Exposure of bonds

[George Bilkis]

If a bank purchases a bond for discounted value, what is then the exposure?
The PRM handbook says that the exposure of the bond is its face value.

Is it different for initially (at issue) discounted bonds or bonds purchased on secondary market?

Another question: if a bank purchases bonds (on the secondary market), are they accounted in the trading book or banking book?

Thanks,
G

[Jens Kroeske]

I think you need to distinguish between ‘legal claim amount’ (what you claim for in a bankruptcy court) and the somewhat loosely defined notion of ‘exposure’. For a bond, the legal claim amount is the notional amount plus accrued interest (see PRM Handbook III.B.2.6). Exposure should ideally be the replacement value (i.e. what you get in the market for it), which might not always be easy to determine and which might be substantially different from the legal claim amount.

With regards to your second question my guess would be that it depends on whether the bank intends to hold the bond to maturity or whether it intends to actively trade it.

Hope this helps

[George Bilkis]

Thanks for the reply.

I would expect exposure to be not a loosely defined term as a bank has to use it in order to calculate the regulatory or economic capital, and a bank has to chose which number it is going to use.

The PRM Handbook defines exposure for bonds in III.B.3 as “notional + mean accrued value”.

In one of the questions here (riskprep.com) in simulated exams, exposure was defined as a price paid for the loan on the secondary market, i.e. marked-to-market value of the loan.

My question is regarding this discrepancy in definitions between PRM handbook and Riskprep.com?

Question with numbers:
A loan to corporate customer was purchased for 96USD (bank paid 96USD to another party)
Notional amount on the loan: $100, no coupons.
Time to maturity: 1 year
Implied interest rate (continuous compounding) = ln(100/96) = 4.08%
Bank intends to hold the loan till maturity (i.e. banking book, credit risk)

What is the exposure immediately after the deal: is it $96 (market value) or $100 (notional amount)?
What is the exposure 6 month after (6 month before maturity), market value is no longer observable.

Is it the notional discounted with the same discount rate, that is (I assume continuous discounting):
discounted value 6 months prior to maturity: 100*exp(-0.0408*0.5) = $97.98

or is it still $100?

G

[Jens Kroeske]

Let me clarify what I meant by ‘loosely defined term’; In the PRM handbook it is mentioned (III.B.3.1) that ‘in practice many simplifications are used when exposure amounts are estimated’. And later on (III.B.3.3) it says with regards to fixed coupon bonds that ‘A common approximation is to set the exposure constant until maturity’. All this, I think, refers to how ‘exposure is actually handled in practice.

The FRM handbook is actually a bit more precise and defines ‘current exposure’ as Max(PV,0). It also discusses ‘potential exposure’ which can only be estimated given an assumption about the distribution of underlying risk factors. Both would have to be estimated by the institution (rather than being strictly defined).

Therefore I personally would answer your question in the following manner:

1. The current exposure is the current market value, i.e. 96USD at the time of purchase and a best guess at the market value at any time between purchase and maturity.
2. The potential exposure depends on the how you would model the relevant interest rate and the confidence.
3. In practice institutions would probably get away with saying that the exposure is simply the notional amount + accrued.

Anything more sophisticated sounds to me like spurious accuracy given the large uncertainly in other parameters (PD, LGD), but I accept that this is of little help in an exam.

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