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 lferraguti 01-18-2020 04:07 PM

Value-at-Risk Definition

In the past, I've understood Value-at-Risk basically as a percentile.

i.e. The 95% Value-at-Risk of the standard normal distribution (if it's measuring losses) is 1.645 for a given time period. In other words, we can say with 95% confidence that our losses will not exceed 1.645 in a given time period.

However, in VaR Ch. 5, it seems like this is no longer the case. According to the book, VaR is typically a relative measure. And it is measured against the mean of the distribution.

So, for instance, if, in the traditional sense, your VaR is 1.645, but your expected (mean) loss is 1, then your relative VaR is .645.

This leads me to another question. Is VaR typically a measurement of company value or a measurement of losses? It seems like I've come across both in the readings so far, but VaR Ch. 5 uses company value or project value instead of losses.

I think what would help me put all this together is the following question: When a company says, we have a one-day VaR of 15 million at the 99% level, what does that actually mean (in detail)? My current interpretation, based on the book, is this: With 99% confidence, we can say that our company value will not decrease by more that 15 million from its expected value in one day.

 PaulP 01-20-2020 08:37 PM

Good, GOOD question!

There are actually two measures of VaR - relative, and absolute.

For example, let's say we expect to profit \$100, but the 95th percentile is a loss of \$200.
The absolute VaR is \$200 - that is, the actually dollars lost.
The relative VaR is \$300 - this is the difference between what we thought we'd get and the loss.
So, for your answer, it could be either a measure of company value OR losses! It is hard to say what is more typical. They both have their uses. The textbook often gets around this confusion by assuming a mean profit/loss of \$0, so then relative VaR and asbolute VaR become the same.

Traditionally, the SOA has been fairly forgiving on which one we can use (unless they specify). So, if it is on the exam, and they just ask for "VaR," you can pick either one.

The only exception to the above rule is if we are talking about capital. When we talk about capital, we are required to use relative VaR, because we want to know how much in excess of our reserve we need to hold. So if we expect a loss of \$500 at the worst, and we have \$200 of reserves for our expected loss, then we only \$300 of capital.

 lferraguti 01-21-2020 12:29 PM

Excellent, thanks!!

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