A fund manager wishes to hedge a portion of his portfolio by using an equity swap. Specifically, the manager wants to hedge against market drops. The fund manager wants to enter in an equity swap paying the SP$500$ return, and receiving a fixed rate. This way, if the market drops, the fund manager will pay money from the market cash flows, and receive money from the fixed rate. The payments will be semi$-$annual.

Below is the term structure of LIBOR rate.

$($a$)$ Complete the following table by filling in the zero$-$coupon price of a $$1$ bond

$($b$)$ What should be the fair annualized fixed rate?

LIBOR Rate Zero$-$coupon Price

L$(180)0\mathrm{.}0265$

L$(360)0\mathrm{.}0335$

L$(540)0\mathrm{.}0345$

L$(720)0\mathrm{.}0355$