Please help to explain the answer
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.
Correct Answer: A
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
Comments
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.
@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". ?