Note: If not otherwise stated, assume that:

Yield$-$to$-$maturity $($YTM$)$ is an APR, semi$-$annually compounded

Bonds have a face value of $$1,000$

Coupon bonds make semi$-$annual coupon payments; however, coupon rates $(r_C)$ are annual rates, i$.$e$.,$ bonds make a semi$-$annual coupon payment of $\frac{r_C}{2}$

Problem $1$

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).$ Assume all these bonds have the same yield$-$to$-$maturity $(4\%$; APR, compounded semi$-$annually$)$:

A$.$ A bond with $6$ years to maturity and a zero coupon rate $($discount bond$).$

B$.$ A bond with $6$ years to maturity and a $4\%$ coupon rate $($coupons are paid semi$-$annually$).$

C$.$ A bond with $6$ years to maturity and a $4\%$ coupon rate $($coupons are paid annually$).$

D$.$ A bond with $4$ years to maturity and a $7\%$ coupon rate $($coupons are paid semi$-$annually$).$

E$.$ A bond with $4$ years to maturity and a $5\%$ coupon rate $($coupons are 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 want to profit from an unexpected decrease in market interest rates, which bond should you purchase?

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

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