Reference no: EM133117280

Kindly note the following: 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.

Question

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 that the current interest rate is 8%. You currently own 1000 of 15-year 6% coupon bonds. It is important to keep at least 6 decimal digits for all calculations!

a) If you want to hedge your portfolio with 10-year 20% coupon bonds, how many bonds do you need to sell?

b) By how much the value of your unhedged portfolio will change if the interest rate increases by 0.2% from 8% to 8.2%

c) By how much the value of your hedged portfolio will change if the interest rate increases by 0.2% from 8% to 8.2%

d) You just found a risk-free perpetuity with $100 face value and 10% annual coupon rate (paid semi-annually). How many of such perpetuities do you need to sell to hedge your original portfolio? Note: you are using ony perpetuities to hedge you original portfolio of 1000 of 15-year 6% coupon bonds.

e) If you hedge your original portfolio using only perpetuities, by how much the value of your hedged portfolio will change if the interest rate increases by 0.2% from 8% to 8.2%?