8B: Value at Risk (VaR)

Question 1

What is Value at Risk (VaR)?

Answer 1

Value at Risk (VaR) is a measure of potential loss (in money terms) that could be exceeded (minimum loss) at a given level of probability.

It quantifies the potential loss in simple terms, is widely accepted by regulators, and is versatile.

Question 2

How is Daily VaR calculated using the analytical (variance-covariance) method?

Answer 2

Daily VaR = Dollar value of position × Portfolio return volatility

Where portfolio return volatility is defined as the portfolio period standard deviation multiplied by the appropriate Z-score (from the normal distribution normalized Z-scores).

Question 3

What is the 5-percent daily VaR of a $2-million position in the market, which has a 2-percent daily standard deviation in price changes?

Answer 3

Daily VaR = Dollar value of position × Portfolio return volatility
= $2,000,000 × (1.65 × 0.02)
= $66,000

Question 4

What are the three common ways to estimate VaR?

Answer 4

1. Analytical (variance-covariance) method
2. Historical method
3. Monte Carlo simulation method

Question 5

What is the historical method for estimating VaR?

Answer 5

The historical method uses actual daily returns from some user-specified past period to estimate VaR. If you have 1,000 observations, the 1-percent and 5-percent probabilities would be of a loss greater than the 10th or 50th-worst out of the observations, respectively.

Question 6

What is the Monte Carlo simulation method for estimating VaR?

Answer 6

The Monte Carlo method produces random outcomes to examine the effects of particular sets of risks, using a probability distribution for each variable of interest. It can use normal or non-normal distributions for modeling purposes.

Question 7

What are the advantages of VaR?
A:

Answer 7

1. Quantifies potential loss in simple terms
2. Widely accepted by regulators
3. Versatile

Question 8

What are the limitations of VaR?

Answer 8

1. Difficult to estimate
2. Various estimation methods can lead to significant estimate differences
3. Can create a false sense of security for risk managers
4. May underestimate the severity of worst-case returns

Question 9

What criticisms of VaR were made by David Einhorn in the GARP Risk Review?

Answer 9

1. Led to excessive risk-taking and leverage at financial institutions
2. Focused on manageable risks near the center of the distribution and ignored the tails
3. Created an incentive to take “excessive but remote risks”
4. Was “potentially catastrophic when its use creates a false sense of security among senior executives and watchdogs”