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.

t$=1$ t$=2$ Price at t$=0$

Bond A: $$2$ $$2+$$$100$ $$94\mathrm{.}78$

Bond B: $$4$ $$4+$$$100$ $$96\mathrm{.}43$

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

$($b$)$ If yes, find one arbitrage portfolio and determine the price and payoff of that portfolio.

$[3$p$]$