# Value at Risk v.s Short Fall Risk

Shortfall Risk is described as: “Measures the probability that the actual return will be less than the target return.” Value at Risk is described as: “Provides the probability of a return less than a given amount over a specific time period.” I’m having a hard time differentiating conceptually between these 2. For VAR, isn’t the ‘given amount’ in the description = target return? and if so, how does this definition differ from Short Fall Risk. I’ve re-read these two statements several times and they both sound exactly the same with the exception of, “specific time period”. PJStyles

Figured this out… Shorfall Risk is a probability based on target return v.s actual return where as Value at risk is probability of a return less than a DOLLAR amount. Got it lol

PJStyles Wrote: ------------------------------------------------------- > Figured this out… Shorfall Risk is a probability > based on target return v.s actual return where as > Value at risk is probability of a return less than > a DOLLAR amount. Got it lol Value at Risk is not a proability http://en.wikipedia.org/wiki/Value_at_risk “In economics and finance, Value at Risk (VaR) is the maximum loss not exceeded with a given probability defined as the confidence level, over a given period of time” Or maybe wiki is wrong and CFAI is right? Do you have exact page number for CFAI?

Don’t have the CFAI page number but it’s page 71 in Schweser Book 3.

VAR is both a probability and an amount: the probability a given loss will not exceed \$7k is 95%…conversly, the probability the minimum loss will be \$7k is 5%…

strikeshark, it cant be both, VAR is a has precise mathemetical formula, given level of significance

“Precise” I wouldn’t use that to describe VAR since it is based on normal distribution.

bigwilly Wrote: ------------------------------------------------------- > “Precise” I wouldn’t use that to describe VAR > since it is based on normal distribution. Precise meaning there is no ambiguity in defenition

CSK is right. It is precisely what he said. Just because it’s based on assumptions doesn’t mean the definition is not precise.

Precisely.

it is both. you get a dollar value and the associated probability with that dollar value. VAR is based on the assumption of normality - normality is probabilisitic. A VAR with a confidence level of 5% implies a 5% PROBABILITY of losses exceeding a DOLLAR value of some amount. See - that sentence contained both probabilities and an absolute amount. VAR provides both measures. (E(x) - Confidence level * standard deviation)*\$ = VAR. The confidence level is the probability, the VAR represents the dollar value at that confidence level.

It’s not explained well in either Schweser or CFAI, but believe me, VAR is the \$ amount, not the probability. You would say “The 5% monthly VAR is \$10,000,000”.

^ There is a 5% chance that within a given month losses could exceed \$10M.

BigWilly gets it.

That makes sense… 5% monthly VAR is \$10,000,000. I think we are almost nit-picking here a little bit. As far as assumption of normality, I was under the assumption that VAR and Short Fall Risk DO NOT assume normality. I could be wrong but could have sworn I read that in CFAI materials.

TooOld4This Wrote: ------------------------------------------------------- > It’s not explained well in either Schweser or > CFAI, but believe me, VAR is the \$ amount, not the > probability. You would say “The 5% monthly VAR is > \$10,000,000”. agreed.

PJ - VAR uses the normal curve, which is by definition assumes normality. CSK & TooOld. why do you think they put the 5% in the sentence for VAR. Why don’t they simply say the monthly VAR is \$10,000? (the easy why is because that sentence would be incorrect). What is that sentence “the monthly VAR is \$10,000” missing to make it correct?

PJ, you’re right, it doesn’t have to be normal for you to calculate a VAR. (You could use a completely different distribution and use historical or MonteCarlo method to determine VAR.) Also, I note that CFAI discusses whether VARs are additive. (If you have two portfolios each with \$10,000,000 VARs, is your total VAR \$20,000,000?) Obviously not due to correlations between the two portfolios, but the question clearly sees VAR as a value, not a probability. We ARE nitpicking a bit, but the subtle difference might mean getting something right vs wrong on June 7. Just trying to help.

I almost apologize for asking the original question lol

CFAI V2 360: "VAR are MONEY measures of the minimum value of losses expected over a specified time period at a given level of PROBABILITY. V5 Pg 25: “First we see that VAR is an estimate of loss that we expect to be exceeded. Second, we see that VAR is assocaited with a given probability.”