There are three assets in the economy: stock ABC, market index, and risk-free asset. You hold one stock ABC and you can buy or sell other assets. The current price of ABC is $1. Having observed the historical prices, you know that the mean return on ABC is 10%, the standard deviation is 20%, the correlation of ABC with the market portfolio is 0.7, the standard deviation of market portfolio is 12%. The risk-free rate is 5%. Assume the assumptions of the CAPM hold.

a. Construct a portfolio with zero systematic risk (keeping one stock of ABC), i.e. define the amount of wealth invested in each asset.

b. What are the expected return and the standard deviation of the portfolio in (a)?

c. Suppose you add one more stock ABC to the portfolio constructed in (a). Calculate the expected return and the standard deviation of the new portfolio.