# VaR spectrum

Var cannot fully capture the entire spectrum of risk. Can someone elaborate?

I will give a try. VaR represents a quitile of expected distribution. One - expected distribution can’t capture all risk factors, two - since VaR is a quintile, it disregards information to its left.

VAR relies on a normal distribution of returns.

farley013 Wrote: ------------------------------------------------------- > VAR relies on a normal distribution of returns. This is not true. Analytical variance-covariance method for estimating VAR requires normal distribution. But VAR certainly can be calculated from non-normal distributions using other methods.

it all depends on what you use as the underlying loss distribution. If you assume you know the exact probability distribution, basically you can compute out all risk measures. However, I’m more concerned about how one can specify or estimate the parameters in the proposed probability distribution.

>This is not true. Congratulations, you just failed the level 3 exam.

farley013 Wrote: ------------------------------------------------------- > >This is not true. > > Congratulations, you just failed the level 3 exam. You better check level 3 books, before making your claims.

farley, you should really really try not to make tall claims, especially when you are being corrected. For your benefit, read through the whole piece here: http://en.wikipedia.org/wiki/Value_at_risk#Common_VaR_calculation_models

Oops, duplicate post…

There are several ways to do VaR, and not all of them involve assuming normal distributions. For example, one can just look at the historical distribution and use the Nth percentile of that distribution to compute the N% VaR. Of course, that assumes that the historical distribution is sufficiently representative of future distributions, but it doesn’t require a normality assumption.

SS 12 Reading 37: “…many observed distributions of returns have an abnormally large number of extreme events. This quality is referred to in statistical parlance as leptokurtosis but is more commonly called the property of fat tails. Equity markets, for example, tend to have more frequent large market declines than a normal distribution would predict. Therefore, using a normality assumption to estimate VAR for a portfolio that features fat tails could understate the actual magnitude and frequency of large losses. VAR would then fail at precisely what it is supposed to do: measure the risk associated with large losses.” Must be junior league night on this forum.

pacmandefense, Ignore farley013, he’s pretty dumb and doesn’t see the whole picture. bchadwick and the others know a lot more and are a lot smarter.

farley013 Wrote: ------------------------------------------------------- > VAR relies on a normal distribution of returns. That one is going on my profile…check it, lol.

farley013 Wrote: ------------------------------------------------------- > SS 12 Reading 37: “…many observed distributions > of returns have an abnormally large number of > extreme events. This quality is referred to in > statistical parlance as leptokurtosis but is more > commonly called the property of fat tails. Equity > markets, for example, tend to have more frequent > large market declines than a normal distribution > would predict. Therefore, using a normality > assumption to estimate VAR for a portfolio that > features fat tails could understate the actual > magnitude and frequency of large losses. VAR would > then fail at precisely what it is supposed to do: > measure the risk associated with large losses.” > > Must be junior league night on this forum. So what you are saying is this: since there exists a disadvantage of using a normality assumption in estimating VaR, that somehow implies VaR can only be estimated with a normality assumption !!! wow !!! Maybe a logic 101 course is in order for Mr Farley here.

Show me where I used the word “only” anywhere on this thread. If not then either delete your post or take a reading comprehension 101 course. This is what I get for showing my face on junior night.

Actually, I think that farley013 luckily wiggled out of this one.

the CFA risk reading reading barely scratches the surface of risk mgmt. if you want to learn about risk, just read the exam 3 books for PRM. very dense, tough read if you really want to ‘get it’, but at least you’ll avoid ‘junior night out’ jokes (on you). as some others have pointed out, VaR can be computed various ways - analytical (assumes normality, so the tail quantile easily measured), historical (no distributional assumption at all - just based on actual past data, whatever shape its distn), simulation (choose your poison - i.e. distn is what you choose for the MC sim). as for the original question about “spectrum” - whatever the heck it means, i think what they’re saying is what maratikus immediately responded with. VaR is not an expected value - it is a quantile (of which quintile is one example if 20% VaR). CVaR and EVT based approaches address the tail risks more completely. VaR kind of says “well, with x% probability, your loss could be [bottom x% quantile] or greater”. and stops there.

rohufish, excellent! After FRM, I’m really looking forward to the PRM curriculum…it’s sitting on my desk right next to me.

rohufish Wrote: ------------------------------------------------------- > the CFA risk reading reading barely scratches the > surface of risk mgmt. if you want to learn about > risk, just read the exam 3 books for PRM. very > dense, tough read if you really want to ‘get it’, > but at least you’ll avoid ‘junior night out’ jokes > (on you). > > as some others have pointed out, VaR can be > computed various ways - analytical (assumes > normality, so the tail quantile easily measured), > historical (no distributional assumption at all - > just based on actual past data, whatever shape its > distn), simulation (choose your poison - i.e. > distn is what you choose for the MC sim). As you pointed out, VaR is just a quantile, so all methods are used to calculate the quantile with the given loss distribution. In fact, the three methods are not clearly described even in CFA L3 cirriculum. Analytical method can be applied to any loss distribution, as long as there is an easy way to solve F(x) = alpha, where alpha is given (eg 0.05) and F is the cumulative distribution function. (just assume continuous distribution). Normal distribution gives you formula for various alpha. But formula exists for other distribution as well (eg exponential distribution). So analytical method per se does not need to restrict the assumption of the underlying loss distribution to be normal. Historical method, however, implicitly assumes that the loss distribution is given by that estimated using the historical data. And then one can find the quantile (VaR) from that distribution. For MC simulation, as long as one can draw sample from the loss distribution, we can estimate the quantile using the random samples. MC simulation is used only when analytic method is not feasible. (Certainly you can use MC for normal distribution but who would like to waste computing power to draw thousands of samples but still could only get an approximation instead of the exact quantile?) If I am to wrap up the methodology, I would say there are two methods, analytical (exact) and MC simulation (approximation). Which method to use depends on how you model the underlying loss distribution. In particular, if we treat historical data as random samples drawn from the true loss distribution, this is called historical method.

farley013 Wrote: ------------------------------------------------------- > Show me where I used the word “only” anywhere on > this thread. If not then either delete your post > or take a reading comprehension 101 course. This > is what I get for showing my face on junior night. You didn’t use the word only. But, you used that passage to support your previously-expressed absurd point, which is “normality is an assumption of all methods of VaR calculation”. Seriously, you should start thinking about some junior level courses. Logic 101 is a good place to start.