5. A define-benefit pension fund has following holdings in their fixed-income portfolio: Credit Rating Maturity (yr) Coupon Rate Convexity (%) 0.3 7.5 11.5 9.8 1.8 Bond A B C D E US Treasury A1 Aa2 Agency Aa3 3.1 9.8 5.2 6.7 12.1 Modified Duration 2.738 6.452 3.733 4.874 10.921 9.8 56.2 18.5 32.3 128.4 Total Market Value of Position $50,000 $50,000 $50,000 $50,000 $50,000 $250,000 i) Calculate modified duration for this portfolio. ii) the modified duration of pension's liabilities is 6.50 years. Comment on immunization against interest rate risk; iii) how can you increase the convexity of the portfolio while keeping modified duration unchanged? iv) You forecast that both Treasury yields, and credit spreads will decrease in the near future. How will you adjust the existing portfolio according to this view?