CFAI Reading 42 Practice Problem 2

CFA Level II Fixed Income
#1

This question deals with bootstrapping and spot rates, you are given Exhibit 1 and 2 then asked which of three bond prices is correct.

Exhibit 1

Three-Year, €100 par, 3.00% Coupon, Annual Pay Option-Free Bond

Exhibit 2

Yield to Maturity Par Rates for One-, Two-, and Three-Year Annual Pay Option-Free Bonds

One-year Two-year Three-year 1.25% 1.50% 1.70% The answer is C 103.7815 Euros What I don’t understand is why Year 2 spot rate (z2): 100 = 1.5/1.0125 + 101.5/(1+z2)^2 = 0.015019 why is the coupon 1.5? Is that the BEY is that the Two-year YTM, it says in exhibit one a 3.0% coupon so I want to use 3 as the coupon. I’ve looked elsewhere online and I haven’t come up with a solid explination.

#2

I don’t see this in the 2015 curriculum.

Where is it located?

#3

I guess no one else started with the new and changed material… I swear it is in my digital copy.

#4

Remember what a par curve is: the coupon rate for bonds priced at par. Thus, the par rate for a given bond is its YTM (a bond will be priced at par if its coupon equals its YTM).

So, a 2-year bond priced at par will have a 1.50% coupon. A 3-year bond priced at par will have a 1.70% coupon.

The spot rates are derived like this:

_s_1 = 1.25%

100 = 1.50 / 1.0125 + 101.50 / (1 + _s_2)²

(1 + _s_2)² = 101.50 / (100 − 1.50 / 1.0125) = 1.030263

1 + _s_2 = 1.015019

_s_2 = 1.5019%

100 = 1.70 / 1.0125 + 1.70 / 1.015019² + 101.70 / (1 + _s_3)³

(1 + _s_3)³ = 101.70 / (100 − 1.70 / 1.0125 − 1.70 / 1.015019²) = 1.052023

1 + _s_3 = 1.017049

_s_3 = 1.7049%

Take it from here.

#5

I think the subject should be CFAI reading 43 not 42.