Fixed Income Forward Pricing Model

CFA Level II Fixed Income
#1

I am super confused about the wording of the sentence " (2) entering into a one-year forward contract to purchase a one-year zero-coupon bond for DF 1 = 0.95.*" in the explanation below. While I understand the concept of the forward pricing model, this sentence does not any make sense to me, what does it mean?*

Full excerpt below:

The forward pricing model describes the valuation of forward contracts.

𝐷𝐹𝐡=𝐷𝐹𝐴×𝐹𝐴,π΅βˆ’π΄

The discount factors DFA and DFB represent the respective prices for period A and a longer period B needed to derive the forward price, FA,B–A, a contract which starts in the future at time A and ends at time B.To understand the reasoning behind [Equation 2], consider two alternative investments: (1) buying a two-year zero-coupon bond at a cost of DF 2 = 0.93 and (2) entering into a one-year forward contract to purchase a one-year zero-coupon bond for DF 1 = 0.95.* Because the payoffs in two years are the same and the initial costs of the investments must be equal, the no-arbitrage forward price F 1,1 must equal 0.93/0.95, or 0.9789.*

#2

anyone? or it is just badly written cfa material

#3

The two alternatives are
(1) Year 0 purchase the 2-year zero for DF 2 = 0.93
Year 2 the 2-year zero matures

(2) Year 0 enter into the forward
Year 1 purchase the 1-year zero for DF 1 = 0.95
Year 2 the 1-year zero matures

As the question says, the payoffs in Year 2 are the same so the initial costs of the investments must be equal

#4

thank you but how can β€œYear 1 purchase the 1-year zero for DF 1 = 0.95” be true? DF1 is the price of 1 year zero at time 0, not time 1? That is what is messing with my head

1 Like
#5

you’re buying a 1-year zero that runs from year 1 to year 2.
The price you pay for that 1-year zero is set by the forward contract.

#6

I get that part, I totally understand what the first alternative investment is since that is purchasing a 2 year zero at DF2, a known price at 0.93.

But for the second alternative, I do not understand what it means to purchase a 1-year zero for 0.95 at year 1, when it should be purchase the 1 year forward at the agreed upon forward price? I guess I am super confused what the right hand side of the equation’s alternative investment really is, 𝐷𝐹𝐡=𝐷𝐹𝐴×𝐹𝐴,π΅βˆ’π΄.

Does DF1 mean something different? I thought it is equivalent to price of 1 year forward at time 0.