HELP for approximation method to find Forward Rate

CFA Level I Fixed Income
#1

Hi

I cannot seem to get the correct answer when I tried the Approximation method to calculate the forward rate.

Please help!! Thank you so much!

Question:

Yrs to maturity - Spot Rate

0.5 - 4%

1.0 - 4.4%

1.5 - 5%

2.0 - 5.4%.

What is the 6 month forward rate 1 year from now? (0.5F1)

What is the 1 year forward rate 1 year from now? (1F1)

#2

2 × S1 + 0.5F1 ≈ 3 × S1.5

2 × 4.4% + 0.5F1 ≈ 3 × 5%

8.8% + 0.5F1 ≈ 15%

0.5F1 ≈ 6.2%

(The true value is 6.2053%.)

2 × S1 + 2 × 1F1 ≈ 4 × S2

2 × 4.4% + 2 × 1F1 ≈ 4 × 5.4%

8.8% + 2 × 1F1 ≈ 21.6%

2 × 1F1 ≈ 12.8%

1F1 ≈ 6.4%

(The true value is 6.4049%.)

#3

Correct…

#4

Sometimes that happens.

I usually lie down until it stops.

#5

When you are there… the only thing left for me to write is: “Correct” :slight_smile:

#6

Thanks!

#7

To simplify the calculation we need to make time line first,

0years—-4%(S1)----.5years----4.4%(S2)-------1years-----5%(S3)----1.5years----5.4%(S4)-----2years

To calulate 6 month forward rate 1 year from now.

(1+S3)^3 = (1+.5F1)(1+S2)^2

(1+5%)^3 = (1+.5F1)(1+4.4%)

1.1576 = (1+.5F1)(1.0899)

1.1576/1.0899 = (1+.5F1)

1.0621 = 1+.5F1

.5F1 = 6.21%( ANS )

And the second one is 1 year forward rate 1 year from now.

(1+S4)^4 = (1+1F1)^2 (1+S2)^2

(1+5.4%)^4 = (1+1F1)^2 (1+4.4%)^2

1.2341 = (1+1F1)^2 (1.0899)

1.2341/1.0899 = (1 +1F1)^2

(1.1323)^ .5 = 1+1F1

1.0641 = 1+1F1

1F1 = 6.41%(ANS)

#8

Unless this problem is ignoring the common convention in writing interest rates, this is incorrect.

The common convention in writing interest rate is to give annual, nominal rates; thus, you need to divide each by 2 before doing the compounding.

#9

couldnt agree more

#10

I love this! Finwizards all in a virtual world.