need some help on a spot and forward question

[Swissfox]

Hi,

The question is: suppose that the six-month spot rate is equal to 7% and the two-year spot rate is 6%. The one-and a half-year forward rate starting six months from now has to:

be more than 6%

be less than 6%

lie between 6 and 7%

the answer is less than 6%

for this calculation, I used the approximation formula, namely:

((6x2)-(7x0.5))/2= 4.25

Is that correct? because when I used the “correct and complete” formula, I got a result different (arount 5.2%). I’m asking because Schweser is not very wordy on that approximation formula, so I’m not sure that it’s correct.

Thanks

[S2000magician]

@Swissfox

Hi,

The question is: suppose that the six-month spot rate is equal to 7% and the two-year spot rate is 6%. The one-and a half-year forward rate starting six months from now has to:

be more than 6%

be less than 6%

lie between 6 and 7%

the answer is less than 6%

for this calculation, I used the approximation formula, namely:

((6x2)-(7x0.5))/2= 4.25

Is that correct? because when I used the “correct and complete” formula, I got a result different (arount 5.2%). I’m asking because Schweser is not very wordy on that approximation formula, so I’m not sure that it’s correct.

Thanks

As it’s the 1½-year forward rate, the approximation should be:

((6% × 2) − (7% × ½)) / 1½ = 5.6667%

The actual value is:

(1.06^2 / 1.07^0.5)^(2/3) – 1 = 5.6687%

[Swissfox]

great, thank you very much s2000magician!

there are not so many information about this approximation, now I have all the composents of the formula