A fixed income arbitrage hedge fund focuses on Treasury bond trading. Bond A is a ten$-$year

Treasury bond $($Notes$)$ which was issued eight years ago in a low interest environment. Bond

B is a three$-$year Treasury bond $($Notes$)$ issued one year ago in a high interest environment.

The two bonds have two years left to maturity each and the following coupon payments, face

value and prices.

$($a$)$ Is there an arbitrage? $[2$p$]$

$($b$)$ If yes, find one arbitrage portfolio and determine the price and payoff of it$.[3$pp$]$

$($c$)$ Another investor who understands arbitrage trading, asks the sales and trading team of

an investment bank to execute a trade of the two bonds such that he makes $$100$

million at $t=1$ and $$0$ at $t=2$ without paying for it$.$ How does it look like? $[2$p$]$

$($d$)$ When executing this arbitrage trade, investors buy bond B$.$ What is the intuition? It is

useful to compare the yields of the two Treasury bonds. $[4$p$]$

$($e$)$ As arbitrageurs are buying bond B$,$ the price of bond $B$ increases to $98\mathrm{.}51.$ Given

$p_A=$$$94\mathrm{.}78$ and $p_B=$$$98\mathrm{.}51,$ is there still an arbitrage? $[1$p$]$

$($f$)$ Given $p_A=$$$94\mathrm{.}78$ and $p_B=$$$98\mathrm{.}51,$ what is the one$-$year yield of a Treasury bond in this

market? $[2$p$]$