3. (15 points) Suppose a Barbell Butterfly is constructed as follows at t=0 Asset Liability 0.5 units of 2-year zero 1 unit of 16 year zero 0.5 units of 30 -year zero Market price of 2 year zero at t=0 is 10,000 Market price of 30 year zero at t=0 is 10,000 Market price of 16 year zero at t=0 is 10,000 Net Equity value at t=0 is 0 The duration convexity and theta of assets, liabilities and net equity are as follows: Asset Liability Net Equity Duration 1600 1600 0 Convexity 452 256 196 Theta 889 1068 -179 a. Sketch the performance profiles of assets and liabilities on the same graph as of t=0. Clearly label the axes and curves on this graph. Provide a short interpretation of the graph. (Hint: Sketch means that suppose you are in an interview and the interviewer gives you this question, paper, and a pen. You are asked to draw on paper by hand what the performance profiles would look like. You do not need to use spreadsheet). b. Sketch the performance profile of net equity as of t=0. Clearly label the axes and curves on this graph. Provide a short interpretation of the graph. c. Sketch the performance profiles of assets and liabilities on the same graph as of t=1. Clearly label the axes and curves on this graph. Provide a short interpretation of the graph. d. Provide the performance profile of net equity as of t=1. Clearly label the axes and curves on this graph. Provide a short interpretation of the graph. e. Your answers to parts (a) through (d) must have highlighted a problem with the delta hedging strategy. Propose an alternative hedging strategy that will eliminate the problem you identified in parts (a) through (d). What will the net equity value be at t=1 if this proposed strategy is followed? Why?