Elise plans to invest in the stock market and intends to form a portfolio of the following two securities:

Security Expected return Beta

Fortes, Inc. $18\%2\mathrm{.}25$

Risk$-$free $6\%$

She believes that CAPM holds.

a$)$ Calculate the expected return on a portfolio equally invested in the two securities$.$

b$)$ Calculate the weight of a portfolio that has a beta of $1\mathrm{.}5.$

c$)$ Calculate the beta of a portfolio that has an expected return of $15\%.$