Question about Swap Rate Curve (fixed income)

CFA Level II Fixed Income
#1

LOS 32.f, volume 5, page 25 (fixed income chapter)

In the example, it says the spot rate for maturity 1 is 3.00%, and therefore…

SFR1/(1+S1) + 1/(1+S1) = 1… plug 3% into S1, and…
SFR1 = 3.00%

however, SFR1 actually = 2.83% when you run the calculation

what is going on here? could someone please help me?

#2

Couldn’t find what you mentioned on Page 25 in the official 2020 textbook.

But assuming it’s a swap that is annually-pay, then the SFR1 should be 3%. Not sure how you computed 2.83% (or was it shown 2.83% in the book?).

\frac{SFR_1}{1+S_1} + \frac{1}{1+S_1} = 1

\frac{SFR_1}{1+ 0.03} + \frac{1}{1+0.03} = 1

\frac{SFR_1}{1.03} = 1 - \frac{1}{1.03} = \frac{0.03}{1.03}

SFR_1 = 1.03 \times \frac{0.03}{1.03} = 0.03 = 3\%

#3

Hey @fino_abama, thanks so much for coming to my rescue

You wrote 1-1/1.03 = 0.03/1.03 in line three, which i do not get

1-1/1.03 is the same as 1-0.97087, or 0.02912. when 0.02912/1.03, i got 0.0283 or 2.83%

am i doing something wrong?

#4

nevermind, i was being an idiot

#5

1 - \frac{1}{1.03} = \frac{1.03}{1.03} - \frac{1}{1.03} = \frac{1.03-1}{1.03} = \frac{0.03}{1.03}

Seems the error is coming from how you solve algebraic equations.

1 - \frac{1}{1.03} = 1 - 0.97087 = 0.02913

Then:

\frac{SFR_1}{1.03} = 0.02913

SFR_1 = 1.03 \times 0.02913

SFR_1 = 0.0300039 \approx 3\%

#6

thank you very much

1 Like
#7

When I run the calculation, I get 3%:

z_1 = \frac{1}{1.03} = 0.970873786
SFR = \frac{1 - z_1}{z_1} = \frac{1 - 0.970873786}{0.970873786} = \frac{0.029126214}{0.970873786} = 0.03 = 3\%
#8

yes, you are right. i was just being stupid

#9

We’ve all been there at one time or another.