Weekly participation question $6$:

You're required to invest $$100,000,$ and the bonds listed below $($labeled A to E$)$ are your only options available today. Assume it's feasible to purchase fractional amounts of bonds to utilize the full $$100,000.$ All bonds have the same yield$-$to$-$maturity $(4\%$; APR, compounded semi$-$annually$)$:

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

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

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

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

E$.$ A bond with $4$ years until maturity and a $5\%$ coupon rate $($coupons paid semi$-$annually$).$

a$)$ Arrange these bonds according to their sensitivity to changes in interest rates, from the most sensitive to the least.

b$)$ If your goal is to benefit from an unanticipated decrease in market interest rates, which bond should you buy?

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

d$)$ If you're concerned about an unexpected rise in market interest rates, which bond should you buy?