Calculation of Cash Flow from FRAs

[gargi.adhikari]

https://learn.bionicturtle.com/topic/instructional-video-hull-chapter-4/

In the screenshot below- Chapter 4 ( link above), how did we derive the Forward Rate to be =5.127 % ? I tried to plug in the values for the discrete Rf into the formula ({ [(1+ R2/m) ^mT2] / [(1+ R1/m) ^mT1] } -1 ) * m where , R2= 4%, R1= 3%, T2= 2, T1=1, m=(2-1)=1 . Using this formula, am getting Rf at T2=2 to be 5.009 instead of a 5.127....guess am missing something here. Could someone break this down for me as how we got the Rf (discrete)at T2=2 to be 5.127 Much gratitude

 

[Deepak Chitnis]

Hi @gargi.adhikari we have given continuous we just convert it to annual discrete (use your calculator for it). like, (e^5%/1)-1=5.127%. Hope that helps!
Thank you

 

[ShaktiRathore]

Hi
Yes the rates are also given are continuous they are not discrete.You can also first convert the continuous rates to discrete so that 1 year rate(discrete)=e^(3%)-1=3.04545%,2 year rate(discrete)=e^(4%)-1=4.081%
Apply the formula for forward rate to get the forward rate=(1.04081)^2/(1.0304545)^1 - 1 =(1.0832854561/1.0304545)-1=1.05127-1=.05127=5.127%.
or directly apply the formula e^(Rc/m)-1 because what we get as 5% is the continuous rate we were dealing with continuous rates to get the 5% now just convert the 5% to discrete rate using the formula e^(Rc/m)-1 ,we know m=1(annual discrete rate required),Rc=5% implies discrete rate=e^(.05/1)-1=.05127=5.127%.
thanks

 

[gargi.adhikari]

@ShaktiRathore @Deepak Chitnis - Thank You so very much !