Methods to Compute Value-at-Risk: A Comparative Study
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Author(s)
Zahradka, Joel
Date Issued
April 8, 2024
Abstract
As a response to numerous international banking failures in the mid-to-late 1900s, the most infamous being the closure of Herstatt Bank, the Basel Committee on Banking Supervision was created to form a regulatory framework for financial institutions and to stabilize countries’ banking systems. The BCBS set one of the most important regulations pertaining to market risk in 1996 through their Market Risk Amendment to Basel I, introducing the risk measure Value-at-Risk to calculate a financial institution’s capital requirements. Having given different methods for banks to internally determine the VaR measure, the goal of my study is to pursue how greatly the number of violations, where actual returns are less than the Value-at-Risk, differ when utilizing a simple historical approach, moving historical method, parametric approach, and a Monte Carlo simulation in order to determine if one model is better at capturing risk than the others. After performing the methods above for 30 stocks from the S&P 500, 15 currencies, and 10 commodity futures, many assets have violations within the range of 0-2 for each approach, yet all the methods experience some instances where the number of violations is extreme, such as 8 or more. In general, it seems the two historical models performed better than the two assuming normality, and the moving historical simulation appears to more accurately model risk than the simple approach, as the mean and median number of violations for each asset class are closest to the expected value of 2.52 violations for one year of 252 trading days. Unfortunately, it is difficult to make clear conclusions from this data, as 2022-2023 was a bearish year, whereas 2023-2024 was bullish, so the amount of violations between 0 and 2 could simply be due to overall market performance rather than the efficacy of the models. Therefore, in the future I will employ different sample sizes to calculate VaR, such as one, three, five, and ten years, with the goal of assessing whether such differences change my current results.
Major
Business
Honors
Business and Economics, 2024
First Reader(s)
Navarro-Sanchez, Francisco
Other Reader(s)
Bianco, Timothy P.
Department
Business and Economics
Type of Publication
Senior Project Paper
Subjects
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Methods to Compute Value-at-Risk_ A Comparative Study.pdf
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