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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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Hedonic Pricing in the Sneaker Resale Market

By Kevin Ma and Matthew Treiber

This paper explores the secondary resale market for high-end and limited-edition sneakers, specifically analyzing the determinants that affect what value sneakers trade for in the secondary market. While it is common knowledge that the sneaker resale market is a thriving and active secondary market, there is little to no empirical research about what exactly causes such sneakers to sell for exorbitant prices in the resale market. The study utilizes a hedonic pricing approach to investigate the determinants of sneaker resale price. We use a dataset of sneaker resale transactions from the online marketplace StockX between the years of 2016 and 2020 as the basis for our research. After analyzing the results, we have determined that the amount of “hype” that surrounds a sneaker as well as supply scarcity are statistically significant factors when determining the resale price premium a particular sneaker commands in the secondary market. This work adds to the sparse literature on the sneaker resale industry and brings an econometrics-approach to determining the price a given pair of sneakers commands in the resale market.

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Advisors: Professor Kyle Jurado, Professor Michelle Connolly, Professor Grace Kim| JEL Codes: C2, C20, J19

Leverage and Varying Metrics of Firm Performance

By Preston Jiateng Huang

This paper sets out to examine the effect of leverage on company performance. Drawing on the methodology of key prior research, this study finds that leverage has a consistent negative effect on firm growth; by contrast, no such negative impact was found on return on equity. Importantly, such patterns hold throughout the entire period under study (1970-2017), during which several disruptive economic events have occurred. These results highlight the importance of selecting appropriate company performance measures when studying the effect of debt load on a firm as well as the misalignment of incentives for policymakers and company management. Other implications are also discussed.

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Advisor: Professor Kyle Jurado | JEL Codes: G24; G31; G32

Questions?

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