Problem $2$

You must invest $$100,000$ and the bonds listed below from A to E are the only investments available today $($assume that it

is possible to buy a fraction of a bond in order to invest the full $$100,000-$ for example it is possible to buy $148\mathrm{.}45$ of bond

C$).$ The same $5\%$ market interest rate $($APR$,$ compounded semi$-$annually$)$ applies to all of these bonds and they have the

following additional characteristics:

A$.8$ years to maturity and $5\%$ coupon rate $($coupons paid annually$).$

B$.3$ years to maturity and $7\%$ coupon rate $($coupons paid semi$-$annually$).$

C$.8$ years to maturity and $0\%$ coupon rate $($discount aka zero$-$coupon bond$).$

D$.8$ years to maturity and $5\%$ coupon rate $($coupons paid semi$-$annually$).$

E$.3$ years to maturity and $5\%$ coupon rate $($coupons paid semi$-$annually$).$

$($a$)$ Rank these bonds according to their interest rate sensitivities$,$ from the most interest rate sensitive to the least interest

rate sensitive$.$

$($b$)$ If you are worried that market interest rates might increase unexpectedly, which bond should you purchase?

$($c$)$ What is the duration of the bond you selected in part $($b$)?$

$($d$)$ If you want to profit from an unexpected decrease in market interest rates, which bond should you purchase? $($Note:

assume your research leads you to conclude that interest rates will decline, but you have not shared this information with

anyone $-$ i$.$e$.$ the decline is unexpected for everyone else$).$