All interest rates are annual interest rates with semi-annual compounding unless specified otherwise. All coupon rates are annual coupon rates paid semi-annually unless specified otherwise.

Problem 1 (7 points): Consider three securities: S1, S2, and S3 with current prices of $5,000, $8,000, and $12,000 respectively. Security S1 has Duration=5 and Convexity=20. Security S2 has Duration 10 and Convexity=60. Security S3 has Duration=15 and Convexity=130.

d) (1 point) Find DV01 of a portfolio that consists of 1,000 units of S1

e) (1 point) How many units of S2 do you need to buy or sell to hedge a portfolio that consists of 10,000 units of S1

f) (2 points) How many units of S2 and S3 do you need to buy or sell to hedge a portfolio that consists of 10,000 units of S1