Value-at-Risk and Expected Shortfall

Posted: August 26th, 2021

Student’s Name

Instructor’s Name

Course

Date

Value-at-Risk and Expected Shortfall

Value-at-Risk (VaR)

The Value-at-Risk (VaR) refers to a statistical measure that determines and quantifies the financial risk level for a portfolio, position, or a firm estimated within a given period(Kheir 13). It is a common metric among commercial and investment banks as it is applied in ascertaining the occurrence and the extent of potential losses for the organization portfolio(Kheir 13). Equally, risk managers often utilize the measure to assess and manage risk exposure. At the same time, VaR calculations can be applied in measuring risk exposure of particular positions or the whole firm or its portfolios. In this assessment, the historical stock data for five companies, namely; NVS, DVAX, VXRT, PG, and PFE, is collected, and their VaR determined at 90% and 95%. Their portfolio value is $ 1 million.Thus, according to Kheir (27) and Krause & Paolella (2014), the following is an analytical method for calculating VaR for each of the five companies; V_p

Whereby;

 Ȓ refers to expected portfolio return, z is the z-value at the desired level of significance, in this case, 10% = 1.645 and VaR and 5% VaR = 1.96,  is the standard deviation of the portfolio returns. At the same time,represents the value of the portfolio. The calculations and results of VaR are completed on the excel worksheet (See Excel Sheet 1&2).

Expected Shortfall (ES)

The expected shortfall is also referred to as conditional value-at-Risk (CVAR). It is a tail-risk measure applied in ascertaining expected returns or losses based on a percentage of worst occurrences(Krause & Paolella 22). Whereas VaR informs on the extent of a loss based on given amounts, the expected shortfall estimates the average loss that will occur once the VaR limit is breached(Krause & Paolella 56; Kheir 32). Although CVaR is the average of VaR, the following formula can be applied in calculating CVaR;

Whereby; p(x) dx refers to the probability density for obtaining a return with value “x,” c is the cut-off point on distribution under which the VaR break-point is set while VaR is the agreed VaR level. The CVaR for the five companies is completed in the excel worksheet (See Excel Sheet 1 & 2).

Works Cited

Kheir, I. GARCH Modeling of Value at Risk and Expected Shortfall Using Bayesian Model Averaging”. Hunter College, Department of Economics, 2019. Print.

Krause, J. & Paolella, M., S. A Fast, Accurate Method for Value at Risk and Expected Shortfall
Volume 14; Volume 40 of Research paper series: Swiss Finance Institute. Swiss Finance Inst., 2014. Print.