Can you please write down the solutions on paper? Don't use excel.

At date t, the portfolio P to be hedged is a portfolio of Treasury bonds with various possible maturities. Its characteristics are as follows: Value $1,450 YTM 6% MD 4.25 Convexity 55 We consider Treasury bonds as hedging assets, with the following features: Bond Bond 1 Bond 2 Bond 3 Price ($) 108 118 Coupon Rate (%) 6 5 4 Years to Maturity 3 years 4 years 5 years 98 Coupon frequency and compounding frequency are assumed to be annual. Face value of the three bonds is assumed to be $100. We DONOT force the hedging portfolio to have the opposite value of the portfolio to be hedged. 1. (5 Marks) What is the number of hedging instruments necessary to implement a modified duration / convexity hedge? Explain why? 2. (10 Marks) Compute the YTM, modified duration and convexity of the hedging assets needed. 3. (5 Marks) What are the number of hedging asset that we have to consider to hedge the portfolio P (i.e., find the hedge ratio for duration and convexity hedge)? 4. (5 Marks) Explain every equation you write. Why is it important to satisfy the conditions that you write for a perfect immunization? At date t, the portfolio P to be hedged is a portfolio of Treasury bonds with various possible maturities. Its characteristics are as follows: Value $1,450 YTM 6% MD 4.25 Convexity 55 We consider Treasury bonds as hedging assets, with the following features: Bond Bond 1 Bond 2 Bond 3 Price ($) 108 118 Coupon Rate (%) 6 5 4 Years to Maturity 3 years 4 years 5 years 98 Coupon frequency and compounding frequency are assumed to be annual. Face value of the three bonds is assumed to be $100. We DONOT force the hedging portfolio to have the opposite value of the portfolio to be hedged. 1. (5 Marks) What is the number of hedging instruments necessary to implement a modified duration / convexity hedge? Explain why? 2. (10 Marks) Compute the YTM, modified duration and convexity of the hedging assets needed. 3. (5 Marks) What are the number of hedging asset that we have to consider to hedge the portfolio P (i.e., find the hedge ratio for duration and convexity hedge)? 4. (5 Marks) Explain every equation you write. Why is it important to satisfy the conditions that you write for a perfect immunization