The 3-year rate is 2.85%. The 5-year rate is 3.35%. First, interpolate the 4-year interest rate: r4

=

(2.85% + 3.35%)/2 = 3.10%. Buy $1,000 of the 4-year, zero note and short $1,000 of the 3-year, zero note (2.85%/year). Today, you receive and pay $1,000, so the transaction does not cost you anything. In 3-

years, you need to pay the 3-year note—that is, you need to pay $1,000 . 1.02853 ≈ $1,087.96. In 4 years, you receive from the 4-year note $1,000 . 1.0314 ≈ $1,129.89. This is the equivalent of saving at an interest rate r3, 4 of 3.85%. A visual representation follows:

Transcribed Image Text:

t=0 t=1 t=2 t=3 t=4 4-year Treasury -$1,000 (buy) +$1,129.89 t=0 3-year Treasury +$1,000 (short-sell) t=0 Net position $0 t=1 t=2 t=3 t=4 -$1,087.96 t=1 t=2 t=3 t=4 -$1,087.96 +$1,129.89