CFA CFA Level 3 Risk Management-VAR

# Risk Management-VAR

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If the one-day value at risk of a portfolio is \$50,000 at a 95 percent probability level, this means that we should expect that in one day out of:
A)20 days, the portfolio will decline by \$50,000 or less.
B)95 days, the portfolio will lose \$50,000.
C)20 days, the portfolio will decline by \$50,000 or more.

Reason given: This means that 5 out of 100 (or one out of 20) days, the value of the portfolio will experience a loss of \$50,000 or more.

My understanding of VAR is that for the problem is, In a given day, there is 95% probability that we will lose a minimum of \$50,000. How can we say that it is 1 out of 20 days? Please help. @alta12, @jwa, @Marc‌ , @Sophie

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Going by historical method, It is correct as it means that 5 out of 100 (or one out of 20) days, the value of the portfolio will experience a loss of \$50,000 or more

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@RaviVooda‌ If this is the literal phrasing of the question and answer, then they made a mistake somewhere, because their reason given for choosing A would be correct for C – which is the answer I think is correct. Where did you find this question?

VAR – Value at Risk is a metric that defines what your upper bound for losses are “within a certain confidence level”. The way I interpret VAR of \$50,000 at 95% probability level is in only 5% of the situations would you love \$50,000 or more. As @jwa mentioned though, it could be that they have their probabilities reversed and this could mean that in 95% of the cases would you lose \$50,000 or more, in which case answer A is correct.

By the way, this is highly unlikely – I can’t even think of any normal situation in which you would hold a portfolio where you EXPECT TO LOSE \$50,000 OR MORE IN ALMOST ALL SITUATIONS. This hypothetical portfolio should have a huge upside if you’d be willing to have such a downside loss. I can only think of a portfolio of way-out-of-the-money options expiring in the near future. There is a huge probability of them being worth nothing, so value will go down to zero, but in the rare case that they become in the money, you can make a lot of profit.

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@Jwa, my wording was wrong. It should say “In a given day, there is 5% probability that we will lose a minimum of \$50,000”

@MM12
, the question is from schweser pro.

@Betankrich
, Considering we follow historical method, if we take a data of 30 days and when we calculate its monthly VAR, should we say “there is x% probability of losing \$Y or more in one month period” or “there is x% probability of losing \$Y or more in one day“. ?

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@Betankrich, I had this doubt, because we calculate VAR differently for day, month and year. I think I understood the question. In this question, we take historical data day wise, then sort and take data based on the probability. However I am doubtful of the wording that 1 out of 20 days.

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@raviVooda i believe “there is x% probability of losing \$Y or more in one day” this would be correct

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@RaviVooda – Is that the exact phrasing of the question? Is it saying there is a 95% probability that it will lose \$50,000 or more on a given day? In which case there is a 5% probability that it will lose no than \$50,000. I guess is is saying that on 19/20 days (0.95) or 95/100 days (0.95), the portfolio will lose more than \$50,000 and therefore on 5/100 days (0.05) or 1/20 days (0.05) it will lose no more than \$50,000. Seems an odd question to me, like the probabilities are the wrong way round…. I hate VAR.

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@Ravivooda – Yes wording is ambiguous and possibly who will not find this to turn up on exam like above