Risk aversion and Investment

Consider an investor who has available the sum of $15,000 for investment, and is considering investing in stocks X1, X2, and X3. The prices of these stocks during the last 12 months are provided in the table below. The investor also has an option of keeping the money and not investing (Cash). The objective is to maximize net profits (revenues minus costs).

						Month
	1	2	3	4	5	6	7	8	9	10	11	12
X1	40	42	44	40	46	48	50	41	48	38	40	40
X2	120	118	120	116	122	115	123	124	117	119	118	116
X3	60	61	58	52	54	49	55	37	38	40	39	45

The prices (these are not net returns) shown are the closing prices on the last business day of each month. Assume that you are currently in the end of month 12. i.e. purchasing prices for stocks are those of month 12.

For risk aversion coefficient assume the values of 0, 0.0005, 0.0006, 0.0007, 0.0008, 0.0009, 0.001, 0.002, 0.01, 0.2, 0.3

1.Turn in the mathematical formulation of this problem (NO GAMS). Carefully, cleanly, and clearly define all your sets and variables.

2.Use expected prices, based on past observations, for forecasting and determine the EV frontier (Expected value- Variance graph, otherwise also known as locus of efficient portfolios). Turn in the graph of the EV frontier.

3.Hand in your GAMS code which should include a report writing parameter. Report writing parameter should display the following information in this exact format in the .lst file.

X1 X2 X3 Cash E(profit) Var (shadow price of funds available)

0

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0.002

0.01

0.2

0.3