a) In class, we have reviewed the relative performance between inflation, Treasury bonds, small-cap stock index and large-cap stock index. Suppose you are 20 years old now and plan to save for retirement and will deposit $500 per month into your Roth IRA account for the next 40 years. How would you optimally allocate your assets? Prepare a short investment proposal based on what we have learnt in class detailing your asset allocation in different types of securities and discuss necessary adjustments to be made when you turn 30, 40, and 50 years old. Justify your answers based on lecture content and class discussions. (10 points)