The question is on page 3 and the answer is given on page 16. In the answer to (ii), it says that since the risk-free rate is included, the efficient frontier is a straight line, which I agree. But it also says that because it is a straight line, the returns on any efficient portfolio are perfectly correlated with those of the market, hence rho_ZM = 1. I do not understand this latter part, do we know for sure that as long as the efficient frontier is a straight line, there is a perfect correlation of the efficient portfolio and the market portfolio? And even if there is a perfect correlation, it could be either +1 or (-1), so I do not fully get what is meant here.
The efficient frontier is a straight line passing through (0,r) and the market portfolio. If the expected return on the market portfolio increases, then the efficient frontier essentially pivots anticlockwise about (0,r). If the expected return on the market portfolio decreases then the whole efficient frontier rotates clockwise about (0,r). Therefore the expected returns of every efficient portfolio move in the same direction as the market portfolio.
