According to CAPM, \(\mu_{X}\) is a linear function of \(\beta_{X}\). The graph of \(\mu_{X}\) versus \(\beta_{X}\) in the \((\beta, \mu)\) plane is called the security market line (SML).

(a) What is the coordinate of the risk-free asset in the \((\beta, \mu)\) plane?

(b) What is the coordinate of the market portfolio in the \((\beta, \mu)\) plane?

(c) For a portfolio \(X\) on the CML with \(R_{X}=w R_{0}+(1-w) R_{M}\), what is its coordinate in the \((\beta, \mu)\) plane?

(d) Can the beta of a portfolio be negative? Can it be larger than 1? Explain.

(e) Show that the beta of a portfolio is the weighted average of the betas of the portfolio's assets, where the weights are the asset allocations of each asset in the portfolio.

(f) Show that the diversifiable risk, \(\operatorname{Var}\left(\epsilon_{X}ight)\), of a portfolio \(X\) on the CML is zero.