Vanda Capital allocates $15m to be managed by a boutique equity sub-fund, for which you are the portfolio manager. Suppose the risk-free rate is 5% and your sub-fund can borrow and lend at the risk-free rate. Your research analyst finds that the investable equity market index against which your sub-fund is benchmarked has an expected return of 10% and standard deviation of 18%. He suggests that you invest 100% of the funds in the equity of PMJ Ltd, because the risk-return for this company sits on the efficient frontier of risky assets, with an expected return of 12% and standard deviation of 40%. By suitably combining the investable market index with the risk-free asset, construct a portfolio that has either (i) a higher expected return but the same standard deviation as PMJ Ltd, or (ii) the same expected return as PMJ Ltd but a lower standard deviation. Also, you should also explain how your portfolio dollars are invested, and demonstrate that your constructed portfolio is strictly preferred to PMJ Ltd.