## Var

prince11595
Posts: 3
Joined: Mon Jun 15, 2015 3:49 am

### Var

A and B enter into a fixed for floating swap for 10 years with semi-annual payments. Compute the discount factor for 1 year given the following fixed rate:
T6months: 4.0%
T12months: 4.8%
T18months: 5.6%
a. 1.96% Incorrect
b. 4.54% Correct
c. 2.87% Incorrect
d. 3.24% Incorrect
Discount rate for 6 months: 100/ [100+(4/2)] = 0.9804 or 1.96%
Discount rate for 12 months: 100/ {[100+(4.8/2)] + [(4.8/2)/ (1+1.96%)]} = 0.9546 or 4.54%.

How did you get discount rates and the percentage of the discount rates found ?

prince11595
Posts: 3
Joined: Mon Jun 15, 2015 3:49 am

### Re: Var

Compute the effective duration for a 1% change in annualized yield, of a US corporate bond with 10 years of maturity, semi-annual coupon of 6%, face value of \$1000 and currently trading at par.
a. 74.50 Incorrect
b. 149.01 Correct
c. 163.51 Incorrect
d. 81.76 Incorrect
Data provided:
FV = \$1000, N = 20, PMT = \$30, PV = \$1000, I/Y = 3% (trading at par)
Now calculate the PV with I/Y as 2.5% and 3.5%, we get \$1077.95 and \$928.94 respectively.
Calculate duration as:
Duration = 1077.95 – 928.940/2*100*0.5%
= 149.01

Here the hange in yield is taken as .5% . But originally the rate of vhaqnge in yield is given 1%. Pls explain

edupristine
Finance Junkie
Posts: 722
Joined: Wed Apr 09, 2014 6:28 am

### Re: Var

For the 1st question:
D(Discount factor)= 100/(100+P)^n
= 100/(100+4/2)^1 (4/2 because payment is semi-annual )
=0.9804
=100%-98.04%
=1.96%
Discount rate for 12 months= 100/ {[100+(4.8/2)]^1 + [(4.8/2)/ (1+1.96%)]} (for the d of 1st six months and next six months period of the)
= 0.9546
=100%-95.46%
=4.54%

Solution 2: Here the change in yield is taken as 0.5% because basis of payment is given semi-annually(semi-annual coupon of 6%), So the yield become half of the original yield given i.e 1%/2 = 0.5%

saichitale1994
Good Student
Posts: 12
Joined: Mon Jun 15, 2015 3:48 am

### Re: Var

Got it.Thanx .

edupristine
Finance Junkie
Posts: 722
Joined: Wed Apr 09, 2014 6:28 am

Pleasure..