Need Help with a Swap Rate Curve Problem!

CFA Level II
#1

Below is a blue box question in Schweser for a Swap rate curve problem on page 143 in the fixed income section. Sadly, I seem to be having a problem with the algebra and don’t know how they are coming up with the answer. It feel like they have skipped a step or two to get to the answer. Any assistance would be appreciated.

Example: Swap rate curve

Given the following Libor spot rate curve, compute the swap fixed rate for a tenor of 1, 2 and 3 years (i.e., compute the swap rate curve).

Maturity Spot Rate

1 3.00%

2 4.00%

3 5.00%

Answer:

  1. SFR1 can be computed using the equation:

SFR1/(1+S1) + 1/(1+S1) = 1

SFR1/1.03 +1/1.03 = 1; SFR, = 3.00%

  1. SFR2 can be similarly computed:

SFR2/(1+S1) + SFR2/(1+S2)^2 +1/(1+S2)^2 =1

SFR2/1.03 + SFR2/(1.04)^2+ 1/(1.04)^2 =1; SFR2 = 3.98%

  1. Finally, SFR3 can be computed as:

SFR3/(1+S1) + SFR3/(1+S2)^2 +SFR3/(1+S3)^3 +1/(1+S3)^3 =1

SFR3/1.03 + SFR3/(1.04)^2 + SFR3/(1.05)^3 + 1/(1.05)^3 = 1; SFR3 =4.93%

I think I know how they come up with 3% in answer 1 (but please provide your thoughts on this problem as well), but I am not sure how they come up ith 3.98% and 4.93%, any help would be appreciated.

You may already know but the “^2” and the “^3” notations represent square root and cubed root functions. I couldn’t find a way to superscript on the site.

#2

think of finding the swap fixed rate leg as using discount factors and follow accordingly

ie.

2yr SFR= 1-S^2( 2yrSpot rate discount factor)/(S1 discount factor + S2 discount factor)

1yr discount factor= 1/1+.03=.97087 2yr discount factor= 1/(1+.04)^2=.92455

2yr SFR= 1-.92455/(.97087+.92455)= 3.98%…

the 3yr SFR = 1-S3^3 (discount factor)/(S1+S2+S3(all discount factors))

I know its tricky but keep going through problems w/ this formula and see how quick it you will pick it up. Hope this helps a bit

#3

I wrote an article on pricing swaps that covers exactly this issue: http://financialexamhelp123.com/pricing-plain-vanilla-interest-rate-swaps/

#4

Exact Article that REALLY helped me understand! thanks S200magician, and looking forward to class on Sat

#5

Glad to hear.

But why do you discount me by 90%?

#6

*discount unintended * S2000magician