Seminar: " Evaluation of mutual fund performance and estimation of bond default probability using Stochastic Dominance Algorithms" by Prof. Sree Vinutha
While the possibility for investment A to dominate investment B under the first and second order stochastic dominance framework can be tested only at the points of jumps in probabilities of the distributions, the comparison at interior points is also essential under third order, due to the non-linearity in the difference in the third order stochastic dominance integral. Further, the quantile approach used to test for the first and second order dominance was proved to be inaccurate under the third order dominance. These points were overlooked in the previous studies, thereby casting doubts on the earlier reported results. In this work, we implement the recently established third order algorithm that corrects for the errors. In the process, we derive the expressions for the functions essential for testing the possibility of dominance at the interior points and arrive at their restrictions on the common grid of the pair wise investments under consideration. We develop a program to determine the efficient funds and the funds superior and inferior to the benchmark indices at a fast pace. We find that the size of the efficient set reduces drastically under third order. Also, several funds are found to be superior to indices under second and third order.
While Government bond is expected to be default free, corporate bond with the highest rating is generally associated with low probability of default in comparison with other bond categories. Neither Government bond nor corporate bond is expected to dominate the other under second order, as the combination of low risk and high return is not characterized by either. However, if we were to look at bonds that did not default in the past, the highest rated bond category is expected to have offered higher return without risk, and therefore is expected to have dominated the Government bond. Now, from the cumulative distribution of the corporate bond, a new distribution is generated to incorporate the probability of default. With the introduction of default probability for corporate bond, the possibility of the government bond or default free bond, dominating the risky corporate bond arises. The default probability is modified till neither the Government bond nor the corporate bond, under the modified distribution framework, dominate each other. This comparison of cumulative distributions is done holding factors other than default risk constant. Similar comparisons can be made against various bond categories. The estimate of the default probability of the portfolio of bonds obtained can also be compared during periods of economic stability and recession.
Sree Vinutha V completed Ph.D from IIT Bombay and currently teaches at IIT Kharagpur. Prior to joining IIT Bombay, she worked in the Analytics division of GE and subsequently pursued Advanced Financial Risk Management Programme from IIM Bangalore. Her graduation was in Mathematics and post graduation was in Management. She is also a certified Internal Quality Auditor in ISO 9001:2000 standards. Her current areas of interest include Financial Econometrics, Financial Management, Econometric Analysis and Investment Analysis. She has presented papers in International Conferences including the conference organized by the International Finance and Banking Society in UK in association with the University of Cambridge, University of Warwick and University of Leicester and has published in journals such as risk management-a palgrave journal and the journal of quantitative economics.