Question on Fixed-Floating Swap valuation

CFA Level II Portfolio Management
#1

A $10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8 percent. The fixed rate on the swap is 5 percent, current 90-day LIBOR is 5 percent and 270-day LIBOR is 5.4 percent. What is the value of the swap to the fixed rate payer?

What I did:

I find that the present value of the fixed-rate payments is:

(0.05*(180/360)*1) / [1+0.05*(90/360)] + (0.05*(180/360)*1+1) / [1+0.54*(270/360)] = 0.025/1.0125 + 1.025/1.405 = 0.754228724

First floating rate payment = 0.048 * (180/360) = 0.024

The market value of the rest of the floating payments is 1, so the present value of all the floating rate payments is: (0.024+1) / [1+0.05*(90/360)] = 1.011358025

So if the notional is $10million then the value of the swap to the fixed-rate payer is:

(10000000*1.011358025) - (10000000 * 0.754228724) = $2571293.01

Is this correct?

#2

NO!

2 Mill in 90 days… on 10 Mill $? You must be joking.

Fixed: 0.025 * 0.9877 + 1.025 * 0.9611 = 1.00982

Floating: 1.024 * 0.9877 = 1.0114048

Pay fixed, receive floating = -1.00982 + 1.0114048 = 0.0015848

or 15848 for 10 Million .

#3

Me got the result of 15,503 USD ( a bit different due to the rounding)

#4

Thank you people!! youve been really helpful :)). i went over the exercise again and got $15680 (rounding difference)…cash flows are the same as cpk123. i had no idea if i was close to the correct answer. thanks again

#5

A $10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8 percent.

Are we assuming this 4.8% LIBOR is a 180-days LIBOR 90 days ago?

#6

I get $20,571. Assume you pay fixed and receive float.

The fixed value now (after 3 months from initiation) = $10,097,947…basically, you will pay 5%/2 in 3 months, plus 5%/2 in 9 months, plus $10 million in 9 months.

The floating part pays $245,000 after 3 months, discounting to today = $241,975

Plus $10,000,000 due in 3 months = $9,876,543

Total floating part you will receive = $241,975 + $9,876,543 = $10,118,518

Difference = $10,118,518 - $10,097,947 = $20,571 that you will receive.

That’s my understanding.

#7

i get $15,603 so in the same ball park as most of the others. Dreary the floating part pays $240k in 3 months, i think that’s why your answer is a bit different

#8

Scary, in that I am comfortable with the workings, but running to 4 decimal places, gives me an answer of exactly 15000.

#9

ok, I see…good you noticed that.

What you are all assuming is that the swap resets every six months, which is fair to assume since it is a semi-annual pay bond… is this always the case? I don’t know, but I think it is possible that the swap rests every 3 months even if it is a semi-annual pay…in that case, the calculation might be different.