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Hi all,
Prepping like crazy, writing on the 4th July so would really appreciate any help!
1. RAROC, page 37 – How do they get to the Debt values in Table III.0.2 and the Asset and EC values in Table III.0.3?
2. Historical VaR, page 89 – How do they calc the AW weights? I know they refer to EWMA but I can’t get the same values.
3. CreditMetrics, page 289 & 299 – For the life of me I don’t get 0.7365 for the joint probability, or 0.000054 for the joint probability of default, or the correlation of 0.019. Driving me crazy!
Any help would be awesome!Regarding AW weights, the first one for Age = 5 is 0.97^4/[((1-0.97^150)/(1-0.97)]= 0.02684. So the numerator is lambda^(Age-1). The denominator is the sum of all of the lambda’s for 150 days, which is the sum of a geometric progression: 1, lambda, lambda^2, lambda^3,……. The reason for using (Age-1) as the exponent for lambda in the numerator is that the most recent observation for 1 day ago is just the value, while for two days ago it is lambda^1, and for 3 days ago it is lambda^2,…
As for RAROC, I’m as perplexed as you. Is it possible that there are errors in the tables. The top table for Asset 2 has EC = 3.8, whereas it should be 3.6. So that’s definitely one error. Are there any others?
As for the CreditMetrics material, how are you checking the value of 0.7365. As far as I understand it, you would need to use a table, or similar, for the Bivariate Normal Distribution. I think it’s pretty tricky to do these calculations (I tried something approximate using Excel and got 0.7387 as opposed to 0.7365), so I just accepted the textbook figure as being true. You would similarly need to use the Bivariate Normal Distribution to check that the Prob (rA < -3.24,rBB<-2.3)=0.000054. These z-values are the Default z-value thresholds for A and BB entities as per table III.B.5.8. But once you accept 0.000054 as being true, then the default correlation works out as 0.019 using formula III.B.5.1 with p1=0.0006, p2=0.0106 and p12=0.000054. Remember that asset return correlations and default correlations are not the same. So don't put asset return correlations into formula III.B.5.1.
Well that’s my somewhat limited knowledge of this area – so I can’t guarantee that what I have said is correct!Jim
Great, thank you so much that really helps! If I may ask one more thing…
Page 235, value of interest rate swap – how do they calculate the value of the annuity?
Thanks again!I can’t reproduce the figures exactly, not sure why. But for example, take the bottom table for Time = 6 with floating rate = 11.87%. So at time = 6 there is 4 years to go to reach the maturity of the 10-year swap. I thought that the value of an annuity at time t=6 should be 1/1.1187 + 1/1.1187^2 + 1/1.1187^3 + 1/1.1187^4 = 3.05, but the textbook has 3.09.
Now take the top table for time= 7 years and rate = 4.13%. I figured that the annuity should be 1/1.0413 + 1/1.0413^2 + 1/1.0413^3 = 2.77 while the texbook has 2.79. I keep seeing these smallish discrepancies everywhere.Jim
OK, I was trying the same method and thought I was missing something basic because I couldn’t get the same values.
Thanks Jim!Jim,
Thank you for answering the questions – in agreement with you on the small differences in the annuity factors.
Wanted to add to the question re the RAROC calculations on page 38. Obviously, the 3.8 in the table is a typo, it should be 3.6 (as even the cross totals for the table don’t tie up unless this value is 3.6).
The debt values in Table III.0.2 are equal to the difference between the asset values and the EC value. Essentially the way this table works is that for each asset invested in (ie the 60 and the 40), calculate the maximum allowable debt that the asset can support assuming the worst case at the desired confidence level occurs. So if there is an asset of say, $100, and at the end of the year it could end up at at $65, then the economic capital required against such an asset is $35 and $65 will be max debt to hold against this asset without having to go into default.
In this case, for Asset Class 1 (the $60 asset), the rate of return is 7%, and the debt grows by 5%. The max rate of loss is 18%. This means the max debt this asset can support at the end of the year without going bust (ie asset ends up less than the debt) is $60*1.07/1.05*(1-18%) = 50.137. (Note that we are dividing by 1.05, this is to account for the fact that the debt has to be discounted back to today’s dollars.) The economic capital is the balance, ie 60 – 50.137 or 9.86.
The calculations for Asset Class 2 are identical.
Now Table III.0.3 is similar, ie Assets – Debt = EC. But the values in the ‘assets’ line are hypothetical ones, ie the realized value at the end of the year (as the worst case loss of 18% did not occur). Wish the authors of the chapter had mentioned this because I am confident that nearly everyone who read this has tried various calculatory combinations to see if they could get to the same number…only to realize after a while these were just made up numbers. The ‘Debt’ row numbers are nothing but the initial debt values from the previous table multiplied by 1.05.
Given I am responding a bit too late, unsure if this will be of help, but maybe someone else might be saved some time in the future.
Best regards,
Mukul
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