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Michael is considering investing in three stocks. He has 1000 available to invest in these three stocks. Let Si be the random variable representing the

Michael is considering investing in three stocks. He has £1000 available to invest in these three stocks. Let Si be the random variable representing the annual return on £1 invested in stock i. So, if S1 = 0.12, £1 invested in stock i at the be-ginning of a year is worth £1.12 at the end of the year. John is given the following information: E(S1) = 0.14, E(S2) = 0.11, E(S3) = 0.10, Var(S1) = 0.20, Var(S2) = 0.08, Var(S3) = 0.18, Cov(S1, S2) = 0.05, Cov(S1, S3) = 0.02, Cov(S2, S3) = 0.03. Determine the minimum-variance portfolio that attains an expected annual return of at least 0.12.

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