On October $22$nd$,2018,$ Dealer A purchased $$1$ million face amount of a $7\mathrm{.}25\%,$ May $15,2028,$ Government of Canada bond. Assume that October $22$nd is the settlement date for the bond purchase and the day count convention is actual$/365$ days.The above table shows the auction results for the $2-$year Government of Canada

benchmark bond. Assume the bond pays coupons semi$-$annually and has an

actual$/365$days day count convention. The Issue date is the same as the Settlement

date for pricing purposes.

a$)(4$ pts$)$ Using the information above, what was the average clean price for the $2-$

year bond? How much accrued interest was there on the bond on December ${13}^{th},$

$2023?$

b$)(3$ points$)$ After the auction, there was $16\mathrm{.}5$ billion of the $2-$year bond outstanding.

Assume the total bids received from the primary dealers was $12\mathrm{.}496$ billion. What

was the size of this $2-$year benchmark bond auction? Briefly explain.

c$)(3$ pts$)$ Briefly explain the auction tail. Should the Bank of Canada want a 'wide' tail or

a 'tight' tail? Briefly explain.$[][$nb