Stuart D Moncrieff
Member
There was a question that seemed to be as follows (the numbers are wrong but the idea is the same, I think):
There are three grades of bonds. AA, BB and C. P(default) for each of them is 0.1, 0.25 and 0.4. If a bond defaults, what is the probability that it is a BB or C bond?
The way I calculated it was as such: (0.25+0.4)/(0.1+0.25+0.4).
Please correct me if I am wrong. Also please correct me if I am remembering the question wrongly.
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Another question on margin requirement. I got the loss on Day 1 as 54,000. As the initial margin is 8000*4 = 32,000, this meant the balance at the end of Day 1 was 32,000 - 54,000 = -22,000.
What is the answer for the status of the account on Day 2? I put it as a variation margin of 54,000...is that correct?
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There was a question on hedging with DV01. I can't recall which I used as the denominator, but I got a hedge ratio of 0.5, therefore half the amount of the current position required to hedge. In my case, I believe the current position was 48mil and so the hedge amount was 24mil (could be wrong with the figures but this is the idea).
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There was a question to find the std dev and covariance of returns of three data that were provided. I used the formula as SUM[(X - Xbar)*(Y - Ybar)]/(N-1) for the covariance and a similar formula for the std dev. I know the answer I got was 0.04 for std dev and 0.0016 for covariance. However, the other answer was 0.03 for std dev and 0.11 for covariance. For this question, was the denominator for the std dev and covariance just supposed to be N or N-1? In my case I took it as N-1 but am not certain about it.
I thought that since the price remained unchanged on the second day the variation margin should have been 0 since the margin should be updated daily. I wasn't certain though.
For the probability question I remember I constructed a table like David used most in his examples - method was similar to you but I think I might have applied the odds of it being an AA, BB or C bond on top of the probability of defaults. Can't quite remember the wording of the question but I remember constructing the table.