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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