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The expected rate of return of an equity index fund is 12% and the standard deviation of return of this fund is 25%. The rate of a Treasury bill is 4% in the market. You have $2,000,000 investment budget to invest in a portfolio. 

Required: 

a. You would like to invest 60% of your total investment in the equity index fund and 40% in the Treasury bill. What is the expected rate of return and standard deviation of the return on your investment portfolio?  

b. Suppose you decide to invest in the equity index fund with a proportion y of your total investment so that the overall portfolio will have an expected rate of return of 14%. What is the proportion y and what is the standard deviation of the return on your investment portfolio? 

c. With your total $2,000,000 investment budget, what is your dollar amount of investment in the equity index fund and Treasury bill respectively in terms of the results in 'b'? Explain. 

d. Your risk aversion coefficient is A = 3.5. What proportion, y, of your investment should be invested in the equity index fund to have your optimized portfolio, and what is the expected value and standard deviation of the rate of return on your optimized portfolio?