. E2.7 (easy) An investor is seeking to choose a portfolio into aet of stocks wisely. To...

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E2.7 (easy) An investor is seeking to choose a portfolio into aet of stocks wisely. To do this s/he has collected historical data of mean return and covariance of the set of stocks. Assume that the available stocks to invest in is denoted by T. For each i e I, we assume that the historical mean rate of return when investing 1 SEK is r. Further, for each pair i, j € I, let q, denote the historical covariance of the rate of return when investing 1 SEK into both stocks i and j (note that qu > 0 denotes the variance of investing 1 SEK in the stock i). Finally assume that the investor has M SEK of money available for investment. Formulate an optimization model for minimizing the risk of investment (measured as the covariance of the return of the portfolio), subject to the constraint that the expected return of the portfolio is at least Ro, for some Ro > 0. Under what conditions can you guarantee that your model has an optimal solution? Under what conditions can you guarantee that it has optimal solution if we assume that the investor has an infinite amount of money available for investment (i.e., M 0)? E2.7 (easy) An investor is seeking to choose a portfolio into aet of stocks wisely. To do this s/he has collected historical data of mean return and covariance of the set of stocks. Assume that the available stocks to invest in is denoted by T. For each i e I, we assume that the historical mean rate of return when investing 1 SEK is r. Further, for each pair i, j € I, let q, denote the historical covariance of the rate of return when investing 1 SEK into both stocks i and j (note that qu > 0 denotes the variance of investing 1 SEK in the stock i). Finally assume that the investor has M SEK of money available for investment. Formulate an optimization model for minimizing the risk of investment (measured as the covariance of the return of the portfolio), subject to the constraint that the expected return of the portfolio is at least Ro, for some Ro > 0. Under what conditions can you guarantee that your model has an optimal solution? Under what conditions can you guarantee that it has optimal solution if we assume that the investor has an infinite amount of money available for investment (i.e., M 0)?