Assume that only two companies are listed on an effective capital market: companies A and company B. Capitalization (market value of all shares) of both companies is the same. Expected rate of return from shares of company A is 19%, and the expected rate of return on company shares B is 14%. Standard deviation of the rate of return on shares of company A is 30%, and the standard deviation of the rate of return on the company's shares B is 20%. Correlation coefficient between the rate of return on shares company A and the rate of return on shares of company B is 0.5. Rate of return of risk-free assets is 3%, with investors being able to grant loans at this rate, but it is not possible to borrow loans at a rate of return on risk-free assets. However, it is permissible to take both long and short positions in actions (short sale). I have to:
a) Calculate the equation of the straight line showing the relationship between the expected rate of return and the risk measured by the beta coefficient, on which lie only portfolios composed of shares A and B
b) Calculate the equation of the straight line showing the relationship between the expected rate of return and the risk measured by the beta coefficient, on which, under market equilibrium, there lie an segment containing effective portfolios composed partly of shares and partly of risk free assets.
I compute: $\mu_m=\frac{33}{200}$ (expected return from market porfolio), so i guess that in point b) the line will be: $$\mu_w=R+(\mu_m-R)\beta=\frac{3}{100}+\frac{27}{100}\beta$$ But what answer will be in point a)? I have also point c) to answer but first I need to know what is the line in point a). Can anyone help?
c) Present solutions to tasks in point (a) and (b) in the overview sketch in coordinate system: expected rate of return (axis ordinates), beta factor (abscissa axis). Enter coordinates points that you consider important and justify the solution selection of these points.