Forward Rate problem

CFA Level I
#1

how can you possible calculate this question in under 5min? is there like a shortcut forumla or somthing you can use?

Using the U.S. Treasury fwd rate provided below, the value of a 2.5 year $100 par value Treasury Bond with a 5% coupon rate is closest to:

Period Years Forward Rate

1 .5 1.2%

2 1 1.8%

3 1.5 2.3%

4 2 2.7%

5 2.5 3%

a) 101.52

b) 104.87

c) 106.83

#2

N=5 R=1.5 PMT=2.5 FV=100

#3

If I see a question like this one on the exam I’ll probably skip over it and do it last. Doing it the way specified in the answers not only takes a while to do but theres a high chance of making a calculator error.

#4

No that’s not how you do it. These problems take forever. I can’t believe there were 2 like these practically back to back on the mock.

1 Like
#5

a 101.52

Find the spot rates at each period

accum the rates

1.012

1.0302 = 1.012 * 1.018

1.0302 * 1.023 = 1.0539

1.0539 * 1.027 = 1.0823

1.0823 * 1.03 = 1.1148

2.5/1.012 + 2.5/1.0302 + 2.5/1.0539 + 2.5/1.0823 + 1022.5/1.1148 = 101.51

#6

NO! PROBLEM 106 afternoon.

THis is from the CFAI.

2.5/(1 + .012/2) + 2.5/(1.006*1.009) + 2.5/ (1.006*1.009*1.013) + 2.5/(1.006*1.009*1.013*1.0135)+ 102.5 / (1.006*1.009*1.013*1.0135*1.015)

#7

Ops. Thanks. I was wondering why it said forward rate …

#8

Yup, thegang has the correct answer ©.

#9

For questions like these sometimes you need to halve the rates and sometimes you don’t. Anyone know the reason? I’m guessing they’re always quoted at BEY and we’re supposed to know that. I think these questions class as: Leave, come back and spend some time on them at the end’.

#10

^I’m pretty sure for forward rates you divide by 2, don’t discount them, but instead multiply by each prior forward rate, i.e. coupon 1 divided by (1+period 1 forward/2), coupon 2 divided by [(1+period 1 forward/2)*(1+period 2 forward/2)]… and so on

And for spot rates you just discount each coupon by 1 + the corresponding spot rate

#11

You always adjust BOTH spot and forward rates to semiannual basis (divide by 2) whenever they are given in BEY form. When they are given in a 1-year rate form, you keep the rates as is.