Assume that you have an investment portfolio of $100,000. The investment consists of $60,000 in Alphabet and $40,000 in Apple. You are thinking of rebalancing the portfolio by selling $20,000 worth of Alphabet and $20,000 worth of Apple. You plan to invest the realized proceeds of $40,000 in Facebook stock. Assume that betas of Alphabet (1.2), Apple (1.1), and Facebook (0.6).

What would be the beta of your new portfolio?

Say you decide to sell off all the three stocks and have a new portfolio consisting of only treasury bonds and market portfolio (S&P 500 index funds). How much of $100,000 would invest in treasury bonds to have the same beta that you calculated above.