26. Put in order (from smallest to largest) the following bonds with respect to their duration27. You are managing a portfolio of $1 million. Your target duration is 10 years, and you choose from two bonds: a zero-coupon bond with maturity of 5 years, and a perpetuity, each yielding 5%. (a) How much of each bond will you hold in your portfolio? (b) How these fractious change next year if target duration is now nine years? 28. What is the convexity of bonds? Prove that the convexity is a convex function of the yield-to-maturity. 29. Consider a bond selling at par with modified duration of 10.6 years and convexity of 210. A 2% decrease in yield would cause the price to increase by 21.2% , according to the duration rule (verify!). What would be the percentage price change, if you take the convexity into consideration? 30. You have to pay $10 0(X) in four years. How many zero-coupon two year bonds and zero-coupon ten year bonds with 10% yield-to-maturity can you buy to hedge your risk against changes of the yield-to-maturity. 31. You have to pay 300000 in four years and 4000(x) in six years. How many zero-coupon three year bonds and zero-coupon ten year bonds with 12% yield-to-maturity can you buy to hedge your risk against changes of the yield-to-maturity (par value is 20)0). 32. A zero-coupon one year bond with nominal 909090 has the yield-to-maturity 10%. A 5%-coupon three year bond with nominal 943800 has the yield-to-maturity 10% too. What combination of these two bonds will give you I MO 900 two years later if you have 826 181? 26. Put in order (from smallest to largest) the following bonds with respect to their duration27. You are managing a portfolio of $1 million. Your target duration is 10 years, and you choose from two bonds: a zero-coupon bond with maturity of 5 years, and a perpetuity, each yielding 5%. (a) How much of each bond will you hold in your portfolio? (b) How these fractious change next year if target duration is now nine years? 28. What is the convexity of bonds? Prove that the convexity is a convex function of the yield-to-maturity. 29. Consider a bond selling at par with modified duration of 10.6 years and convexity of 210. A 2% decrease in yield would cause the price to increase by 21.2% , according to the duration rule (verify!). What would be the percentage price change, if you take the convexity into consideration? 30. You have to pay $10 0(X) in four years. How many zero-coupon two year bonds and zero-coupon ten year bonds with 10% yield-to-maturity can you buy to hedge your risk against changes of the yield-to-maturity. 31. You have to pay 300000 in four years and 4000(x) in six years. How many zero-coupon three year bonds and zero-coupon ten year bonds with 12% yield-to-maturity can you buy to hedge your risk against changes of the yield-to-maturity (par value is 20)0). 32. A zero-coupon one year bond with nominal 909090 has the yield-to-maturity 10%. A 5%-coupon three year bond with nominal 943800 has the yield-to-maturity 10% too. What combination of these two bonds will give you I MO 900 two years later if you have 826 181