Your portfolio consists of $10M invested in security AAA and $30M invested in security BBB. AAA has Duration=6 and Convexity=18 while BBB has Duration=10 and Convexity=50

a) Find Duration and Convexity of your portfolio

b) Assume you want to hedge your portfolio with security S1 that has Duration=7.5 and Convexity = 27. How much of S1 (in dollars) you need to buy or sell to best hedge your portfolio?

c) Assume, in addition to S1, you have access to another security S2. Using S1 and S2 you constructed an optimal hedge for your portfolio and such hedge consists of selling $20M of S1 and $30M of S2. Find Duration and Convexity of S2