Question $4(10$ Marks$)$

Suppose you observe the following market data on debt securities:

Note: Data deviates from the current market conditions as it simplifies the calculations.

Required:

$($a$)$ What are the continuously compounded zero$-$coupon yields for $6$ months and one year,

respectively? Report your answer in percentage $(\%)$ with $4$ dps$.$ i$.$e$..\%$

$($b$)$ What is the of the following default$-$free bond portfolio? $(4$ dps $)$

Note: Each bond has a face value of $$1\mathrm{.}00$ and coupons are paid semi$-$annually. You

should assume the zero$-$coupon rate calculated in part $($a$)$ above.

Hint: Use the following formula to measure the duration of the bond portfolio, i$.$e$.,$

$D_B=\frac{{\displaystyle \underset{i=1}{\overset{n}{}}}{t}_i{c}_i{e}^{-r{t}_i}}{{\displaystyle \underset{i=1}{\overset{n}{}}}{c}_i{e}^{-r{t}_i}},$

$i^{th}$ period.