You are managing a portfolio of $1,000,000. Your target duration is 10 years and you can choose from two bonds: a zero coupon bond with maturity of 5 years, and a perpetuity, each currently yielding 5%. How much of each bond will you hold in your portfolio? How will these fractions change next year if target duration is now 9 years? What is the value of perpetuity bond today, assuming it pays $1000 per year? What is the value of the zero coupon bond today? How many of the perpetual and zero bonds would you be purchasing today