6 (2+2+2+3+3+3+3) You can only invest in two securities: ABC and XYZ. The correlation between the returns of ABC and XYZ is 0.2. Expected returns and standard deviations are as follows:

Security E[R] (R)

ABC 20% 20%

XYZ 15% 25%

1. It seems that ABC dominates XYZ in that it has a higher expected return and lower standard deviation. Would anyone ever invest in XYZ? Why?

2. What is the expected return and standard deviation of a portfolio that invests 60% in ABC and 40% in XYZ?

3. Suppose instead that you want your portfolio to have an expected return of 19.5%. What portfolio weights do you select now? What is the standard deviation of this portfolio?

In addition, you have a risk-free security with a guaranteed return of 5%. Let w* be the weight on ABC and 1-w* on XYZ for the tangency portfolio.

4. Construct the equation we need to solve for w*. (You dont need to solve for it)
5. Assume w*=0.7922 (for part d). What is the expected return and s.d. of your tangency portfolio?
6. What portfolio weights will you choose for the risk-free asset and the tangency portfolio to get an expected return of 19.5%.

Compare this portfolio with the one you obtained in (c) of the previous question.