Question

Consider the following spot interest rates for maturities of one, two, three, and four years. 77 = 5.3% 12 = 5.9% 13 = 6.6% 14 = 7.4% What are the following forward rates, where fq. k refers to a forward rate for the period beginning in one year and extending for k years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Answer is complete but not entirely correct. f1,1 |(1,2 6.50 8.01 % 9.84 % % % f1,3

Answer 1

Forward Rate = [ (1 + S1)^ⁿ¹ / (1 + S2)^ⁿ² ] ^ ^[1/(n1-n2)] - 1

where

S1 = Spot Rate until a further future date

S2 = Spot Rate until a closer future date

F(2,1) means one year forward rate two years from now.

Considering this:

1) F(1,1) = [ (1 + 5.9%)^² / (1 + 5.3%)^¹ ] ^ ^[1/(2-1)] - 1

F(1,1) = [ 1.121481 / 1.053 ] - 1

F(1,1) = 1.065034 - 1

F(1,1) = 6.5%

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2) F(1,2) = [ (1 + 6.6%)^³ / (1 + 5.3%)^¹ ] ^ ^[1/(3-1)] - 1

F(1,2) = [ 1.21 / 1.05 ]^^(1/2) - 1

F(1,2) = [ 1.15 ]^^(1/2) - 1

F(1,2) = 1.0726 - 1

F(1,2) = 7.26%

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2) F(1,3) = [ (1 + 7.4%)^⁴ / (1 + 5.3%)^¹ ] ^ ^[1/(4-1)] - 1

F(1,3) = [ 1.33 / 1.05 ]^^(1/3) - 1

F(1,3) = [ 1.26 ]^^(1/3) - 1

F(1,3) = 1.0811 - 1

F(1,3) = 8.11%