Is there anything special to this bond question?

[monsieuruzairo3]

Dear David,

I cam across this question on a forum and can't make much of it. It looks a fairly simple question but the options make me clueless. Please note.

P(0,T) is the price at date 0 of a zero-coupon bond that pays $1 at date T. Given zero-coupon bond prices:
|P(0,4)|= |.8386|;
|P(0,3)|=|.8805|;
|P(0,2)| = |.9245|;
|P(0,1)| =|.9615|;
Compute the 1-year forward rate starting 3 years out, f(3,4).
Choose one answer
1. 1.04
2. 1.05(Correct)
3. 1.06
4. 1.07
Now as per my approach I calculated 3 year and 4 year spot rates as follows
4 year spot rate N=4,PMT=0,PV=.8386,FV=1 ------->S4 =4.5%
3 year spot rate N=3, PMT=0, PV=.8805, FV= 1 ------> S3=4.33%
Now even after converting annualized rates to continuosly compounded rate and using the formula F(3,4)= (4*S4 - 3*S3)/(4-3) I get ~5%. How in the world I am in not getting this one right?
KR
Uzi

 

[ShaktiRathore]

hi,
do it as:
let r be 1 yr forward rate starting today,
(1+r)^1*(1+r3)^3=(1+r4)^4
=>1+r=(1+r4)^4/(1+r3)^3....1
r3 and r4 are 3 and 4 yr spot rates and from z-coupon bond price of maturity 4 yr P(4)=FV/(1+r4)^4 and price of maturity 3 yr is P(3)=FV/(1+r3)^3
thus P(3)/P(4)=FV/(1+r3)^3 divided by FV/(1+r4)^4=(1+r4)^4/(1+r3)^3....2
put 2 in 1 implies,
1+r=P(3)/P(4)
=>r=P(3)/P(4)-1=(.8805/.8386)-1
=>r=1.05-1=5%
i am also getting the 5% the option is giving values in 1+r (1+5%=1.05)form so please don't get confused, its the same as 5%.
thanks

 

[monsieuruzairo3]

Thanks for the prompt response ShaktiRathore