Asymmetric Correlations and Tail Dependence in Financial Asset Returns (Asymmetrische Korrelationen und Tail-Dependence in Finanzmarktrenditen)

Transcription

1 Topic 1: Asymmetric Correlations and Tail Dependence in Financial Asset Returns (Asymmetrische Korrelationen und Tail-Dependence in Finanzmarktrenditen) Besides fat tails and time-dependent volatility, the most commonly observed empirical properties of financial asset returns are related to nonlinear dependence structures, which is an important research aspect when studying multivariate applications. In a probabilistic context there exist two main concepts for modeling those kind of asymmetries. First, conditional correlations are used to separately analyze the dependence structures of assets during upside and downside markets. Second, focusing on the very tail of multivariate return distributions, coefficients of lower and upper tail dependence characterize the behavior of assets in extreme market scenarios. The thesis should cover the methodologies used for the measurement of nonlinear dependencies and review the theory behind models that are able to reproduce those features. In the empirical part, the presence of asymmetric correlations and tail dependence should be illustrated using market data. The candidate should be willing to acquire basic knowledge of MATLAB (licenses will be provided). Ang, A., Chen, J. (2002): Asymmetric correlations of equity portfolios, Journal of Financial Economics (63), p Poon, S., Rockinger M., Tawn J. (2004): Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications, Review of Financial Studies (17), p Master Thesis Topics

2 Topic 2: The Impact of Tail Risk on Expected Stock Returns (Asset Pricing unter Berücksichtigung von Quantilrisiko) The potential loss from extreme market downturns is extensively analyzed in a risk management context from the perspective of individual investors. Focusing on tail risk as a factor in asset-pricing models, other studies aim to describe the influence of rare events within an equilibrium set-up. One alternative approach is to measure tail risk of individual securities using abnormal returns from a factor model and to relate the outcome to the cross-section of average stock returns. Findings suggest that tail risk can require additional compensation for holding risky securities. Within this thesis students should familiarize with measures of tail risk such as value-atrisk, downside beta or co-skewness and employ computational methods to estimate these quantities from the data. One useful approach is to use extreme value theory (EVT)-based risk estimates. Regression analysis is then used to study cross-sectional risk-return relationships. The candidate should be willing to acquire basic knowledge of MATLAB (licenses will be provided). Huang, W., Liu, Q., Rhee S., Wu, F. (2012): Extreme downside risk and expected stock returns, Journal of Banking & Finance, (36), p Master Thesis Topics

3 Topic 3: Risk Measurement Using Copulas (Risikomessung unter Verwendung von Copulas) Nonlinear dependencies between market risk factors refer to the probability of joint (extreme) market movements, hence are important for the estimation of downside risk measures. In finance and insurance applications, copula functions are a very popular tool for modelling dependencies, because they allow marginal distributions of random variables being modelled separately from the multivariate dependence structure. In this thesis, some basic copulas will be used to simulate random sample returns for a benchmark portfolio of assets. Following this, the risk of the loss on the portfolio from adverse co-movements is expressed in terms of the Conditional-Value-at-Risk (CVaR) and compared across different copula functions. The study can be extended to the illustration of diversification benefits induced by different copulas, conducting simple optimizations based on the sampling distributions. The candidate should be willing to review some probability theory and acquire basic knowledge of MATLAB (licenses are provided). Kole, E., Koedijk K., Verbeek, M. (2007): Selecting copulas for risk management, Journal of Banking & Finance, 31 (8), p Kakouris, I., Rustem, B. (2014): Robust portfolio optimization with copulas, European Journal of Operational Research, 235 (1), p Master Thesis Topics

4 Topic 4: Mean-Conditional Value-at-Risk Optimal Asset Allocation (Mittelwert-Conditional Value-at-Risk optimale Asset Allokation) The Conditional-Value-at-Risk (CVaR) is defined as the expected loss of a portfolio value given that the loss exceeds a certain quantile level. In contrast to the Value-at-Risk (VaR), which is non-convex and non-smooth for discrete distributions, this risk measure proofs efficient in optimization based on empirical distributions (Rockafellar and Uryasev, 2000). The aim of the thesis is to implement Mean-CVaR portfolio optimization strategies using a set of broad asset classes, while demonstrating its dominance over benchmark strategies, like mean-variance optimization in terms of downside risk. The study can be extended by implementing market frictions like trading costs or restrictions regarding the investment policy. The candidate should be willing to review linear programming techniques and acquire basic knowledge of MATLAB (licenses are provided). Rockafellar, R. and Uryasev, S. (2000): Optimization of conditional value-at-risk. Journal of Risk, 2, p Mansini, R., Ogryczak, M., und Speranza, G. (2014): Twenty years of linear programming based portfolio optimization, European Journal of Operational Research, 234 (2), p Master Thesis Topics

5 Topic 5: Cross-Hedging using Commodity Futures (Cross-Hedging mit Rohstofffutures) Short-term hedging strategies aim to reduce the risk of a given position in the spot market by selling futures on the corresponding underlying. In case that no instruments are available for the given underlying, cross-hedges can be established using futures that are sufficiently correlated with the spot portfolio. The return on the hedge position is subject to a non-negligible amount of basis risk, which gives rise to the search for the appropriate hedge ratio, as opposed to, e.g., the case of stock hedging, where already naïve hedging strategies can be well suited for reducing risk. Within the master thesis, empirical examples of industry specific hedging problems should be analyzed. After retrieving and preparing data, econometric models for the implementation of minimum-variance hedge ratios, which include multivariate GARCH processes, should be calibrated and utilized to compute dynamic strategies based on the conditional return distribution. The candidate should be willing to review futures-hedging literature and acquire basic knowledge of MATLAB (licenses are provided). Alexander, C. (2008), Market Risk Analysis III, Pricing, Hedging and Trading Financial Instruments, Chapter III.2, John Wiley & Sons Master Thesis Topics

6 Topic 6*: Mean-Variance Portfolio Optimization under Solvency II (Portfoliooptimierung mit dem Erwartungswert-Varianz-Ansatz unter Solvency II) Portfolio optimization based on modern portfolio theory aims at maximizing the portfolio expected return for a given amount of portfolio risk as measured by the portfolio return standard deviation by choosing the proportions to be allocated to individual assets. As for the insurance sector, the new risk-based capital standards of Solvency II require the provision of solvency capital, which for different asset-side market risk types can be computed using standard formulae provided by the regulator. The aim of the thesis is to analyze the effect of the capital charges on strategic asset allocation decisions. First, the optimization problem has to be implemented incorporating budget restrictions, short-sale and other industry specific investment constraints. Next, the applying capital charges should be computed and compared to an exogenous value of available own funds, identifying unfeasible allocations along the efficient frontier. The candidate should be willing to review insurance specific literature and acquire basic knowledge of MATLAB (licenses will be provided). Braun, A., Schmeiser, H., Schreiber, F. (2013): Portfolio Optimization Under Solvency II: Implicit Constraints Imposed by the Market Risk Standard Formula, Working Paper Master Thesis Topics

7 Topic 7*: Asset-Liability Management of Life Insurance Policies (Asset-Liability Management von Lebensversicherungen) Asset-Liability Management (ALM) refers to the alignment of actuarial obligations to policy holders and investment activities, in a way that ensures maximum profit and maintains a certain solvency-level. In participating (with-profit) life insurance contracts, the policy holder gets a fixed interest guarantee and, in addition, participates in the investment performance of the insurance company. The thesis comprises a simulation of balance sheet items of a life insurer using typical product parameters and a market model for the performance of stocks and bonds while taking account of German legislation. Decisions regarding asset allocation, bonus distribution and shareholder participation are analyzed focusing on their influence on the risk exposure of the insurance company. The study can be extended by incorporating surrender options and other contract specifications. The candidate should be willing to review insurance specific literature and acquire basic knowledge of MATLAB (licenses are provided). Gerstner, T., Griebel, M., Holtz, M., Goschnick, R., Haep, M. (2008): A general asset liability management model for the efficient simulation of portfolios of life insurance policies, Insurance: Mathematics and Economics, 42 (2), p Master Thesis Topics