You want to invest in two exchange-traded funds: Fund A, which tracks S & P 500 index and Fund B, consisting of stocks related to gold. The summary statistics for these funds are shown in the table below:

The Correlation coefficient between return on these two funds is 0.1.

a. Construct a portfolio of these two funds, which is expected to pay a 9% return.

b. What is the standard deviation of your portfolio in part a?

c. Now construct the new portfolio of funds A and B, such that it pays a 15% return.

d. Explain the weights of funds A and B in your portfolio in part c.

e. What is the standard deviation of the portfolio, which you constructed in part c?

f. Compute the weights for the minimum variance efficient (MVE) portfolio, consisting of funds I8 and B. You can use Solver to answer this question, but you need to explain in details, which problem your Solver actually solves. Alternatively, you can simply use calculus.

i. Write down your objective function with numbers plugged in.

ii. What are you doing with this function? iii. What variable(s) can you choose?

iv. Do you have any constraints? Write them down.

g. What is the expected return and standard deviation of MVE portfolio?

Fund A Fund B Expected Return 10% 8% Standard Deviation 18% 9%