4. An endowment fund uses a core-satellite approach to allocate amongst different managers. The managers' active risk, active return, and allocations (in endowment portfolio) are given in following table. What is (are) the investor's core position? Calculate the endowment fund's overall active return, active risk, and information ratio. If you do not have enough information to make the calculation, list the assumptions you need and the reasons. Expected Active Return Expected Active Risk Allocation Passive Index 0.00% 0.00% 20% Enhanced Indexing 0.70% 1.50% 30% Active Manager A 1.00% 2.50% 25% Active Manager B 2.00% 3.00% 15% Active Manager C 2.40% 4.20% 10% 5. A define-benefit pension fund has following holdings in their fixed-income portfolio: Bond Credit Rating Maturity (yr) Coupon Rate Modified Convexity (%) Duration Market Value of Position A US Treasury 3.1 0.3 2.738 9.8 $50,000 B A1 9.8 7.5 6.452 56.2 $50,000 C Aa2 5.2 11.5 3.733 18.5 $50,000 D Agency 6.7 9.8 4.874 32.3 $50,000 E 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?