Limited Time Offer: Save 10% on all 2021 and 2022 Premium Study Packages with promo code: BLOG10    Select your Premium Package »

Extensions of VaR

Extensions of VaR

Conditional Value at Risk (CVaR)

Rockafellar and Uryasev introduced conditional value-at-risk (CVaR) in 2000. CVaR is a tail risk metric that quantifies the amount of the expected losses beyond the VaR cutoff point at a specific confidence level. It is also known as the expected shortfall (ES), average value at risk (AVaR), or expected tail loss (ETL). CVaR is a weighted average of the losses in the tail of the return’s distribution beyond the VaR level.

Conditional Value at RiskCVaR is mathematically complex to obtain when the parametric method is used. This can be attributed to the fact that this method cannot be used in the determination of the magnitude of losses more magnificent than the VaR.

Incremental Value at Risk (IVaR)

Kevin Dowd introduced incremental value at risk in 1999. Incremental value at risk (IVaR) measures the impact of small changes as a result of taking different positions of the portfolio on the VaR. To obtain IVaR, VaR is repeatedly calculated considering different positions of the portfolio. The difference between the new VaR and the original is the IVaR.

Marginal VaR (MVaR)

Marginal VaR is a measure of the impact of removing a position from a portfolio on the overall VaR. It is different from IVaR because it measures the impact of removing an entire portfolio holding rather than making small changes, in the portfolio position, on VaR.

Relative VaR

Relative VaR measures the risk resulting from the underperformance of a portfolio relative to a benchmark portfolio. Assuming a 95% confidence level, a 1-day relative VaR of $5,000 for portfolio B implies that, on average, the portfolio would underperform only for five days in a hundred days, relative to the benchmark by more than $5,000 due to market changes.

Question

Which of the following statements about the extensions of VaR is the most accurate ?

  1. Marginal VaR is a tail risk metric that quantifies the amount of expected losses beyond the VaR cutoff point.
  2. Conditional VaR is a measure of how removing a position from a portfolio may affect the overall VaR.
  3. Incremental VaR measures the impact on the VaR resulting from small changes caused by taking different positions of a portfolio.

Solution

The correct answer is C.

Incremental value at risk (IVaR) measures the impact on the VaR resulting from small changes caused by taking different positions of a portfolio. To obtain IVaR, VaR is repeatedly calculated considering the different positions of the portfolio. The difference between the new VaR and the original is the IVaR.

A is incorrect. Marginal VaR is a measure of how the removal of a position from a portfolio may affect the overall VaR. It is different from IVaR because it measures the impact that the removal of an entire position rather than making small changes in a portfolio has on VaR.

B is incorrect. Conditional value-at-risk (CVaR) is a tail risk metric that quantifies the amount of the expected losses beyond the VaR cutoff point at a specific confidence level.

Reading 40: Measuring and Managing Market Risk

LOS 40 (e) Describe extensions of VaR.

Featured Study with Us
CFA® Exam and FRM® Exam Prep Platform offered by AnalystPrep

Study Platform

Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Online Tutoring
    Our videos feature professional educators presenting in-depth explanations of all topics introduced in the curriculum.

    Video Lessons



    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.
    Nyka Smith
    Nyka Smith
    2021-02-18
    Every concept is very well explained by Nilay Arun. kudos to you man!
    Badr Moubile
    Badr Moubile
    2021-02-13
    Very helpfull!
    Agustin Olcese
    Agustin Olcese
    2021-01-27
    Excellent explantions, very clear!
    Jaak Jay
    Jaak Jay
    2021-01-14
    Awesome content, kudos to Prof.James Frojan
    sindhushree reddy
    sindhushree reddy
    2021-01-07
    Crisp and short ppt of Frm chapters and great explanation with examples.