Interest Rate Swaps

[allalongthewatc]

Hello All,
I am not sure about this one:
Example – Bank A enters into a $1M quarterly-pay plain vanilla interest rate swap as the fixed rate payer of 6% based on a 360-day year. The floating-rate payer agrees to pay 90-day LIBOR plus a 1% margin. 90-day LIBOR is currently at 4%. Calculate amounts Bank A pays or receives 270 days from now.
90-day libor rates are :

• 4.5% 90 days from now.
• 5% 180 days from now.
• 5.5% 270 days from now.

OA = $0
Here’s what I did :
270 days libor = 5.5%; Add Margin => 6.5%
Therefore, outstanding payment = {(fixed rate) * 270/360} - {6.5% * 270/360 } = -0.0375%*$1M =$-3750, which is wrong unfortunately.
Can someone please help me what I am missing here?
Question #2- What’s the difference between these two terms? “90-day LIBOR is currently at 4%.” and “90-day libor rate is 4.5% 90 days from now.” Why are these two rates different (i.e. 4% and 4.5% – aren’t these 90-day Libor)? Can someone please also talk about this? I would appreciate any help.
I understand that if 90-day Libor is say 5%, effective rate = 5% * (90/360). Now, I don’t know what’s the difference between the two terms above.
Thanks in advance.

 

[adekunle]

Question 1: The LIBOR to be used is the 180 days LIBOR, I.e., 5%+ the 1% margin, that’s 6%, hence, the 0 net pay. The LIBOR rate used is usually that of a period before the actual period, why? I’m not sure. I think the rate is usually set in advance.
Question 2: I don’t know

 

[carthurj]

Question 1: that is right adekunle, for the floating side the rate is reset at the beginning of each period, with payments at the end of the period. so they both pay 6% for that 3 months, so on a net basis, the payment is zero.
Question 2: the difference is that the first term is a spot rate for 3-month libor (90 day libor is right now…) the second term is a forward rate for 3-month libor (what it will cost to borrow for 3-months, starting in 3-months).

 

[allalongthewatc]

carthurj wrote:
Question 1: that is right adekunle, for the floating side the rate is reset at the beginning of each period, with payments at the end of the period. so they both pay 6% for that 3 months, so on a net basis, the payment is zero.

Thanks for your response. I still didn’t understand why we chose 180-day LIBOR for this one. Is this a convention? Do you mind explaining this a bit.

 

[S2000magician]

allalongthewatchtower wrote:

carthurj wrote:Question 1: that is right adekunle, for the floating side the rate is reset at the beginning of each period, with payments at the end of the period. so they both pay 6% for that 3 months, so on a net basis, the payment is zero.

Thanks for your response. I still didn’t understand why we chose 180-day LIBOR for this one. Is this a convention? Do you mind explaining this a bit.

Swap floating rates are set in advance but paid in arrears; i.e., the floating rate that is paid at time t is the current rate at time t – 1. For a quarterly-pay swap, time is measured in 90-day chunks, so the current floating rate on day 0 is paid on day 90, the current floating rate on day 90 is paid on day 180, the current floating rate on day 180 is paid on day 270, and so on.
By the way, make sure that you’re using the terminology correctly (it’ll help solidify your understanding). You’re not using 180-day LIBOR: 180-day LIBOR is an interest rate for a 180-day loan. You’re using 90-day LIBOR, but you’re using the 90-day rate that is current (i.e., is the market rate) 180 days after the start of the swap.

 

[adekunle]

S2000magician wrote:

allalongthewatchtower wrote:

carthurj wrote:Question 1: that is right adekunle, for the floating side the rate is reset at the beginning of each period, with payments at the end of the period. so they both pay 6% for that 3 months, so on a net basis, the payment is zero.

Thanks for your response. I still didn’t understand why we chose 180-day LIBOR for this one. Is this a convention? Do you mind explaining this a bit.

Swap floating rates are set in advance but paid in arrears; i.e., the floating rate that is paid at time t is the current rate at time t – 1. For a quarterly-pay swap, time is measured in 90-day chunks, so the current floating rate on day 0 is paid on day 90, the current floating rate on day 90 is paid on day 180, the current floating rate on day 180 is paid on day 270, and so on.
By the way, make sure that you’re using the terminology correctly (it’ll help solidify your understanding). You’re not using 180-day LIBOR: 180-day LIBOR is an interest rate for a 180-day loan. You’re using 90-day LIBOR, but you’re using the 90-day rate that is current (i.e., is the market rate) 180 days after the start of the swap.

What I don’t understand is, if I know my current fixed rate exposure is less than the LIBOR exposure, why enter the swap when I know I’ll have to pay in the end? What’s the incentive? My thoughts have always been “it is unknown, you don’t know if you’ll gain or lose, so you just take a stab at it” and with that understanding, I’ve gotten a fair number of questions right.

 

[S2000magician]

The incentive is that you expect in the future to receive higher payments than you’re paying, so that the expected present value is zero.

 

[allalongthewatc]

Hello S2000magician,

S2000magician wrote:
Swap floating rates are set in advance but paid in arrears; i.e., the floating rate that is paid at time t is the current rate at time t – 1. For a quarterly-pay swap, time is measured in 90-day chunks, so the current floating rate on day 0 is paid on day 90, the current floating rate on day 90 is paid on day 180, the current floating rate on day 180 is paid on day 270, and so on.

Thank you so much for your response. I have two follow-up questions. How do we know the length of the chunk? For instance, in the example above, is it “The floating-rate payer agrees to pay 90-day LIBOR plus a 1% margin”? However, here 90-day LIBOR is a spot rate. I am not sure whether I can equate chunks to spot rate. The question doesn’t mention the frequency of payment. I could be wrong in questioning the question. However, please help me.

S2000magician wrote:
By the way, make sure that you’re using the terminology correctly (it’ll help solidify your understanding). You’re not using 180-day LIBOR: 180-day LIBOR is an interest rate for a 180-day loan. You’re using 90-day LIBOR, but you’re using the 90-day rate that is current (i.e., is the market rate) 180 days after the start of the swap.

Thank you for correcting me, S2000magician. I believe 90-day LIBOR is a spot rate, and 90-day LIBOR 180 days from now is a future rate. I was a bit confused when I wrote that post. I hope I am correct now. Please let me know your thoughts.
Thanks in advance

 

[S2000magician]

allalongthewatchtower wrote:Hello S2000magician,

S2000magician wrote:Swap floating rates are set in advance but paid in arrears; i.e., the floating rate that is paid at time t is the current rate at time t – 1. For a quarterly-pay swap, time is measured in 90-day chunks, so the current floating rate on day 0 is paid on day 90, the current floating rate on day 90 is paid on day 180, the current floating rate on day 180 is paid on day 270, and so on.

Thank you so much for your response. I have two follow-up questions. How do we know the length of the chunk?

It’s the time between payments.

allalongthewatchtower wrote:For instance, in the example above, is it “The floating-rate payer agrees to pay 90-day LIBOR plus a 1% margin”? However, here 90-day LIBOR is a spot rate. I am not sure whether I can equate chunks to spot rate. The question doesn’t mention the frequency of payment. I could be wrong in questioning the question. However, please help me.

The applicable LIBOR rate is always the rate for the time between payments. If you make payments every 90 days, you use 90-day LIBOR. If you make payments every 180 days, you use 180-day LIBOR. And so on.
Here, it’s a quarterly-pay swap: payments every 90 days. Use 90-day LIBOR.

allalongthewatchtower wrote:

S2000magician wrote:By the way, make sure that you’re using the terminology correctly (it’ll help solidify your understanding). You’re not using 180-day LIBOR: 180-day LIBOR is an interest rate for a 180-day loan. You’re using 90-day LIBOR, but you’re using the 90-day rate that is current (i.e., is the market rate) 180 days after the start of the swap.

Thank you for correcting me, S2000magician. I believe 90-day LIBOR is a spot rate, and 90-day LIBOR 180 days from now is a future rate. I was a bit confused when I wrote that post. I hope I am correct now. Please let me know your thoughts.
Thanks in advance

Their language wasn’t as clear as it could have been. If I talked (today) about 90-day LIBOR 180 days from now, you’re correct: it’s a forward rate. (Note: forward rate, not future rate.) What they were trying to convey is that these are not rates known today; what they meant is that the (i.e., today’s) current 90-day LIBOR rate is 4.0%, if we wait 90 days, we’ll see that the (then) current 90-day LIBOR rate is 4.5%, if we wait 180 days, we’ll see that the (then) current 90-day LIBOR rate is 5.0%, and so on.

 

[allalongthewatc]

Thank you S2000magician. Apart from these and FRNs, do you know any other security for which payments are made in arrears? This is just out of my curiosity and general knowledge. Thanks in advance.
Best regards