girishkhare
New Member
This question is related to ‘concept checker’ question 4 in Schweser 2009 FRM notes page 98 of Book 2. The question is:
"Use the following information to determine the value of the swap to the floating rate payer using the bond methodology. Assume we are at the floating rate reset date.
$1 million notional value, semi-annual, 18-month maturity.
Spot LIBOR rates: 6-months, 2.6%, 12-months,2.65%, 18-months, 2.75%
The fixed rate is 2.8% with semiannual payments.
Alternatives
-$66
$476
$3,425
$5,077
I solved the problem using bond methodology and got the answer as $476, which is one of the alternatives given and that is the correct answer, according to Schweser.
I also tried to solve the problem using FRA methodology. My calculations are as follows
For 6-12 month, forward continuously compounded rate
(2.65×12-2.6×6))/((12-6) )=2.7%
For 12-18 month, forward continuously compounded rate (2.75×18-2.65×12))/((18-12) )=2.95%
Converting the continuously compounded rates into semiannual compounding rates--
e^(2.7/100 )=(1+R/2)^2gives R_(6-12)=2.718307%
Similarly
e^(2.95/100 )=(1+R/2)^2gives R_(12-18)=2.971864%
Now following calculations emerge
Time Fixed Floating Effective Discounting
payment payment payment factor PV
0.5 14000 $1,000,000×2.6/100=13,000 1000 e^(-0.026*0.5)=
0.987084 987.084
1 14000 $1,000,000× 2.718307/100=
13,591.54 408.46 e^(-0.0265*1)=
0.973848 397.778
1.5 14000 $1,000,000× 2.971864/100=
14,859.32 -859.32 e^(-0.0275*1.5)=
0.959589 -824.594
Total 560.267
Now the question bothering me is how can answers from the two approaches be so radically different? As given in Hull's books, the two approaches give the same answer. Even after considering some rounding off errors, we cannot expect the difference to be of the order of 20%.
That means I am going wrong somewhere but unable to figure out where.
Can anybody help me on that? Apologies for bad formating but no matter what I do, it is appearing the same way.
Thanks in advance
"Use the following information to determine the value of the swap to the floating rate payer using the bond methodology. Assume we are at the floating rate reset date.
$1 million notional value, semi-annual, 18-month maturity.
Spot LIBOR rates: 6-months, 2.6%, 12-months,2.65%, 18-months, 2.75%
The fixed rate is 2.8% with semiannual payments.
Alternatives
-$66
$476
$3,425
$5,077
I solved the problem using bond methodology and got the answer as $476, which is one of the alternatives given and that is the correct answer, according to Schweser.
I also tried to solve the problem using FRA methodology. My calculations are as follows
For 6-12 month, forward continuously compounded rate
(2.65×12-2.6×6))/((12-6) )=2.7%For 12-18 month, forward continuously compounded rate
(2.75×18-2.65×12))/((18-12) )=2.95%Converting the continuously compounded rates into semiannual compounding rates--
e^(2.7/100 )=(1+R/2)^2gives R_(6-12)=2.718307%
Similarly
e^(2.95/100 )=(1+R/2)^2gives R_(12-18)=2.971864%
Now following calculations emerge
Time Fixed Floating Effective Discounting
payment payment payment factor PV
0.5 14000 $1,000,000×2.6/100=13,000 1000 e^(-0.026*0.5)=
0.987084 987.084
1 14000 $1,000,000× 2.718307/100=
13,591.54 408.46 e^(-0.0265*1)=
0.973848 397.778
1.5 14000 $1,000,000× 2.971864/100=
14,859.32 -859.32 e^(-0.0275*1.5)=
0.959589 -824.594
Total 560.267
Now the question bothering me is how can answers from the two approaches be so radically different? As given in Hull's books, the two approaches give the same answer. Even after considering some rounding off errors, we cannot expect the difference to be of the order of 20%.
That means I am going wrong somewhere but unable to figure out where.
Can anybody help me on that? Apologies for bad formating but no matter what I do, it is appearing the same way.
Thanks in advance
