Where A is the spot rate over 2 years , B is the spot rate over 1 year.
So the foward rate on a 1 year term , 1 year from now
is SQRT( (1+0.05/2)*(1+0.055/2)*(1+0.06/2)*(1+0.065/2) / (1+0.05/2)*(1+0.055/2) )
= 1.03125
And the annualized rate is 6.25%作者: spreads 时间: 2011-7-13 13:15
Your answer: B was incorrect. The correct answer was A) 6.25%.
The 2 year spot rate is 5.7492 meaning the return that should be earned after 2 years would be 5.7492 + 5.7492 = 11.498%. The 1 year spot rate is 5.2498 therefore the 1 year forward rate 1 year from now must be the difference between the 11.498% earned over the 2 year spot rates and the 1 year spot rate. Thus the 1 year forward rate 1 year from now is 11.498 − 5.2498 = 6.2486 or 6.25%. (Study Session 14, LOS 53.e)
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The above explanation is kind of strange to me. Atleast I have not seen anywhere in text where we subtract 1yr spot rate from 2yrs spot rate to get 1yr forward rate 1yr from now....作者: SFoyil 时间: 2011-7-13 13:15
That's the approximate way.
The exact way is to divide : (1+2YrSpot)^2/(1+1YrSpot)
so Forward rate for 1 year , 1 Year from now = (1.057492^2)/1.052498
which gives you in one stroke 1.06251 , or 6.25%作者: MiniMe7 时间: 2011-7-13 13:15
in this case I would not calc anything
just look at given forward rates
12 作者: random_walker47 时间: 2011-7-13 13:15
you are right Dreary, if there were more choices between 6 and 6.5, it would be necessary to calc either your way or:
(1+0.06/2)x(1+0.065/2)
Edited 1 time(s). Last edit at Saturday, May 22, 2010 at 02:32PM by pfcfaataf.作者: madaochenggong 时间: 2011-7-13 13:15
Dreary , you got the wrong rate in there man.
Only LIBOR can be divided by 2 , 4 etc. Spot rates are compund rates , never simple return rates.
You are dividing 057492/2.
i.e. Spot Rates / 2 . Thats a no-no. Instead it can be ( 1+ LIBOR/2)
You want to compound the spot rates that's fine . But don't divide by 2 . Take Sqrt if you have to .
The answer is so close to 6.25 % that it is impossible to say its rounding error. It looks very close to exact.作者: bolligerallstar 时间: 2011-7-13 13:16
I thought for Futures/Forwards we always go with compounding (take it to the power ^) and not add -on....作者: MiniMe7 时间: 2011-7-13 13:16
I refreed to Schweser's Lvl I refresher handbook Page 89.
They show the foward rate estimation using spot rates , and they clearly show the compounding taking place.
I do remember hitting the divide in TVM calculations .
I am now confused becuase there was stuff about B.E.Y etc that's totally out of scope now.
But this year ( Lvl II ) I am taking care to do it only for LIBOR , never for spot rates.
In fact if you look at the spot rates in the table above , they are built up entirely by bootstrapping the forward rates , 1 step at a time , using compounding作者: Rasec 时间: 2011-7-13 13:16
The issue here is not compounding, you have to compound in the above because you are talking about rates over many years (that has nothing with LIBOR or not). The LIBOR issue comes up in a different case, whether to multiply by 90/360 o raise that to 90/360. In the above regardless of the rate, you have to raise to number of periods.
This is a little tricky I know, but I'm sure in L1 CFAI textbook, there is an example which shows 6-month rates, where you divide by 2 before compounding. Also, if quarterly, you divide by 4, before compounding.作者: maryli 时间: 2011-7-13 13:16
I have always been of the mind that you /2 for LIBOR only as simple compounding is being used by definition (i.e. in FRA's, interest rate options etc.)
For spot rates & forward rates, these work with compounding therefore you must ^2 or ^(1/2)作者: SFoyil 时间: 2011-7-13 13:16
(1.057492^2)/1.052498 - 1
is approximately the same as
2 * .057492 - 052498
.... to the fifth decimal place. While the former is "exact" , at a pinch you can do the latter in an exam and get the right answer out of the choices.
Aztec's answer and the reasoning is correct .作者: tarunajwani 时间: 2011-7-13 13:16
ok lets try this
same question, same given rate curve, you know that LIBOR is rate p.a. simple rate so 6m interest is calced LIBOR/2
