An investor holds 100,000 units of a bond whose features are summarized in the following table. He wishes to be hedged against a rise in interest rates. Maturity Coupon Rate YTM Price 18 years 9.50% 8% 114.181 Characteristics of the hedging instrument, which is here a bond are as follows: Maturity Coupon Rate YTM Price 20 years 10% 8% 119.792 Coupon frequency and compounding frequency are assumed to be semiannual. YTM stands for yield to maturity. The YTM curve is flat at an 8% level.

What is the quantity of the hedging instrument that the investor has to sell?

We suppose that the YTM curve increases instantaneously by 0.1%.

a) What happens if the bond portfolio has not been hedged? (b) And if it has been hedged

Same question as the previous one when the YTM curve increases instantaneously by 2%.