Estimating the Value of a Euro- Bund Forward Position

yl0077 · August 18, 2020, 2:49am

Probably dumb question but really lost on the fixed-income futures/fowards section.
I don’t understand why don’t we add in the accrued interest .0833 to the questions below? I initially did 148(1+.001)^(1/12) + .0833*(1+.001)^1.5/12 to get to price of t at time T and then take the difference between that and 145 and discount it back to time t. Is .0833 not needed b/c it’s already included in the forward price?? So confused

Suppose that one month ago, we purchased five euro- bund forward contracts
with two months to expiration and a contract notional of €100,000 each at a
price of 145 (quoted as a percentage of par). The euro- bund forward contract
now has one month to expiration. Again, assume the underlying is a 2% German
bund quoted at 108 and has accrued interest of 0.0833 (one- half of a month since
last coupon). At the contract expiration, the underlying bund will have accrued
interest of 0.25, there are no coupon payments due until after the forward
contract expires, and the current annualized one- month risk- free rate is 0.1%.
Based on the current forward price of 148, the value of the euro- bund forward
position will be closest to:

A €2,190.
B €14,998.
C €15,000.
Solution:
B is correct. Because we are given both forward prices, the solution is simply
Vt(T) = PVt,T[Ft(T) – F0(T)] = (148 – 145)/(1 + 0.001)^1/12 = 2.9997

yl0077 · August 18, 2020, 3:12am

I think I answered my own question but feel free to give any additional thoughts, but most likely that interest IS included. I looked up the note and it says “If given the forward price directly, the value (to the long party) is simply the present value of the difference between the current forward price and the original, locked-in forward price.”

S2000magician · August 18, 2020, 3:18am

It’s not that the accrued interest is included; in fact, it’s just the opposite: the accrued interest is excluded.

Bond forwards/futures do not accrue interest. Although you have technically purchased the bond when you enter into the long position, you don’t take legal ownership until maturity when the bond is delivered; therefore, you’re not entitled to any accrued interest because you don’t yet own the bond.

yl0077 · August 18, 2020, 3:34am

Thank you sir, let me ask this as I don’t want to make the wrong assumption again. I understand that accrued interest should be excluded (like the highlighted .25 below) but why is .083 added to the initial spot price? So to make it a full price for calculation?

I’ve seen a lot of your responses when I seek answers here ~ very grateful for all your contribution!