The bank you work for has recently loaned one of its business clients $$24$ million to purchase new

equipment for its production facility. The customer is paying the bank $$5\mathrm{.}45$ million each year for $5$ years

to repay the loan. The bank has customers who have deposited $$24$ million in certificates of deposit for

the next two years, it currently must pay these depositors $$1$ million each year in interest on their

deposits. After year two, the CDs mature and the rate the bank will need to pay its depositors will likely

increase as the overall level of interest rates in the economy are expected to increase $($in other words the

rate it must pay is a floating rate$).$ The bank is worried that its profit margin of $$5\mathrm{.}45$ million $-$ $$1$ million $=$

$$4\mathrm{.}45$ will decrease during in years $3,4,$ and $5.$ To offset this risk you suggest undertaking a swap in years

$3,4,$ and $5$ that allows the bank to pay a fixed $$1$ million each period and receive a floating rate on the

notional value of the swap based upon the $5$ year treasury rate at the beginning of each year. The cash

flows are diagramed below with FL representing unknown floating cash flows.

Your boss looks at this solution and says that she thinks that there are two potential problems with the

swap. $(5$ points each$)$

a$.$ She believes that there is basis risk associated with the swap in years $3,4$ and $5.$ Explain what she

means by basis risk and use the example to illustrate why she believes there is a basis risk.

b$.$ She thinks that the swap creates a potential new risk for the first two years of the swap, design a swap

that lasts two years that would eliminate the bosses concern.