# Pricing a swap greater than one year

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% ---- 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).

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.

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

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.

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?

they expect us to multiply it in CFAI world

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.

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.

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

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!

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 )

pfcfaataf Wrote: ------------------------------------------------------- > 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. I agree, but I am talking about a short cut here. Therefore, I was mentioning about positive slope yield curve. In this case, the average forward rates will for sure stay above the average spot rates, thus eliminate the two other options. If I were to calculate the forward rates to do a shortcut, I may as well do the complete swap calculation.

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as some of mentioned, these are not libor rates. there is no mention of libor in the question–theyre just called spot rates. therefore i guess it is right to take the e xponent. and its highly unlikely to see libors for over one year.