Vanilla Swap question

[ammor]

Hi David,

This is a question i found in the FRM past exam, can you please provide me with detailed answer, should we convert the libor 5.75% to descrete or not?

"" A bank entered into a 4 year tenor plain vanilla swap three years ago. The agreements of the swap are to pay 6.5% annually, based on annual compounding a 30/360 day-count convention, fixed rate on a $50 million notional, and receive 1 year LIBOR. The continuously compounded LIBOR for 1 year obligations is currently 5.75%. The 1 year Libor at the beginning of the period was 6.25%. the value of the swap is closest to:
a) $110,000
b) $800,522
c) - $257,020
d) - $110,000

Thanks & Regards.

 

[David Harper CFA FRM]

Hi ammor,

I can't get any of the answers. Can you source it specifically, so that we might identify the possible error.

To answer your question: we don't need to convert the 5.75% to discount to PV;
however, IMO for purposes of the final floating coupon, we should indeed (ie., "agreement of the swap to pay based on annual compounding") pay the final floater on an annual basis: = 5.92% = EXP(5.75%)-1
.... i.e., determination of the future swap cash flows (yes, convert to annual in this case) is a separate issue from discounting (could be either)

I input into a modified version our IRS pricer: http://sheet.zoho.com/public/btzoho/0705-swap-ammor
(see rows 37 & 38 for final)

This assumes value at time 0 and including time 0 swap payments; i.e, = -400,000 125,000
... however, if excluding the time 0 and only including the final T+1 cashflows, then = -274,500
... due to this imprecision (unstated assumption) could be either, but i would have assumed to EXCLUDE time 0.

I have tried to change assumptions to reflect apparent imprecisions in the question, but i cannot find any answer that matches any given. I'd appreciate any answer you might have to see if i am mistaken or if the question misleads. Thanks!

David

 

[ammor]

Thanks David for your prompt reply,

I took this question from Scheweser Qbank, find below the Scheweser answer:

the correct answer was D) -$110 000

fixed rate component of the swap is 50*1.065*exp(-0.0575)=$50.27M
floating rate component 50*1.0625*exp(-0.0575)=$50.16M

Hence the value of the swap is 50.16M- 50.27M= -$110,000

This is completely wrong that's why i wanted your valuable Help ;-) .

They didn't convert the continuous rate to discrete.


Thanks David

 

[David Harper CFA FRM]

Ammor - thanks.

Another problem is: the floater must be worth par or ~50 (as this is immediately after a "coupon" payment). Put another way, the question discounts at a different 1-year LIBOR different than the 1st annual coupon (??), employing two different simultaneous LIBOR rates.

David