You want to invest in two stocks, Pfizer (PFE) and Moderna (MRNA). The table below presents the summary statistics for these two stocks:

	Expected Return	Standard Deviation
PFE	9%	15%
MRNA	17%	55%

The correlation coefficient between returns on these two stocks is 0.5.

1. Construct a portfolio of these two stocks that is expected to pay 12% return.
2. What is the standard deviation of your portfolio in part a?
3. Now construct the new portfolio of PFE and MRNA that is expected to pay 20% return.
4. Explain the weights of PFE and MRNA in your portfolio in part c.
5. What is the standard deviation of the portfolio, which you constructed in part c?
6. Compute the weights for the minimum variance efficient (MVE) portfolio, consisting of PFE and MRNA. 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.

1. Write down your objective function (as a formula) with numbers plugged in.
2. What are you doing with this function?
3. What variable(s) can you choose?
4. Do you have any constraints? Write them down.

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