Sensitivity Risk Measures

Sensitivity measures quantify how a security or portfolio will react if a single risk factor changes.

• Beta measures the sensitivity of an equity's expected return to the equity risk premium.
• Duration and convexity measures reflect the sensitivities of a bond's price to changes in interest rates.
• Delta, gamma, and vega are used to measure the sensitivities of an option's price to changes in the underlying.

Risk managers can use deltas, gammas, vegas, durations, convexities, and betas to get a comprehensive picture of the sensitivity of the entire portfolio.

Note that sensitivity measures do not indicate which portfolio has greater loss potential.

Scenario Risk Measures

VaR measures based on recent historical data can fail to identify extreme events that could cause severe losses, so they should be supplemented by scenario analysis and stress testing.

Scenario measures are risk models that evaluate how a portfolio will perform under certain high-stress market conditions.

• They focus on extreme outcomes. Sensitivity risk measures such as beta and duration are not suited for handling such extreme movements.
• They are not bound by recent historical events, or assumptions about parameters or probability distributions.
• Stress tests apply extreme negative stress to a particular portfolio exposure. They are closely related to scenario risk measures.

Scenario measures can be based on actual historical scenarios or on hypothetical scenarios.

Historical scenarios are scenarios that measure the portfolio return that would result from a repeat of a particular period of financial market history.

The drawbacks are the limited number of extreme events and ascribing the probability of a given scenario.

Hypothetical scenarios model the impact of extreme movements and co-movements (that have not previously occurred) in different markets. They consider situations that are absent from historical data or not well represented but nonetheless likely. A process called reverse stress testing is often used to stress the portfolio's most significant exposures.

Sensitivity and Scenario Risk Measures and VaR

Each of these measures has unique features. It is important to understand each one's limitations and benefits. No one measure works perfectly on its own. They are most effective in combination.

VaR tells us the probability of a given value change, but it does not tell us which factors are driving the risk. Sensitivity and scenario risk measures can complement VaR:

• They do not need to rely on history.
• Scenarios can be designed to overcome an assumption of normal distribution.
• Liquidity can be considered in these measures.

Limitations of scenario measures include the following:

• Historical scenarios are unlikely to re-occur in exactly the same way.
• Hypothetical scenarios may incorrectly specify how assets will co-move and may get the magnitude of movements wrong.
• It is difficult to establish appropriate limits on a scenario analysis or stress test.