Quippy Inc ("Quippy") and Whippy Inc ("Whippy") have common shares listed on the New York Exchange. Assume that the S&P 500 Index represents the market portfolio.
An equal-weighted portfolio of Quippy's shares and a risk-free asset has an annual variance of 0.04.
An equal-weighted portfolio of the S&P 500 Index and a risk-free asset has an annual variance of 0.01.
An equal-weighted portfolio of Quippy's shares and the S&P 500 Index has an annual variance of 0.08.
The risk-free asset has an expected annual return of 3%, and the S&P 500 Index has an expected annual return of 7%.
(a) Calculate the beta of Quippy's shares.
(b) Suppose you want to put together an equal-weighted portfolio of Quippy's and Whippy's shares. Whippy's shares have the same beta as the S&P 500 Index. What is the required annual return of this portfolio?
(c) Suppose you can change the weights in the portfolio in (b) above. What percentage of the portfolio must be invested in the shares of Quippy in order to achieve a required annual portfolio return of 12%?