5. A define-benefit pension fund has following holdings in their fixed-income portfolio: Bond Credit Rating Maturity (yr) Coupon Rate Modified Convexity Market Value (%) Duration of Position ABCDE US Treasury 3.1 0.3 2.738 9.8 $50,000 A1 9.8 7.5 6.452 56.2 $50,000 Aa2 5.2 11.5 3.733 18.5 $50,000 Agency 6.7 9.8 4.874 32.3 $50,000 Aa3 12.1 1.8 10.921 128.4 $50,000 Total $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? 8. You have a portfolio with three assets. The forecasted inputs are showed in following table. Calculate expected marginal contribution to total risk (MCTR) and absolute contribution to total risk (ACTR) of each asset. Mean Portfolio Covariance Matrix Weight Asset 1 Asset 2 Asset 3 Asset 1 8% 25% 0.00860 0.00823 0.00071 Asset 2 10% 40% 0.00823 0.00972 -0.00313 Asset 3 6% 35% 0.00071 -0.00313 0.03987