# spot rates

1 year 4.40 2 year 4.75 3 year 5.00 Three year 5.25% bond that pays interest annually. Using the forward rates determine the approximate value of this bond. A) 98.75 B) 99.13 C) 100.52 D) 101.49 not sure how to solve this… I would ((1.0440 * 1.0475 * 1.05) ^ .3333333) -1 = .047 So do I use this to find the present value?

I’d go with D

D as well

My original answer was 100.7323 (i did not compound the interest semiannually.) PV of the first year’s 5.25 is 5.0287, 2nd year is 4.7847, 3rd year of principal + interest is 90.9189. Then I realized the rates it was given are the forward rates… not spot rates as I perceived from this thread’s topic. So my answer is D as well.

So what is the difference between spot and forward rate? spot = annual? forward = semiannual? Could someone please give the calculations on how you solved this problem… it is D? I’d look it up but I’m at work = )

I’d go with C. 5.25 / 1.044 + 5.25 / (1.0475)^2 + 105.25 / (1.05)^3 = 100.73 Please throw some light as to what the answer is and what the methodology to solve this is.

SConnery Wrote: ------------------------------------------------------- > So what is the difference between spot and forward > rate? > spot = annual? > forward = semiannual? > > Could someone please give the calculations on how > you solved this problem… it is D? > I’d look it up but I’m at work = ) Yes I am interested in knowing this information, and have read it 5 times. When I am reading it, it makes perfect sense, but trying to explain this i can’t remember a word.

The ans. is D [5.25 /1.044] + [5.25 /(1.044)(1.0475)] + [105.25 /(1.044)(1.0475)(1.05)] = 101.49 Thanks

sachin123 Wrote: ------------------------------------------------------- > The ans. is D > > [5.25 /1.044] + [5.25 /(1.044)(1.0475)] + [105.25 > /(1.044)(1.0475)(1.05)] = 101.49 > > Thanks which is: [Coupon/(1+f1)] +[Coupon/(1+f1)(1+f2)] + [Coupon/(1+f1)(1+f2)(1+f3)]

Here is how I would figure it out: on the CF on the calc: put in 5.25 in CF1, calculate NPV for I = 4.40 NPV = 5.03 clear CF put in 5.25 for CF2, CF1 = 0, calc NPV for I = 4.75 NPV = 4.78 put in 105.25 for CF3, CF1 = 0, CF2 = 0, calc MPV for I = 5 NPV = 90.92 add all NPVs together and I get 100.73 too. I think that is for spot rates though, not sure how to work in the fwd rates. I am checking.

Sachin, just found that in the LOSs on Schweser.

amberpower Wrote: ------------------------------------------------------- > Here is how I would figure it out: > > on the CF on the calc: > > put in 5.25 in CF1, calculate NPV for I = 4.40 > NPV = 5.03 > > clear CF > put in 5.25 for CF2, CF1 = 0, calc NPV for I = > 4.75 > NPV = 4.78 > > put in 105.25 for CF3, CF1 = 0, CF2 = 0, calc MPV > for I = 5 > NPV = 90.92 > > add all NPVs together and I get 100.73 too. > > I think that is for spot rates though, not sure > how to work in the fwd rates. I am checking. Man, if you look at the formula, you have just discount by 1. Hence, simply divide each coupon payment by the denominator

sachin123 Wrote: ------------------------------------------------------- > The ans. is D > > [5.25 /1.044] + [5.25 /(1.044)(1.0475)] + [105.25 > /(1.044)(1.0475)(1.05)] = 101.49 > > Thanks Good to know the calculation. (Haven’t gotten that far on how to calc. it yet) I just picked D b/c we know that when I rates go down the price of the bond goes up.

But rates in this example are going up, not down. So just based on that you would assume that the price of the bond went down. On the other hand, coupon is still > market rates, so bond trades at a premium. But you have to premiums as a choice. Just bear in mind that spot rates are “packages” of future rates that would produce the same value for asset being analyzed.

forward rates are the *forward looking rates*… (ya i like cyclical definitions) The 2nd year forward rate is interest rate you would earn had you invested on the first year. The 3rd year rate is the interest rate you would earn had you invested in the 2nd year. On the other hand the spot rate is current rate (year 0) you would earn had you held on to the money from year 0 to the year of maturity. Think of spot rates as the equivalent of bond’s yield to maturity. Man this is hard to explain, I give CFAI credit for it. They do a much better job. Which is why sachin is right: [5.25 /1.044] + [5.25 /(1.044)(1.0475)] + [105.25 /(1.044)(1.0475)(1.05)] = 101.49