Question $4$

Consider the following information on three government bonds:

$($a$)$ Calculate the clean and dirty prices for each of the above $3$ bonds $($use

Excel functions to answer this question$).$

$($b$)$ Calculate the current yields of the $3$ bonds. How do they compare with

the adjusted coupon yields? Using Bond $x$ as an example, plot the $2$

yields across a range of prices. What do you observe?

$($c$)$ Using a data table, show the sensitivity of Bond Z$\text{'}$s prices to changes in

yield across a range of settlement dates. Comment on your results.

$[20\%]$

$($d$)$ Using Bond $x$ as an example, show the effect on its duration when the

bond's maturity increases. Plot the result. What happens to duration as

the number of years increases?

$($e$)$ Assuming that you can lock in at the spot interest rate of $4\mathrm{.}85\%$ as at

$30/06/2011$ for a one$-$year investment horizon, what would be the

implied forward rate based on the two$-$year zero$-$coupon Bond Y$?$ What

do the results suggest about the shape of the term structure? Explain

your answer.