Question

Had enough yet? Okay, plow on for more. These should be free points by now. you have the following assumptions and spot rates - solve for the implied forward rates to t2 ??? ??? ??? 0.860% One-year rate Two-year rate Three-year rate Four-year rate ??? 1.120% 1.340% 1.840% at time t+1 (in one year) Implied forward 1 year rate,f al time 1+2 (in nvo years) Implied forward 1 year rate ,2f at time t+1 (in one year) Implied forward 2 year rate,f Implied forward I year rate ,.f at time t 3 (in three years) Implied forward 2 year rate ,f at time t+2 (in tnwo years)

Answer 1

Formula for the relationship between 2 spot rates & implied forward rate is given by

, where z refers to spot rate & IFR _A,B-A refers to forward rate for B-A periods after A periods

(1 + 2A)4+ (1+IFRA.B-A) B-A = (1 + <B)

a. Implied forward 1 year rate _t+1 f ₁ is the 1 year forward rate after 1 year:

Here A=1, B=2

So

(1+1)*(1 +IFR1,1)' = (1+2)

(1+0.0086) * (1+f ₁) = (1+0.0112)²

(1+f ₁) = (1.0112)² / 1.0086 = 1.0138

f ₁ = 0.0138 = 1.38%

b. Implied forward 1 year rate _t+2 f ₁ is the 1 year forward rate after 2 years:

A = 2, B = 3

So

(1+2)*(1 +IFR2.1)' = (1 + 23)

(1+0.0112)² * (1+f ₁) = (1+0.0134)³

(1+f ₁) = (1.0134)³/ (1.0112)² = 1.017814

f ₁ = 0.017814 = 1.78%

c. Implied forward 2 year rate _t+1 f ₂is the 2 year forward rate after 1 year:

A = 1, B = 3

So

(1+1)*(1 +IFR1.2) = (1 + 23)

(1+0.0086) * (1+f ₂)² = (1+0.0134)³

(1+f ₂)² = (1.0134)³ / (1.0086) = 1.031867

(1+f ₂) = 1.031867^ 0.5 = 1.015809

f ₂ = 0.015809 = 1.58%

d. Implied forward 1 year rate _t+3 f ₁is the 1 year forward rate after 3 years:

A = 3, B = 4

(1 + 3)*(1 +IFR3.1) = (1+2)

(1+0.0134)³ * (1+f ₁) = (1+0.0184)⁴

(1+f ₁) = (1.0184)⁴ / (1.0134)³ = 1.033549

f ₁ = 0.033549 = 3.35%