 # Calc Forward Rate (Bonds)

The following info is on BEY basis for treasury securities: Year to Maturity – Spot Rates (BEY) % 0.5 – 4.15 1.0 – 4.45 1.5 – 4.66 2.0 – 5.07 2.5 – 5.59 3.0 – 5.90 What’s the 2 year forward rate, one year from now on a BEY basis: a) 2.37% b) 3.31% c) 4.75% d) 6.63% Please show how you got the answer. Thanks.

(1+r6)^6 = (1+r2)^2 * (1+r)^4 1.0295^6 = 1.02225^2 * r^4 r = 3.30% so BEY = 6.60% --> D

[[(1.0295)^6]/[(1.02225)^2]]^1/4, multiplied by 2 = 6.63%

so basically multiply all the ^ by 2, easy enough. thanks cpk. i chose D coz i did it the non-BEY method and it came close.

of course because they say BEY ==> means you have to divide the rates inside by 2… as well.

I don’t get any of this. Are we calcing 2f1 here? Can you guys walk me through this? I’m not sure why we’re using those spot rates in particular. A general formula will be huge help. Thanks much.

we are not calculating 2f1 here. We are calculating 4f2 actually. 1+r6^6 = 1+r2^2 * 1+4f2^4 everything is multiplied by 2 because of the BEY thing If you calculated 1+r3^3

The intuition can be explained as follows. Assume you have a friend that is investing at the 6 period spot rate for six periods. You are investing at the 2 period spot rate for 2 periods, and need to find the semi-annual rate to apply to all the remaining periods so that you arrive at the end of the 6 periods with the same total return as your friend. Since the friend is getting 5.9% for all periods and you started for two periods at 4.45%, it stands to reason that you need a rate above 5.9% for the remaining periods to catch up to the friend. Since 6.63% is the only rate above 5.9%, this question can be answered on intuition alone.

lola, forget for a moment the BEY assumption. #1. what would the 1 year forward, 1 year from now be? year1…year2 1.0445…x… 1.0507…1.0507 1.0445*x=1.0507^2 x=1.0507^2/1.0445 #2. 2 year forward rate, one year from year1…year2…year3 1.0445…x…x 1.059…1.059…1.059 x=sqrt(1.059^3/1.0445) #3. 1 year forward rate, 2 years from now. year1…yr2…yr3 1.0507…1.0507…x 1.059…1.059…1.059 x=1.059^3/1.0507^2 hope this helps.

coolio cpk EDIT - DAAAAMMNNN chebychev, ur so nailin this! btw whenever i see/hear chebyshev, my fat, snotty, college stats prof’s face comes before my eyes, she was a nut job.

I like to think about these visually…we’re asked for a 2 year fwd 1 year from now…so I break it down like so… YR 0.5 1 1.5 2 2.5 3 0----1-----2----3----4----5----6 || this is what we’re asked so, the ends dictate what spots we need (in this case, the 2nd and the 6th): (1 + Spot-PV6)^6 = (1 + Spot-PV2)^2 * (1 + FV)^X where X = the exponent diff between the PV6 and PV2 (6 - 2) = 4 Finally…always check the question to see if you’re being given annual or semi and use the spots accordingly Hope that helps! OOPS: the lines didnt line up but its supposed to be from 2 thru 6

You guys are the best! Thanks cpk123, chebychev, barthezz and dpak.

yeh i also find it helps to visualise things: we’re given the various spots, and need to find the 2yr forward, 1yr from now…so: |______|______?______| --> (1+s1)(1+i)^2 |______-______-______| --> (1+s3)^3 now just equate them… so, (1+s1)(1+i)^2 = (1+s3)^3