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. Keep at least 6 decimal digits in all your calculation and answers, unless specified otherwise.

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%