Suspected Mistake in Level I Annotated Boot Camp

[Liming]

Dear David,

Can I check with you if the following practice question answer is wrong?

Question 26:
A bank holds USD 60 million worth of 10-year 6.5% annual coupon bonds. Assume LIBOR is flat (i.e., same for all maturities) at 6.25%. (Note: annual coupons implies annual compounding). The bank is worried by the exposure due to these bonds but cannot unwind the position for fear of upsetting the client. Therefore, it purchases a total return swap (TRS; a.k.a, TROR) in which it receives annual LIBOR + 100 bps in return for the mark-to-market return on the bond. For the first year, Libor is set at 6.25%.

26a. By the end of the year, LIBOR increases to 6.6%. What is the bank‘s (i.e., the TROR payer) net receipt/payment?
Your Answer: By the end of the year, LIBOR increases to 6.6%. What is the bank‘s (i.e., the TROR payer) net receipt/payment? Bond price @ Beg Year = PV(6.25%, 10, $6.5, 100) = $101.82 Bond price @ End Year = PV(6.6%, 9, $6.5, 100) = $99.34 Bank receives: (6.25%+1%)*$60 MM = $4.35 million Bank pays: (6.5% * $60 MM) + [(99.34% - 101.82%)*$60 MM] = $2.41 million Net bank receives = $1.94 million

I think the blue figure was input incorrectly as the LIBOR rate at the beginning of the year. I think it should be 6.6% to reflect the LIBOR rate change that occurs by the year end.

Thank you for your opinion!

Cheers
Liming
16/11/09

 

[Liming]

Err.. Now I think I may be wrong.. as the receipt from Total return swap floating leg should be accrued over the whole year, thus the LIBOR rate should be the rate set at the beginning of the year. Is this correct?

Thanks
Liming
16/11/09

 

[Liming]

Dear David,

May I also check with you concerning your answer to the added question 26f (see below)? Does a position "long a credit default swap + short a risk-free asset" equal to "short a bond", which is exactly the kind of position the bank in the question wants to establish so as to unwind the original bond position? Just like to long a bond, but opposite to it,
long a bond = short a credit default swap + long a risk-free asset ;
short a bond = long a credit default swap + short a risk-free asset

26f. Simulate the bank‘s position with (instead) a credit default swap (CDS) The bank can simulate with: long a credit default swap + short a risk-free asset, assuming the both CDS and TRS are marked-to-market.

Thanks!
Liming
16/11/09

 

[David Harper CFA FRM]

Liming,

The answer is correct as given: bank receives 6.25% + 1% because bank receives LIBOR (at beginning of period) + 100 basis points.
Bank pays the coupon plus the change in value.

Regarding 26f, yes that is correct:
long a bond = short a credit default swap (i.e., writing protection) + long a risk-free asset ;
short a bond = long a credit default swap (i.e., buying protection) + short a risk-free asset

to write a CDS (short the CDS) is to take a synthetically long position in the reference, then the additional "long a risk-free asset" is to address the funding: if you buy the bond, you invest the principal. But if you write CDS, you don't fund it, so this is the "diverted" principal

David