2. Assuming in December of 2014, the term structure of Treasury securities inclu

Question

2. Assuming in December of 2014, the term structure of Treasury securities included the following rates: Security Annualized Yield (%) 3-month bill 4.50 6-month bill 4.57 1-year note 4.52 2-year note 4.51 3-year note 4.48

a) The six-month annualized yield expected in the second half of year 2015 (forward rate for 6-month bill in June 2015)

b) The one-year expected yield for year 2017 (forward rate for 1-year note in December 2016)
c) Suppose the 8-year spot interest rate is 8 percent and the 3-year spot rate is 4 percent. What is the implied forward rate on a 5-year bond originating 3 years from now?

d) Suppose the 5-year spot interest rate is 6 percent. Under the expectation hypothesis the forward rate on a 3-year bond originating 2 years from now was estimated. The estimated forward rate is 5.5 percent. What is the 2 -year bond spot rate?

Explanation / Answer

2a) Given rates convered to semiannual

=[(1+4.52%/2)^2/(1+4.57%/2)]-1

=2.29% and for annual it is 2.29%*2=4.57%

2b)[(1+4.51%)^2/(1+4.52%)]-1

=4.5%

c)The formule used is
[[(1+y8)^8/(1+Y3)^4]^(1/5)]-1
=[[(1+8%)^8/(1+4%)^4](1/5)]-1
=10.47%

d)5.5%
[[(1+y5)^8/(1+Y2)^2]^(1/3)]-1
=[[(1+6%)^8/(1+y2%)^1](1/3)]-1
by solving we get y2=5.5%

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