The Analysis and Valuation of Bonds, Investment Analysis and Portfolio Management1. The following table shows spot rates on US Treasury securities as of January 1, 2019:Term to Maturity CalculatedSpot Rates1 Year 3.50%2 Years 4.50%3 Years 5.00%4 Years 5.50%5 Years 6.00%10 Years 6.60%Based on the data on the tablea) Calculate the one-year implied forward rate, four years from now.b) Calculate the 2-year implied forward rate, two years from now.

Question
Asked Aug 12, 2019

The Analysis and Valuation of Bonds, Investment Analysis and Portfolio Management
1. The following table shows spot rates on US Treasury securities as of January 1, 2019:
Term to Maturity Calculated
Spot Rates
1 Year 3.50%
2 Years 4.50%
3 Years 5.00%
4 Years 5.50%
5 Years 6.00%
10 Years 6.60%
Based on the data on the table
a) Calculate the one-year implied forward rate, four years from now.
b) Calculate the 2-year implied forward rate, two years from now.

check_circleExpert Solution
Step 1

a.

Calculate the one-year implied forward rate as follows:

(1+
f =
(1
-1
Here,
The one-year implied forward rate is "f"
The spot rate in year 4 is ""
The spot rate in year 3 is "
(1+)
(1+
f =
-1
(1+5.5%)
(1+5%)
1.238824650625
-1
1.157625
=1.070143311197-1
-0.070143311197 or 7.01%
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(1+ f = (1 -1 Here, The one-year implied forward rate is "f" The spot rate in year 4 is "" The spot rate in year 3 is " (1+) (1+ f = -1 (1+5.5%) (1+5%) 1.238824650625 -1 1.157625 =1.070143311197-1 -0.070143311197 or 7.01%

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Step 2

b.

Calculate the two-year implied f...

(1+72)
f =
-1
(1+)
(1+4.5%)
-1
(1+3.5%)
1.092025
1.035
1.05509661835749-1
0.05509661835749 or 5.51%
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(1+72) f = -1 (1+) (1+4.5%) -1 (1+3.5%) 1.092025 1.035 1.05509661835749-1 0.05509661835749 or 5.51%

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