Suppose that a company has a portfolio consisting of...

Name: Problem 6, Chapter 18: Options, Futures, and Other Derivatives
Uploaded: 2023-06-06T23:37:07-08:00
Duration: 1 min 40 s
Channel: Jennifer Stoner
Description: Suppose that a company has a portfolio consisting of positions in stocks, bonds, foreign exchange, and commodities. Assume that there are no derivatives. Explain the assumptions underlying (a) the linear model and (b) the historical simulation model for calculating VaR.

Suppose that a company has a portfolio consisting of positions in stocks, bonds, foreign exchange, and commodities. Assume that there are no derivatives. Explain the assumptions underlying (a) the linear model and (b) the historical simulation model for calculating VaR.

Key Concepts

Value at Risk (VaR) Overview

Value at Risk (VaR) is a statistical measure used to estimate the maximum potential loss on a portfolio over a given time period at a certain confidence level. It summarizes the extent of possible losses in a portfolio by assigning a probability level to a loss amount, making it a critical tool for risk management and regulatory purposes.

Linear Model Assumptions

The linear model for calculating VaR assumes that the portfolio’s value changes linearly with respect to changes in underlying risk factors. This involves approximating the portfolio’s returns using a linear combination of individual asset returns, typically via a delta approximation. Under this assumption, small changes in risk factors proportionally translate to changes in portfolio value, and the impact of higher-order (nonlinear) effects is considered negligible.

Historical Simulation Assumptions

The historical simulation model assumes that historical market movements and changes in risk factors are representative of future patterns. It relies on historical data to generate the distribution of portfolio returns without assuming any specific parametric form for the return distribution. This non-parametric approach presumes that the past observed market behavior and correlations among risk factors will repeat in the future, thereby allowing direct computation of VaR based on actual historical outcomes.

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