Consider the following economy of ComplexLand:

• There are 600 risky securities in the economy. The total market value of all these securities is $10 billion
• A risk-free asset exists with a return of 5%
• There are twenty six mutual funds (named A-Z) that hold various combinations of the 600 traded risky securities. In this economy, mutual funds do not invest (long or short) in the risk-free asset. They also do not charge any fees
• The Capital Asset Pricing Model (CAPM) prices all securities correctly
• If you were to invest $500 in mutual fund F, $100 in fund I, and $400 in fund N, you would get a portfolio that is mean variance efficient (MVE) a.k.a. the tangency portfolio. The expected return on this portfolio is 20%, and the standard deviation is 40%
• If you were to invest $800 in mutual fund F, $200 in fund I, and $ 1000 in fund N, you would get a portfolio that lies on the mean variance frontier. Call this portfolio MVF. The expected return on this portfolio is 10%, and the standard deviation is 20%

Using the above information, answer the following questions a., b. and c.

a. Find the covariance between the MVE and MVF portfolios.

b. Assume that you wish to invest $3 million and earn an expected return of 40%, but that you are prohibited from borrowing at the risk-free rate. However, you can buy (but not short) any mutual funds. How should you invest your money, i.e., calculate the proportions of your portfolio invested in mutual funds F, I and N? Calculate the standard deviation of your portfolio's return.

c. How much lower would your portfolio's return standard deviation be (at an expected return of 40%), if you were allowed to i) short mutual funds, and ii) borrow at the risk-free rate?}