Calculating forward rate using spot rates

[maz1987]

6-month risk-free spot rate = 5%
12-month risk-free spot rate = 6%

Question: Calcluate 6-month forward rate in 6 months' time.


I answered this using (what I thought was) the fact that:

(1 + y_1/2)^(1/2) x (1 + f_1/2,1/2)^(1/2) = (1+y_1)

However the answer in the examiner's report misses out the bolded bit in the formula. Is this correct?

 

[John Lee]

6-month risk-free spot rate = 5%
12-month risk-free spot rate = 6%

Question: Calcluate 6-month forward rate in 6 months' time.


I answered this using (what I thought was) the fact that:

(1 + y_1/2)^(1/2) x (1 + f_1/2,1/2)^(1/2) = (1+y_1)

However the answer in the examiner's report misses out the bolded bit in the formula. Is this correct?

September 2007 Q5
You don't actually need the forward rate. I did:

K = (900-50×1.05^(-0.5)-50×1.06^(-1)) × 1.06 = 852.28

Can't see this on the examiners solution - but perhaps I'm being a bit thick!

Perhaps they were working with a half-yearly instead of annual rate?

 

[maz1987]

Thanks for the reply, but the question is exactly as I wrote it. It is Q6 of Sept 2009 paper. It doesn't have to do with calculating the forward price (that was asked in the question just before it).

 

[John Lee]

Thanks for the reply, but the question is exactly as I wrote it. It is Q6 of Sept 2009 paper. It doesn't have to do with calculating the forward price (that was asked in the question just before it).

Oops!

Yes they express it as a 6 monthly effective rate of 3.4454% rather than as an annual effective rate of 1.034454²-1 = 7.0095%.

 

[maz1987]

Thanks. So without the question requesting the "effective rate" or "per annum", I should leave it as 3.4454% as opposed to 7.0095%? Hope I wouldn't lose marks for missing that!

 

[John Lee]

Thanks. So without the question requesting the "effective rate" or "per annum", I should leave it as 3.4454% as opposed to 7.0095%? Hope I wouldn't lose marks for missing that!

Both were marked correct in this exam (presumably as long as you clearly stated your units "per half-year" or "pa" however I would advise going for the annual rate as standard - as that's what's usually in the solutions.

 

[mary_t]

Confused!

September 2007 Q5
You don't actually need the forward rate. I did:

K = (900-50×1.05^(-0.5)-50×1.06^(-1)) × 1.06 = 852.28

Can't see this on the examiners solution - but perhaps I'm being a bit thick!

Perhaps they were working with a half-yearly instead of annual rate?

Can someone please explain why the solution is not:

K = (900-50×1.05^(-0.5)-50×1.06^(-1)) × (1.05^0.5) x (1.06)

Why do we only multiply by the 6% spot rate of interest and ignore the 5%?

 

[John Lee]

Can someone please explain why the solution is not:

K = (900-50×1.05^(-0.5)-50×1.06^(-1)) × (1.05^0.5) x (1.06)

Why do we only multiply by the 6% spot rate of interest and ignore the 5%?

Because we are accumulating to the end of the term (ie 31/3/8) in one year's time.