Problem 1 (7 points): Consider three securities: S1, S2, and S, with current prices of $5,000, $8,000, and $12,000 respectively. Security S, has Duration 5 and Convexity=20. Security Sy has Duration 10 and Convexity 60. Security S, has Duration=15 and Convexity=130. a) (1 point) Find Duration of a portfolio that consists of 100 units of S., 50 units of S2, and 30 units of S; I b) (1 point) Find Convexity of a portfolio that consists of 100 units of S., 50 units of S, and 30 units of S c) (1 point) Find DVOI of S, d) (1 point) Find DVOI of a portfolio that consists of 1,000 units of S. e) (1 point) How many units of S, do you need to buy or sell to hedge a portfolio that consists of 10,000 units of si f) (2 points) How many units of S and S, do you need to buy or sell to hedge a portfolio that consists of 10,000 units of Si