Question on RAROC numerator

[ahnnecabiles]

Hi David,

In the RAROC formula (and in Crouhy’s example):

RAROC numerator = Loan revenue (on the $1,000) + Return on EC (on the $75) – Interest Expense, i.e. cost of fund [on the $925 i.e. $1,000 (loaned) - $75 (required buffer)] – Operating Costs – Expected Loss

I just can’t get the rationale behind deducting interest expense (cost of fund) only on the $925 lent. Aren’t we supposed to deduct interest expense on the $1,000 lent? After all, our cost on this risky $1,000 loan is really our funding cost from the $1,000 deposits that we have gathered, unless the net proceeds of the loan is only $925, in which case the borrower is the one bearing the required capital charge? But the fact that we have added the return on the required buffer of $75, I think it is indeed more appropriate that we deduct the cost on the whole $1,000. What do you think? Thanks.

P.S. I also posted a question on Basis risk topic by Sridhar (‘Nagging questions on basis risk’), I just really want to know your view on my understanding of basis risk.

Thanks so much.

 

[David Harper CFA FRM]

Chinquee, OM, and jayamani:

You each surfaced an issue with the RAROC calculation, either Crouhy's example in the assigned reading (Capital Allocation and Performance Measurement) and/or my slide example on page 62 of OpRisk B. Please note, if you are interested, there is some discussion this year here; and even last year when we first identified the original "error" in Crouhy.

If you would like to see the illustration of the two versions, here they are on an EditGrid. On the left, my slide 62 example, on the right Crouhy's RAROC (two versions of each)

Why two versions? Because Crouhy has TWO prints of the chapter (where the only difference, with no errata/update/discussion, is the liabilities of 925 versus $1,000). The first print gives RAROC of 19.17% and the second print gives RAROC of 13.17%. The difference relates to the point you have raised: the deposits (liabilities) probably should match the loan (assets). Specifically, we (probably) should fund $1 billion in loan assets with $1 billion in deposit liabilities. In short, I agree with your point.

My slide 62 does not do this; because the exam has previously deducted EC from assets to get the liabilities (i.e., where Crouhy's example uses 950 liabilities and gets therefore a RAROC of 19.2% instead of the more recent 13.17%), I decided to maintain the original Crouhy approach as it was consistent with prior exam uses. But as the new print uses $1 billion liabilities, I wish i hadn't. So, i did not mean to confuse. You can see at the bottom of the XLS, I show the "balance sheet" perspective; this supports exactly your points, that if the balance sheet reconciles, $1 billion deposits should fund $1 billion liabilities.

You'll note in the Q&A;thread, Rajiv asked "what is correct for the exam?" to which I answered, "The exam question will (should) give you the deposits, you should not need to solve for the deposits."

Please let me know if a closer look at the XLS lends any insights/disagreements/etc.

Thanks,
David

 

[ahnnecabiles]

Thanks so much David.