## Friday, December 14, 2018

### Analyst Corner - Understanding Value At Risk (VAR)

VAR in its many forms is a common measure of a portfolio's downside risk. If you work in investments, you may see this terminology repeatedly in common practice. Here is a quick summary of the common VAR acronyms, their benefits and some of their limitations.

Value At Risk (VAR)
VAR essentially says that there is an X% probability that the portfolio will lose \$Y or more, during time period Z. So it has three basic components, the probability of loss (X), the minimum amount of loss (Y), and the time period within which the loss would occur (Z). It's a downside risk estimate, not a prediction, that portfolio managers can use for risk budgeting purposes and investors can use as a risk estimation metric when looking at a particular portfolio. People calculate VAR in a number of ways, including (1) looking at historical losses over a long period of time and using the historic loss data to calculate VAR; (2) using Monte Carlo simulation to project what VAR should be, based on establishing risk factors and assigning probabilities to those risk factors; or (3) using a variance-covariance method to determine the 1% or 5% left-hand tail of a portfolio's return distribution (assuming normal distribution, taking the mean portfolio return and then subtracting the product of 1.65 times the standard deviation of the portfolio's return in the case of 5% VAR - for example).

Conditional Value At Risk (CVAR)
CVAR is the expected dollar amount of loss, given the fact that you're in a VAR situation (i.e., the X% probability situation described above actually occurs... and you're facing a loss of at least \$Y... how much is that loss expected to be exactly? What's the expected shortfall?). Calculating CVAR can be simple or complex, depending on the situation. The easy way is to simply take all the VAR values in your historic data sample or Monte Carlo simulation and average them. If you're using the variance-covariance method it can be more complicated because we don't have a finite limitation for the left-hand data tail... so there should be some formula explanation showing how CVAR is calculated in such cases.

Incremental Value At Risk (IVAR)
IVAR is the dollar amount change in VAR that results from a percentage increase or decrease in a security's weight within a portfolio. For example, if a 3% increase in a portfolio's security holding changes the portfolio's VAR from \$1 Million to \$1.3 Million, then the IVAR for this 3% increase in portfolio weight is equal to \$300 Thousand.

Marginal Value At Risk (MVAR)
MVAR is related to IVAR. It simply measures the change in VAR for a one percent change in a security's portfolio weight.

Ex Ante Tracking Error (also known as Relative VAR)
Ex Ante Tracking Error (Relative VAR) measures the VAR of the difference between a portfolio's return and the return of the benchmark index against which that portfolio is compared for performance evaluation purposes. You can calculate this VAR as a combination of a long position in the portfolio and a short position in the benchmark index. An X% monthly Relative VAR of Y% means that X% of the time, the portfolio will under perform the benchmark index by Y% or more.