Arbitrage Free Valuation or the Law of One Price: On February $15,2008,$ traders could buy and sell two US Treasury securities with the same maturity $T=9\mathrm{.}5$ years, but with different coupon rates. In particular a T$-$note with coupon rate $C=4\mathrm{.}750\%$ and a T$-$note with coupon rate $C=8\mathrm{.}875\%$ were available. Table $2$ below gives the term structure of interest rate or yield curve on February $15,2008.$ Columns $1$ to $6$ display coupon rates, maturities, and quotes of the latest issued US Treasury securities as of February $15,2008.$ Column $7$ displays the discount prices or factors $Z(0,T)$ obtained from the bootstrapping procedure discussed in class. Using he information in Table $2$ conduct the following analysis:

$($a$)$ Determine the fair price or arbitrage free value of the $4\mathrm{.}750\%$ coupon $T-$note and $8\mathrm{.}875\%T-$Note, by viewing each bond's cash flows as portfolio of zero$-$coupon bonds.

$($b$)$ Are the securities fairly priced, underpriced or overpriced, using the information contained in the Tabel $2,$ then discuss briefly which security is cheap and which is expensive and why.

$($c$)$ Discuss briefly which security you will short and which you will long and why.

$($d$)$ Determine the yield$-$to$-$maturity of each Treasury security.

Table $2$: Term Structure on February $15,2008$

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