HELP for approximation method to find Forward Rate

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raffythebuggy

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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 × 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%.)
 
When you are there… the only thing left for me to write is: “Correct” :)
 
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)
 
edupristine wrote: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)
Click to expand...
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.
 
S2000magician wrote:
edupristine wrote: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)
Click to expand...
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.
Click to expand...
couldnt agree more
 
exotichedge wrote:
S2000magician wrote:
edupristine wrote: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)
Click to expand...
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.
Click to expand...
couldnt agree more
Click to expand...
I love this! Finwizards all in a virtual world.
 
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