Suppose you are given the mean return vector and variance-covariance matrix for 20 risky assets as...

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Suppose you are given the mean return vector and variance-covariance matrix for 20 risky assets as well as the risk free rate rf. Assume that all the CAPM assumptions are satisfied and you are performing mean-variance portfolio optimization. (a) (10pt) Sketch the risky efficient frontier as well as the capital market line (CML). In your sketch: Label the x- and y-axes (, , and/or ). Indicate whether your sketch is meant to be a hyperbola or a parabola. Label the risk-free rate rf on one of the two axes. Label the market portfolio M. Label minimum risk portfolio m on the risky efficient frontier and mark its mean return and risk on the corresponding axes. Below your sketch, please specify whether the expected return of the above min-risk portfolio should be greater than or less than the risk-free rate and justify why that should be the case. When you are done, make 2 additional copies of the efficient frontier (3 copies in total). You should submit 1 copy to part (a), and the other two copies will be used in part (b) and (c). (c) (10pt) Suppose, in the portfolio optimization in part (a), with the only exception of the market portfolio, all other portfolios on the risky efficient frontier requires short-selling (i.e., these portfolios all have at least one element in Wopt that is negative). You don't like short-selling, so you perform mean-variance portfolio optimization again with all 20 stocks, but this time short-selling is prohibited (i.e., you add non-negativity constraints to all the portfolio weights.) On a copy of the efficient frontier in part (a), sketch a risky efficient frontier that prohibits short-selling. In your sketch, please clearly indicate the two risky efficient frontiers. In your sketch, please label the market portfolio on both risky efficient frontiers. Below you sketch, please comment on whether or not the two risky efficient frontiers coincide. If so, at what point(s) do they coincide. Suppose you are given the mean return vector and variance-covariance matrix for 20 risky assets as well as the risk free rate rf. Assume that all the CAPM assumptions are satisfied and you are performing mean-variance portfolio optimization. (a) (10pt) Sketch the risky efficient frontier as well as the capital market line (CML). In your sketch: Label the x- and y-axes (, , and/or ). Indicate whether your sketch is meant to be a hyperbola or a parabola. Label the risk-free rate rf on one of the two axes. Label the market portfolio M. Label minimum risk portfolio m on the risky efficient frontier and mark its mean return and risk on the corresponding axes. Below your sketch, please specify whether the expected return of the above min-risk portfolio should be greater than or less than the risk-free rate and justify why that should be the case. When you are done, make 2 additional copies of the efficient frontier (3 copies in total). You should submit 1 copy to part (a), and the other two copies will be used in part (b) and (c). (c) (10pt) Suppose, in the portfolio optimization in part (a), with the only exception of the market portfolio, all other portfolios on the risky efficient frontier requires short-selling (i.e., these portfolios all have at least one element in Wopt that is negative). You don't like short-selling, so you perform mean-variance portfolio optimization again with all 20 stocks, but this time short-selling is prohibited (i.e., you add non-negativity constraints to all the portfolio weights.) On a copy of the efficient frontier in part (a), sketch a risky efficient frontier that prohibits short-selling. In your sketch, please clearly indicate the two risky efficient frontiers. In your sketch, please label the market portfolio on both risky efficient frontiers. Below you sketch, please comment on whether or not the two risky efficient frontiers coincide. If so, at what point(s) do they coincide.