# Sensitivity and Scenario Risk Measures

## Sensitivity Risk Measures

Sensitivity analysis involves determining how changes in risk factors affect the value of an asset or a portfolio. This process measures the sensitivity of the value of the assets to one or more risk factors. Sensitivity analysis may be applied to help predict the returns of a portfolio. Unlike VaR methods, sensitivity analysis does not give the probability of positive or negative price changes.

## Scenario Risk Measures

Scenario analysis is the estimation of changes in the value of an asset or a portfolio under extreme market conditions. There are two types of scenarios that can be used to measure risk: historical and hypothetical scenarios.

### 1. Historical Scenarios

This approach is based on scenarios obtained from periods in the past, where extreme market conditions have been experienced. Some of these volatile scenarios include the ERM crisis, the 1995 Tequila crisis, the 1998 volatile markets, among others. The historical scenarios approach to risk measurement fetches data from relevant historical scenarios. The data are then used in the valuation of a portfolio based on historical simulation to measure the potential future losses.

### 2. Hypothetical Scenarios

This approach is based on scenarios that have not necessarily happened in the past. In this approach to risk measurement, data can be simulated randomly and used for the valuation of a portfolio based on a set of changes in various risk factors, not just a past event. These risk factors should have a non-zero probability of happening in the future. The Monte Carlo method is based on hypothetical scenarios.

## Question

Scenario analysis is a process used for estimating changes in the value of an asset of a portfolio under extreme market conditions. Which of the following scenarios is the most applicable in the Monte Carlo method of obtaining VaR?

1. Tweaking scenarios.
2. Hypothetical scenarios.
3. Historical scenarios.

#### Solution

Hypothetical scenarios approach is based on scenarios that have not necessarily happened in the past. Data can be simulated randomly and used for the valuation of a portfolio based on a set of changes in various risk factors, not just a past event. These risk factors should have a non-zero probability of happening in the future. The Monte Carlo method is based on hypothetical scenarios.

A is incorrect. Tweaking involves filling inputs through guesses in cases where inputs for VaR calculations are either missing or inaccurate. This process is done to improve the performance of the VaR algorithm. However, it is not considered as a scenario.

B is incorrect. Historical scenarios approach uses a set of variations in risk factors that have occurred in the past, especially changes that are accompanied by financial disruption and stress such as the ERM crisis, the 1995 Tequila crisis, the 1998 volatile markets, among others.

Reading 41: Measuring and Managing Market Risk

LOS 41 (f) Describe sensitivity risk measures and scenario risk measures and compare these measures to VaR.

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