Question $1$

On $1$st September $2008,$ Copula, a mutual fund, approaches a trading desk to sell $$100$

million face value of a $90-$day T$-$bill currently trading at a discount rate of $5\mathrm{.}1\%.$ To obtain

the funds needed, the trading desk repos out the T$-$bill to MSFT who has an enormous amount

of cash to lend in the repo market. Specificly, the trading desk enters into a $14-$day repo with a

repo rate of $4\mathrm{.}85\%$ p$.$a$.$ Note that in the repo markets, we use the convention of $360$ calendar days

in a year.

How much $($in millions$)$ does MSFT lend to the trading desk?

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If MSFT imposes a haircut of $3\%,$ how much $($in millions$)$ will they lend to the trading desk?

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For the rest of the question, let's assume that there is no haircut.

$14$ days later, on $15$ th September $2008,$ the trading desk gets in contact with Alupoc,

a pension fund, who is willing to buy the T$-$bill from them. But the trading desk, first, needs to

get the T$-$bill back from MSFT$.$

a$)$ If on $15$th September, the $76-$day T$-$bill trades at a discount rate of $6\%$:

How much $($in millions$)$ will the trading desk have to pay to buy back the T$-$bill from MSFT$?$

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How much $($in millions$)$ will the trading desk receive from Alupoc?

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What is the trading desk's profit $($in millions$)$ in this case?

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b$)$ If on $15$th September, the $76-$day T$-$bill trades at a discount rate of $3\%$:

How much $($in millions$)$ will the trading desk have to pay to buy back the T$-$bill from MSFT$?$

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How much $($in millions$)$ will the trading desk receive from Alupoc?

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What is the trading desk's profit $($in millions$)$ in this case?

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Bonus question: what discount rate the $76-$day T$-$bill must trade at so that the trading desk will

break even? $($This question is not easy $-$ only try it if you have time$)$

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