Pricing a swap greater than one year correct, annual

stockjaguar

If the one year spot rate is 5%, the two-year spot rate is 5.5%, and the three year spot rate is 6%, the fixed rate on a 3-year annual pay swap is closest to:

A) 5.96%.

B) 1.99%.

C) 4.50%.






Your answer: B was incorrect. The correct answer was A) 5.96%.


The fixed rate on the swap is: [1-(1/1.06^3)]/[(1/1.05)+(1/1.055^2)+(1/1.06^3)]

=1-0.8396 / [0.9524 + 0.8985 + 0.8396]

=0.1604/2.6905 = 5.96%


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My Q: For each consecutive year why do they take the corresponding exponent on the denominator? I would expect that, since for Day N you multiply the rate only on the denominator by day N's fraction over 360, you can do the same if it's more than one year.

For example, in my calc, for year 2 I did: 1 / [(1 + (0.055)(720/360)]. They however did 1 / [(1 + 0.055)^2).

RepoToronto

720/360=2...
1080/360=3

I see you are asking the question about why they are using the to the power of, instead of the * by notation .... that is a Schweese only please phenomenon....

they have done the same on one of the end-of chapter session exam questions as well.

CP



Edited 1 time(s). Last edit at Saturday, May 8, 2010 at 05:28PM by cpk123.

wilslm

even if you did it the usual way = you get 5,65% and A) is the closest answer.

CP

firat

elcfa: CFAI wont be that generous on exam day and will give better answer choices.

cpk: have u seen a problem like this in cfai books? if so, do THEY calculate it "correctly" i.e. multiplying the rate in the denominator by the Nth year?

spreads

they expect us to multiply it in CFAI world

CP

tianxin

elcfa Wrote:
-------------------------------------------------------
> Actually, you don't need to calculate since the
> swap rate need to be around to the average of the
> 3 spot rates (esp in the classic positive slope
> yield curve), thus eliminate the two other
> options.

average of forward rates not spot rates

1y forward rates are roughly 5, 6, 7. average 6.

kickthatcfa

CP

You are correct in less than one year case.
However, for multi year case, it is normal to compound, i.e., 1/(1+z)^n.

Suggest you guys check back to level I, bootstrapping method to see what I am talking about.

Rasec

Is LIBOR quoted that far out in practice?

I would say Scweser is correct conceptually since the question does not say LIBOR. Whole different twist to this if it is LIBOR or plain gov yield curve

needhelp1700

There is a logic behind using 1+0.06(90/360) versus (1+0.06)^90/360, which has to do with whether you are compounding the rate or not... but don't ask me to explain!

wxs1986

I should say LIBOR quotes in intervals less than a year ( hence the interpretation of add-on rates ) , but this question literally begs you to compound because the intervals are 1 year and above . ( clearly not LIBOR )