You are managing a bond portfolio of $1 million. Your target duration is 10 years, and you can invest in two bonds, a zero-coupon bond with maturity of five years and a zero-coupon bond with maturity of 15 years, each currently yielding 5%.
(1) What are your weights in these two zero-coupon bonds to have the target duration?
(2) How will these factions change next year if the target duration is still ten years?