Consider a world in which the CAPM model is true. Suppose portfolio M is the portfolio at the efficiency frontier that lies on a line that is tangent to the boundary from the risk-free rate on the vertical axis. Suppose portfolio M has a expected return equal to 9% and a standard deviation of returns equal to 12% for each of the following exercises (even when the risk-free rate is changed).

a) Find the expected return on an asset with = 0.5 assuming that the risk-free rate is 4%.

b) Consider a portfolio made up of two assets: Asset M and risk free asset. Find the expected return and the standard deviation of portfolio returns with  =  0.5 assuming that the risk-free rate is 4 %. (It is valid to borrow at the risk-free rate, which means that the asset without risk can be shorted).