Suppose that the current one$-$year rate $($one$-$year spot rate$)$ and expected one$-$year T$-$bond

rates over the following three years $($i$.$e$.,$ years $2,3,$ and $4,$ respectively$)$ are as follows:

$R_1^1=1\mathrm{.}94\%,E(r_2^1)=3\mathrm{.}00\%,E(r_3^1)=3\mathrm{.}74\%,E(r_4^1)=4\mathrm{.}10\%.$

a$.$ Using the unbiased expectations theory, current $($or today's$)$ rates for one$-,$ two$-,$

three$-,$ and four$-$year maturity Treasury securities should be$?$

b$.$ Plot your results with the time to maturity on the $x-$axis and the yield to maturity on

the $y-$axis.

c$.$ Comment on the value of your results in relation to the class example of liquidity risk.