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$]$

$($c$)$ The hedge fund manager understands arbitrage trading and asks the sales and trading

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

$$200$ million at t$=1$ and $$0$ at t$=2$ as well as obtains some money at t$=0.$ How does this

trade look like? $[2$p$]$

$($d$)$ When executing this arbitrage trade, the hedge fund buys 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

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

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

market?