a) Discuss the relationship of a coupon bond's price, duration, and convexity of the price-yield relationship with respect to changes in the bond's maturity, coupon rate, and the market yield to maturity. Define your terms, state assumptions, and clearly identify the algebraic sign (positive or negative) in the relationships discussed. You may use diagrams to explain your answer, but describe clearly each diagram.
b) Compare the interest rate risk of a noncallable 10-year Treasury coupon bearing bond with a mortgage-backed pass-through security with prepayments related to the level of interest rates – lower market interest rates raise the rate of prepayments. Discuss how the changes in cash flows, arising from prepayments, on a mortgage-backed security affect the duration of such securities. HINT: consider the coupon effect on duration.