Two Essays on Stochastic Dominance and One Essay on Correlation Stress Tests

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GUO, Zhen, 2013. Two Essays on Stochastic Dominance and One Essay on Correlation Stress Tests [Dissertation]. Konstanz: University of Konstanz

@phdthesis{Guo2013Essay-24222, title={Two Essays on Stochastic Dominance and One Essay on Correlation Stress Tests}, year={2013}, author={Guo, Zhen}, address={Konstanz}, school={Universität Konstanz} }

Two Essays on Stochastic Dominance and One Essay on Correlation Stress Tests deposit-license eng 2013 Guo, Zhen This dissertation consists of three research papers that investigate different interesting topics of portfolio risk. Portfolio risk management is of growing interest to investors, regulators, and practitioners, especially during market downturns and financial crises. On one hand, investors might have different and time-varying risk preference and practitioners have to select a general optimal portfolio to meet their agents’ risk preference. However, the popular Mean-Variance technique for portfolio selection suffers the limitation of not being able to generate a general optimal portfolio for all risk-averse investors. Therefore, new techniques for improved portfolio selection are desirable to supplement the traditional Mean-Variance approach. On the other hand, once the optimal portfolio is selected, investors and regulators are more prone to know their portfolio risk in a forward-looking manner and practitioners are requested to provide various risk reports regarding the financial stand of portfolios. Stress tests are regularly conducted to report the portfolio risk in a forward-looking manner. Among them, the correlation stress test is an important category. However, the current correlation stress tests are limited to efficiently stress a high-dimensional correlation matrix and easily maintain all the mathematical properties in the meantime. Therefore, a simple and efficient correlation stress test should be developed to allow perturbations in a high-dimensional correlation matrix and easily satisfy all the mathematical properties of a valid correlation matrix.<br /><br />In this dissertation, the first two papers investigate the second order stochastic dominance approach in portfolio selection and the last one develops a new correlation stress test to evaluate portfolio risk. The first chapter of this dissertation provides a selective literature review on the stochastic dominance rules, tests, and their applications in portfolio selection. This survey compares the performance of popular second and third order stochastic dominance tests under various sampling schemes and data contamination by simulation. For each simulated sampling scheme, I first find the tests that keep the size well and show high power. Among the tests with good performance, I further recommend the one with the highest computational speed to apply in practice. To my best knowledge, this is the first survey to compare the performance of third order stochastic dominance tests. This is also the first survey one to review and summarize the popular second order stochastic linear programs for portfolio selection.<br /><br />The second chapter of this dissertation focuses on portfolio choice based on the second order stochastic dominance rules. The traditional Mean-Variance approach assumes either quadratic utilities or normal return distributions. It has limited applications to skewed distributions and heterogeneous investors’ risk preference. Its optimal portfolio generates extreme portfolio weights and does not have good out-of-sample performance. In contrast, the second order stochastic dominance approach provides an attractive alternative to the Mean-Variance technique. It suits all risk averse investors and accommodates skewed distributions and heterogeneous risk preference. The optimal portfolio selected by the second order stochastic dominance rules generates stable portfolio weights across different periods and its out-of-sample performance is generally better than the Mean-Variance optimal portfolio (Hodder, Jackwerth, and Kolokolova, 2009). However, most of the stochastic dominance linear programs in the literature are designed to test whether a given portfolio is efficient when evaluated by the second order stochastic dominance rules. There are very few linear programs focusing on portfolio construction based on the stochastic dominance rules. In this chapter, I propose a two-step algorithm to approximate the second order stochastic dominance optimal portfolio. First of all, I use the minimum shortfall linear program by Rockafellar and Uryasev (2000) to generate the minimum shortfall efficient set, which is a subset of the second order stochastic dominance efficient set. Next, I select the optimal portfolio within the minimum shortfall efficient set as the portfolio with the highest statistical support by Davidson and Duclos (2006) and Davidson’s (2007) second order stochastic dominance test over the benchmark. The optimal portfolio is then automatically efficient when evaluated by the second order stochastic dominance rules and the computational speed is reasonable. I show that the performance of the minimum shortfall optimal portfolio approximates the performance of the second order stochastic dominance optimal portfolio by simulation and an empirical implementation.<br /><br />The third chapter of this dissertation develops a new correlation stress test for high-dimensional correlation matrices. It is a joint work with Anton Golub, a former Marie Curie Fellow. Stressing a correlation matrix is not an easy task because the post-stressed correlation matrix is likely to lose one or more of the required mathematical properties, say, positive semi-definiteness. Some popular correlation stress tests in the literature are devoted to finding a valid correlation matrix that satisfies all the required properties and approximates the post-stressed correlation matrix best. Other correlation stress tests might meet all the mathematical properties, but have very low computational speed for high-dimensional correlation matrices. The stress test developed in this chapter decomposes the empirical correlation matrix into eigenvalues and eigenvectors and then perturbs one or several eigenvalues while keeping the eigenvectors unchanged. The post-stressed correlation matrix is then automatically positive semi-definite and the computational speed is high. To select and interpret the stressed scenarios, we adopt the Random Matrix Theory to filter information eigenvalues and eigenvectors from noise eigenvalues and eigenvectors. We also use the same theory to differentiate the macro-level eigenvalues and eigenvectors from the micro-level eigenvalues and eigenvectors. We empirically implement our algorithm to the Chinese equity market and conduct some tentative correlation stress tests. All in all, our stress tests show good potential to generate hypothetical extreme scenarios and replicate historical extreme events. 2013-08-06T08:46:13Z 2013-08-06T08:46:13Z Guo, Zhen

Dateiabrufe seit 01.10.2014 (Informationen über die Zugriffsstatistik)

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