Save 30% on all 2023 Study Packages with Code: BLACKFRIDAY30. Valid until Nov. 28th.

# Value at Risk (VaR)

Value at Risk (VaR) measures the probability of underperformance by providing a statistical measure of downside risk.

In the case of a continuous random variable, VaR can be computed as follows:

$$VaR\left(X\right)=-t \text{ where } P\left(X < t\right)=p$$

VaR represents the maximum possible loss on a portfolio over a given period in the future, with a given degree of confidence. The degree of confidence is typically expressed as $$1-p$$.

For instance, if an asset has a one-day 5% VaR of $7,500, then there is a 5% probability that the asset will fall in value by at least$7,500 over one day under normal market conditions. This can also be given in terms of a confidence level, that is, we are 95% (100% − 5%) confident that the asset will experience a loss of at most $7,500 in one day. The following is an illustration of the 5% VaR of a hypothetical portfolio: The above illustration shows that the portfolio’s expected return is$50m. Additionally, the probability of realizing a return of less than $42m is 5%. ## Question A hypothetical portfolio B has an annual 1% VaR of$45,000. Which of the following statements is most likely true about the portfolio?

1. The expected minimum loss over one year, 1% of the time, is $45,000. 2. There is a 99% probability that the expected loss over the next year is more than$45,000.
3. The likelihood of losing $45,000 over the next year is 1%. #### Solution The correct answer is A. An annual 1% VaR of$45,000 means that there is a 1% probability of a loss greater than $45,000. B is incorrect. An annual 1% VaR of$45,000 means that there is a 99% probability that the portfolio will experience a loss of not more than \$45,000 in one year.

C is incorrect. VaR does not specify the probability of losing a particular amount.

Reading 40: Measuring and Managing Market Risk

LOS 40 (a) Explain the use of value at risk (VaR) in measuring portfolio risk.

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

Subscribe to our newsletter and keep up with the latest and greatest tips for success
Shop Actuarial Exams Prep Shop GMAT® Exam Prep

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
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
2021-02-18
Every concept is very well explained by Nilay Arun. kudos to you man!