Reference no: EM133118249

Assume the term structure of interest rates is flat and consider a 1-factor model with a factor equal to that interest rate. Assume also the current interest rate is 8%. Your portfolio consists of $100,000 investment in a 10-year zero-coupon bonds and $200,000 investment in perpetuities that pay semi-annual coupons.

a) Find the Duration and convexity of 10-year zero-coupon bonds.

b) Find the Duration convexity of a perpetuity

c) Find Duration of your portfolio

d) Find Convexity of your portfolio

e) Assume you want to use the securities described in this question to hedge $1,000,000 worth of securities with Duration=25 and Convexity=100. To do so, you have decided spend $Vbond to buy bonds and $Vperp to buy perpetuities (note that negative values means you are selling them). Write down the system of equatuions for $Vbond and $Vperp and find $Vbond and $Vperp.

Please note: All interest rates are annual interest rates with semi-annual compounding. All coupon rates are annual rates paid semi-annually. All bonds have $100 face values. All Durations are "modified Duration" (not "Macauley Duration). Keep at least 6 decimal digits in all your calculation and answers unless specified otherwise.