging effectiveness should be evaluated based on the reduction of risk over standard hedging techniques. MATLAB code for fitting the model is available in the references. Hung, J.; Wang, Y.; Chang, M.; Shih, K.; Kao, H. (2011), Minimum variance hedging with bivariate regime-switching model for WTI crude oil, Energy, 36(5), p Perlin, M. (2015), MS Regress - The MATLAB Package for Markov Regime Switching Models, Available at SSRN Master Thesis Topics

5 Topic 5: Robust portfolio construction based on portfolio resampling (Robuste Portfoliokonstruktion auf Basis von Portfolio Resampling) Sebastian Gohl Even though the classical Markowitz approach for determining efficient portfolios accounts for the risk of random fluctuations in asset returns, it does not take into consideration estimation risks. In the context of a portfolio optimization, estimation risks occur because the required input parameters take on unknown values, which have to be estimated based on historical return time series. Esp. for short estimation windows it can be shown that the estimated parameters might deviate substantially from the true unknown parameters. This is why also the calculated portfolio weights might deviate from the true optimal weights with impact on portfolio efficiency. This is where Michaud s approach Resampled Efficiency comes into place. Resampled Efficiency iteratively samples returns from the return distribution (referred to as Resampling ). Based on these Resampled Returns, for each sample input parameters are estimated and finally the usual portfolio optimization procedure is carried out. This procedure is repeated several times and the resulting portfolio weights are being averaged over the repetitions leading to so called Resampled Efficient Portfolios. In this master thesis, it is expected that an empirical comparison of Michaud s and Markowitz s approach will be carried out based on different objective functions for a number of relevant parameter estimators appearing in the literature. Using a backtest, it will be examined, whether accounting for estimation risks in portfolio optimization leads to better (risk-adjusted) performance. At the same time, transaction costs of all strategies, arising due to shifts in asset weights, are to be compared. The candidate should be willing to review the portfolio optimization literature dealing with robust portfolio construction based on portfolio resampling and be willing to acquire some basic knowledge of MATLAB (licenses are provided). Fabozzi, F. J.; Kolm, P. N.; Pachamanova, D.; S. M. Focardi (2007): Robust portfolio optimization and management, John Wiley & Sons, chapter 12. Albrecht, P.; R. Maurer (2008): Investment und Risikomanagement, 3. ed., Schäffer- Poeschel, chapter Master Thesis Topics

6 Becker, F; Gürtler, M.; M. Hibbeln (2013): Markowitz versus Michaud: portfolio optimization strategies reconsidered, The European Journal of Finance, p Michaud, R.; R. Michaud (2008): Estimation Error and Portfolio Optimization: A Resampling Solution, Journal of Investment Management, Vol. 6, No. 1, p Topic 6: Comparative analysis of selected correlation forecasting models for portfolio allocation (Vergleichende Analyse ausgewählter Korrelationsprognose-Modelle für die Portfolio Allokation) Sebastian Gohl Properly forecasting the conditional correlation matrix of portfolio constituents is central for asset allocation decision making. This is because the covariance matrix directly enters portfolio optimization problems as an input. It is possible to come up with forecasts based on a decomposition of the conditional covariance matrix into the conditional correlation matrix and the diagonal matrix of conditional standard deviations. Using univariate GARCH models to estimate conditional standard deviations it is possible to compare models for forecasting the (multivariate) conditional correlation matrix like the DECO model and the cdcc model. In this master thesis, it is expected that, based on Clements et al. (2014), models used to generate forecasts of the conditional correlation matrix will be investigated and implemented empirically. The evaluation and comparison of the forecasting methods in this thesis is expected to be based on a minimum variance portfolio allocation problem similar to that in Clements et al. (2014). The candidate should be willing to review the literature on correlation forecasting (esp. in the context of conditional heteroscedasticity) and be willing to acquire some basic knowledge of MATLAB (licenses are provided). Clements, A.; Scott, A.; A. Silvennoinen (2014): On the Benefits of Equicorrelation for Portfolio Allocation, NCER Working Paper Series. Master Thesis Topics

7 Topic 7: Minimum variance portfolio construction with factor risk constraints (Minimum Varianz-Portfolio Konstruktion mit Beschränkung von Faktorrisikobeiträgen) Sebastian Gohl Generating well-diversified portfolios is the aim of many portfolio optimization strategies. The question of how exactly to diversify over diverse asset classes cannot be answered easily. Based on linear factor models it is possible to quantify the exposure of portfolio returns to macroeconomic factors as well as asset specific factors. Under the linear factor model, the contribution of each factor to portfolio volatility can be quantified analytically. To generate portfolios, which are well-diversified over those risk factors Boudt and Peeters (2013) suggest an optimization strategy which in their framework leads to diversified portfolios by accounting for constraints on diverse factor risk contributions. The constrained portfolios are compared to an unconstrained minimum variance portfolio, an equally weighted portfolio as well as a risk parity portfolio with respect to diversification, portfolio risk and performance. In this master thesis, it is expected that a backtest will be carried out for these strategies with a focus on minimum variance portfolio construction under factor risk constraints. The main aim is to demonstrate the diversification benefits of the framework by Boudt and Peeters (2013) when compared to strategies, which do not explicitly account for factor risk concentrations. The candidate should be willing to review the literature on minimum variance portfolio construction in the context of factor risk contributions as well as the literature on risk parity and be willing to acquire some basic knowledge of MATLAB (licenses are provided). Boudt, K.; B. Peeters (2013): Asset allocation with risk factors, in: Quantitative Finance Letters, Vol. 1, No. 1, p Albrecht, P.; R. Maurer (2008): Investment und Risikomanagement, 3. ed., Stuttgart: Schäffer-Poeschel, Anhang 7C. Scherer, B. (2011): A note on the returns from minimum variance investing, Journal of Empirical Finance, 18, p Master Thesis Topics