Help with Forward T-bonds vs Future T-bonds

CFA Level II Derivatives
#1

I’m confused why for a forward contract we present value the coupons and why we future value the coupon s on a future?? see examplas.

  1. A 6% Treasury bond is trading at 1 ,044 (including accrued interest) per 1 ,000

of face value. It will make a coupon payment 98 days from now. The yield curve

is flat at 5% over the next 150 days. The forward price per $ 1 ,000 of face value

for a 120-day forward contract, is closest to:

A. $1,014.52.

B. $ 1 ,030.79.

c. $1,037.13.

PV of coupon 30 / (1.05) ^ (98/360) = 29.61

Foward price = (1044-29.61) * 1.05 ^(120/365)= 1030.79

FUTURES

Calculate the no-arbitrage futures price of a 1.2 year futures contract calling for the delivery of a specific bond, a 7% T-bond with exactly 1 0 years remaining to maturity and a price of $ 1 ,040, when the annual risk-free rate is 5%. PVC = ( $35 X 1 .05°·7 ) + ( $35 X 1 .05°·2 ) = 71.56 PP = ( 1,040 x 1 .051.2 )- 71.56 = 1, 03 1 . 1 5

#2
  1. A 6% Treasury bond is trading at 1 ,044 (including accrued interest) per 1 ,000

of face value. It will make a coupon payment 98 days from now. The yield curve

is flat at 5% over the next 150 days. The forward price per $ 1 ,000 of face value

for a 120-day forward contract, is closest to:

A. $1,014.52.

B. $ 1 ,030.79.

c. $1,037.13.

this can also be done with the future value

1044 * 1.05^(120/365) - 30 * 1.05^((120-98)/365)=1060.88 - 30.12 3 = 1030.75 Ans B

they are doing (Face Value - PV Coupon) and then Future valuing that

on PV Coupon - you divide by 1.05^98 and on the FV you multiply by 1.05^120

98, 120 being the # of days

which is the same as Face * 1.05^120 - Coupon / 1.05^98 * 1.05^120 or Coupon * 1.05 ^ (120-98)

#3

the same formula works for both futures and forwards - look at the writeupi above.

#4

Is it easier to use the FV of coupons… when given fractional years (1.2 years) or months…???

and the PV of coupons when given a day ??

I got it!!!

#5

Thank you for your help CPK123

#6

Actually, the time convention has nothing to do with PV or FV. Ultimately, it doesn’t matter whether you bring everything to the present or move everything to the future… the answer will be the same, decimal for decimal.

#7

Best to know both the formulae - so as to not stumble if FV(coupon) is given directly. CPK’s intuition helps a lot.