Forward rate calculation

[jennings92]

I'm little bit confused about calculation of Forward rate.

Indeed i see there is few manner to determine it

F(1,2) = (R2T2-R1T1) / (T2-T1)

F(1,2) = (1+R2)/(1+R1) or exp(R2*T2) / exp(R1T1)

Which is the different between the 2 case and when we use the 1st equation et the 2nd ?

Thanks

 

[David Harper CFA FRM]

Hi jennings,

The only difference is compound frequency. Your first assumes continuous. Your second is not quite correct but means to assume annual: F(1,2) = (1+R2)^2/(1+R1)^1 - 1. However, as I've written often in the forum (search "forward rates"), i think it is really hard to master this without the underlying logic and only memorizing; e.g., your second formula is only good for F(1,2), what about F(3,5)?

In terms of equalizing expectations (we'd expect the same cumulative return left/right),

• Annual: (1+S1)^T1*(1+F)^(T2-T1)=(1+S2)^T2, and solve for forward (F). IMO, the key step is to see why we assume this equality; then we can solve for any frequency, including semi-annual (eg).
• Continuous: exp[S1*T1]*exp[F*(T2-T1)] = exp(S2*T2), and solve for forward (F) gets your first above
• Semi-annual: can you tell me, by extending the same equality concept but under s.a.?

More here

• http://forum.bionicturtle.com/threads/2012-p1-focus-review-4-forward-rates-question.6387/#post-20295 <<-You want this
• http://forum.bionicturtle.com/threads/shortcut-to-forward-rates-if-you-have-bond-prices.4927/
• and a search of "forward rate": http://forum.bionicturtle.com/search/931403/?q="forward rate"&o=date

 

[jennings92]

Thanks david. It's more clear

About semi annual, isn't (1+R1/2)^(2*T1) * (1+F/2)^(2*(T2-T1)) = (1+R2/2)^(2*T2) ?????