Suppose you are given the mean return vector p and variance-covariance matrix for 20 risky assets as well as the risk free rate rs. 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 r- and y-axes (u, o, and/or o?). Indicate whether your sketch is meant to be a hyperbola or a parabola. Label the risk-free rate ry 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). (b) (10pt) Suppose, in the portfolio optimization in part (a), the min-risk portfolio contains only 10 of the 20 stocks (meaning only 10 of the 20 elements in Wopt are non-zero). Moreover, all other portfolios on that efficient frontier has more than 10 stocks with non-zero weights. Because you worry about transaction costs when trading too many stocks, you decide to perform mean-variance portfolio optimization again, but this time only use those 10 stocks in the above min- risk portfolio (i.e., as if the other 10 stocks do not exist). On a copy of the efficient frontier in part (a), sketch a risky efficient frontier based on only 10 stocks. In your sketch, please clearly indicate the two risky efficient frontiers. For example, add arrows pointing to the two efficient frontiers and label them as EF with 20 stocks and EF with 10 stocks". In your sketch, please label the minimum risk 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 p and variance-covariance matrix for 20 risky assets as well as the risk free rate rs. 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 r- and y-axes (u, o, and/or o?). Indicate whether your sketch is meant to be a hyperbola or a parabola. Label the risk-free rate ry 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). (b) (10pt) Suppose, in the portfolio optimization in part (a), the min-risk portfolio contains only 10 of the 20 stocks (meaning only 10 of the 20 elements in Wopt are non-zero). Moreover, all other portfolios on that efficient frontier has more than 10 stocks with non-zero weights. Because you worry about transaction costs when trading too many stocks, you decide to perform mean-variance portfolio optimization again, but this time only use those 10 stocks in the above min- risk portfolio (i.e., as if the other 10 stocks do not exist). On a copy of the efficient frontier in part (a), sketch a risky efficient frontier based on only 10 stocks. In your sketch, please clearly indicate the two risky efficient frontiers. For example, add arrows pointing to the two efficient frontiers and label them as EF with 20 stocks and EF with 10 stocks". In your sketch, please label the minimum risk 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
