$(9$ marks$)$ The following table shows the yield to maturity $($YTM$)$ of various types of bonds on March $15,2022.$

The YTM of a $3-$month T$-$bill is $0\mathrm{.}46\%.$

a$.$ What is the expected yield of a three$-$year Treasury two years from the date

above according to the pure expectations theory?

b$.$ What is the risk premium of a $5-$year T$-$note?

c$.$ What explains the $0\mathrm{.}428\%$ difference in YTM between a $5-$year U$.$S$.$ Treasury

and a $5-$year AAA corporate bond?

$(3$ marks$)$