Problem $2(26$ points$)$

Suppose that the prices of zero$-$coupon bonds each with face value of $$1000$

and maturing in $1,2,3,$ and $4$ years are

$947\mathrm{.}87,885\mathrm{.}81,815\mathrm{.}15,757\mathrm{.}22,$

respectively.

$($a$)(6$ points$)$ Find the term structure of interest rates over the $4$ year period.

$($b$)(6$ points$)$ Find all the one year forward rates over the $4$ year period.

$($c$)(7$ points$)$ Suppose that you are an ideal bank and all of the interest

rates from parts $($a$)$ and $($b$)$ are available to you for borrowing or lending. Now

suppose another bank offers investors a forward rate between years $2$ and $3$ of

$8\%.$ Would an arbitrage opportunity be present? If so$,$ describe in detail a

strategy for creating the arbitrage. If not, explain why not.

$($d$)(7$ points$)$ What is better for a bank, an interest rate environment where

the term structure slopes upward or where the term structure is flatter? Explain

you answer $($be concise and to the point, long responses will result in loss of

points.$)$ Note: this question does not rely on parts $($a$),($b$)$ and $($c$).$