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Category Archives: C01

Bayesian Non-Parametric Risk Metric

By Kiwan Hyun

Abstract
This thesis constructs completely non-parametric Risk Metric models through Dirichlet process in order to account for both the parametric uncertainty and model uncertainty that a Risk Metric may bring.
Value at Risk (VaR), along with its integrated form Continuous Value at Risk (CVaR) / Expected Shortfall (ES), is one of the most frequently used risk metrics in finance. VaR is a quantile value of forecasted return of a portfolio—linear and non-linear. [Siu, et. al., 2006] According to the Basel 95% and 99% VaR are recommended to be posted by the financial institutions for portfolios and assets; 97.5% CVaR/ES value needs to be set aside when making an investment for “capital buffer”. [Obrenovic & Akhunjonov, 2016] Therefore, an accurate estimation of risk is critical for VaR models and CVaR/ES models.
The traditional approach of a normal approximation to VaR and CVaR/ES has been discredited—especially for daily returns—and even blamed by some for causing the 2008 Financial Crisis [Nocera, 2009] Many advancements have been made to the VaR model including Bayesian inference to the normal model [Siu, et. al., 2006], Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) VaR model [Bollerslev, 1986], and Conditional Autoregressive Value at Risk (CAViaR) model [Engle & Manganelli, 2004]. When tested against 6 years (Jan, 2001 – Jan, 2005) of daily returns data of 10 different market indexes, the Bayesian CAViaR model has shown to be the most accurate in predicting daily 95% and 99% VaR. [Gerlach, et. al., 2011]
However, there were certain years for certain indexes where the 99% Bayesian CAViaR VaR did not perform well, especially for years that had multiple > 5% daily drops. Moreover, the Bayesian CAViaR models—though are almost non-parametric—follow a Skewed-Laplace distribution. To even account for the uncertainty of the likelihood model, this thesis constructed daily 97.5% VaRs for 7 different country indexes for 7 years (Jan, 2012 – Dec, 2019) using the completely non-parametric Dirichlet Process.
The Dirichlet Process 97.5% VaR outperformed all Bayesian Normal, Bayesian GARCH, and Bayesian CAViaR models of years when CAViaR models underperformed. The model may be inefficient for normal years since it is overly conservative. Nevertheless, the non-parametric model still seems to be significantly more accurate during fluctuant years.

Professor Kyle Jurado, Ph.D., Faculty Advisor,
Assistant Professor Simon Mak, Ph.D., Faculty Advisor

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The Effect of Minority History on Racial Disparities in the Mortgage Market: A Case Study of Durham and New Haven

By Jisoo Yoon

In the aftermath of the housing market crash, the concentration of subprime mortgage loans in minority neighborhoods is a current and long-standing issue. This study investigates the presence of racial disparities in mortgage markets by examining two cities with contrasting histories of African American and Hispanic establishment: Durham, North Carolina and New Haven, Connecticut. This study examines data by the Home Mortgage Disclosure Act (HMDA), and distills the effect of minority legacy on the perception of racial risk by using econometric instruments to separate the behavior of national lenders and local lenders. The econometric methods allow national lenders to reflect objective risk measures and neighborhood race dynamics, while local lenders reflect subjective attitudes towards certain races. With its longer history of African American presence, Durham shows a positive attitude towards Black borrowers at the local level, while New Haven shows a more favorable attitude towards its Hispanic residents. Nonetheless, racial legacy also materializes as a negative factor in the form of increased residential segregation and spillover effects. Furthermore, a temporal variation analysis of pre- and post-mortgage market reform data affirms the disappearance of racial bias and continued presence of spillover risk in Durham.

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Advisor: Christopher Timmins | JEL Codes: C01, G21, J15, R21, R23, R31 | Tagged: Econometrics, Mortgages, Economics of Minorities, Races, Census, Migration, Population, Neighborhood Characteristics, Housing Supply and Market

Market Power & Reciprocity Among Vertically Integrated Cable Providers

By Jeffery Shih-kai Shen

This paper seeks to investigate the effects of vertical integration on the cable industry. There are two main goals that the research paper will attempt to address. The first is to build upon existing research on favoritism shown by multichannel video programming distributors (MVPDs) to affiliated video programming networks. Second, the paper will use 2007 and 2010 industry data to investigate the possible existence of “quid pro quo” among vertically integrated MVPD cable providers. After evaluating the data with multivariate OLS Regressions, the evidence suggests that MVPD cable providers do tend to carry their own affiliated programming networks. Furthermore, the evidence supports the hypothesis that reciprocity relationships exist among major vertically integrated cable providers.

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JEL Codes: C01, D22, K21 | Tagged: Cable Provider, Empirical Analysis, Programming Distributor, Programming Network, Vertical Integration

Time-Varying Beta: The Heterogeneous Autoregressive Beta Model

By Kunal Jain

Conventional models of volatility estimation do not capture the persistence in high-frequency market data and are not able to limit the impact of market micro-structure noise present at very finely sampled intervals. In an attempt to incorporate these two elements, we use the beta-metric as a proxy for equity-specific volatility and use finely sampled time-varying conditional forecasts estimated using the Heterogeneous Auto-regressive framework to form a predictive beta model. The findings suggest that this predictive beta is better able to capture persistence in financial data and limit the effect of micro-structure noise in high frequency data when compared to the existing benchmarks.

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Advisor: George Tauchen | JEL Codes: C01, C13, C22, C29, C58 | Tagged: Beta, Financial Markets, Heterogeneous Autoregressive, Persistence

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