Exercise $4.$ You look at your terminal to find some information about Treasury Notes and

see the following:

Assume that all the notes pay only an annual coupon and that all the interest rates are

continuously compounded.

$($a$)$ What should the Futures price for delivery in $1$ year of an equity index that pays a

continuously compounded dividend yield of $1\mathrm{.}5\%$ be$?$ The underlying index is trading

at $$1000$ today. Assume forward prices and futures prices are the same.

$($b$)$ What is the price of the $1-$year Note?

$($c$)$ What is the yield of the $1-$year Note?

$($d$)$ Determine the zero$-$rate curve.

$($e$)$ What is the forward interest rate for the third year $($that is$,$ between $T=3$ and $T=4)?$

Assume this rate is $2\mathrm{.}5\%$ if you cannot find the solution to this question.

$($f$)$ What is today's value of a $$100,000$ FRA starting at year $3$ and lasting for one year

with an agreed rate of $2\%?$ The cash$-$flow of this FRA is exchanged on year $3.$ Note

that the FRA uses an annualized rate. Hint: you need to convert a continuously

compounded rate to an annualized rate $(R=e^{r1}-1).$

$($g$)$ What is the duration of the $3-$year Note?

$($h$)$ If the yield curve moves up by $5$ bps$,$ what should the impact to the $3-$year Note be$?$

Does your answer still hold for a $2\%$ upward move?