# spot rate - question

a 3-year option free bond with 9% annual coupon rate has a yield to maturity of 9%. 1-year spot rate and 2-year spot rates are 6.5% & 7.0% respectively. 3 year spot rate is closet too? Answer is 9.2 ( Please explain & show calculation)

shahravi123 Wrote: ------------------------------------------------------- > a 3-year option free bond with 9% annual coupon > rate has a yield to maturity of 9%. 1-year spot > rate and 2-year spot rates are 6.5% & 7.0% > respectively. 3 year spot rate is closet too? > > Answer is 9.2 ( Please explain & show calculation) gimme 90 secs

you got it !

you need to use the bootstrapping method

p.s. daj its been like 8 minutes

i lost my mind on this one , going to FI books and crushng my chinese food which just arrived, see everyone much later

9% coupon 1 year spot 6.5% 2 year spot 7.0% 3 year spot is ?? 9/1.065 + 9/1.07^2 + 109/(1+r)^3 = 100 solve for (1+r)^3

then solve for r

9/1.065 + 9/(1.07^2) + 109/(1+r^3) = 100 correct?

yep…just make sure that if the bond was trading at a premium or discount, you used that instead of 100. Since the coupon = the ytm, this bond trades at par. And for practical purposes, the most accurate spot rate is based off of coupon bonds tradng at par.

YES, I never understood the whole concept of spot and forward rates… I hope, question similar to this appears on exam, or else I have another weapon called - GUESS !!

Well given that the YTM is the same as the coupon, plug in 9% under the PV of year 3 and it gives you 100\$ which is the FV of the bond… I’m a bit lost, I find it weird that the YTM and coupon are the same unless I’m confused. What are the options from A–D?

knowing S2 = .07 1.07^2 = (1.065)(1+1f1) 1f1 = .075 90/1.065 + 90/(1.065*1.075) + 1090/[(1.065)(1.075)(1+x)] = 1000 solve for x = .1376 = 1f2 (1+S3)^3 = (1+S2)^2 * (1+1f2) (1+S3)^3 = (1.07)^2 * (1.1376) Solve for S3 = 9.2 please tell me there’s an easier way to do it…took like 5 minutes… EDIT: nevermind. coulda just done regular boostrapping. kill me now…