A define$-$benefit pension fund has following holdings in their fixed$-$income portfolio:

i$)$ Calculate modified duration for this portfolio.

ii$)$ the modified duration of pension's liabilities is $6\mathrm{.}50$ 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?