Derivatives. Question 9. Reading 40. Value of Floating Side.

Hi, I am trying to work my way through derivatives and has been doing well during the blue boxes in Schweser and also read the post on analyst forum regarding swaps where we look at each payment in terms of $1. Is this possible in this question?

  1. Entered into Swap 1 year ago, ends in 2 years.
  2. Amount: 50 000 000
  3. Fixed Swap Rate (Since inception): 3%.
  4. Current equilibrium 2 year swap rate is 1%. ( I do not understand what this means).
  5. Annual Resets.

Discount factors:

Year 1: 0.990099

Year 2: 0.977876

Year 3: 0.965136

My Calculations:

PV of Fixed side payments:

Year 1: 0.03 x 0.990099 = 0.029703

Year 2: 1.03 x 0.977876 = 1.007212

Value of fixed side: 1.036915

How can I based on the information above calculate the value of the Floating Side?

To arrive at the correct answer, I need to arrive at a Value of 0.997556 for the Floating Side. But how do I get to this number?

Value Fixed Rate Payer = ( Value Floating(??) - Value Fixed ( 1.036915)) x USD 50.000.000 = - USD 1 967 975.

Thanks for the help!

There are two years remaining, so add up the Year 1 and Year 2 PV factors to get 1.967975

The equilibrium swap rate is the rate at which you would be able to lock in a new swap. You are currently locked in at a 3% rate, when you COULD be locked in at a 1% rate instead.

(.03-.01) * 1.967975 = 1,967,975

That is your answer. Maybe this excerpt from the curriculum will help: “We now turn to interest rate swap valuation. Following a similar pattern as forward contracts, Exhibit 18 shows the cash flows for a receive-fixed interest rate swap initiated at Time 0 but that needs to be valued at Time t expressed per unit of the underlying currency. We achieve this valuation through entering an offsetting swap—receive-floating, pay-fixed. The floating sides offset, leaving only the difference in the fixed rates.

@AnalystDude123 - Having dejavu…

Thank you sir. That is very helpful. Instead of trying to value the floating side like I did above, I can use this approach for similar questions. Much simpler. Thank you. Is anyone also knows how I can value the floating side to follow my top approach, that would be very interesting to know. Thank you.

@ejs190 yeah me too haha. Maybe he should check the Schweser errata.

Sorry if this is an old topic, however I am stuck on the same question.

My question is, why do we use the PV terms for year 1 and year 2? My intuition would have told me to use the PV terms for year 2 and year 3, as we would like to know the value at t=1 (which means we discount the year 3 value by the year 3 PV term and the year 2 value by the year 2 PV term).

Somehow it doesn’t really make sense to me. Can anyone please clarify?

Many thanks.

There’s an error in this question: the quoted fixed swap rate is wrong.

I alerted CFA Institute about it back in February.

Check the errata.