Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected...

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Finance

Problem 3: You have access to two investmentopportunities. Mutual Fund A, which promises 20% expected returnwith a variance of 0.36, and Mutual Fund B, which promises 15%expected return with a variance 0f 0.12. The correlation betweenthe two is 0.084.
2. In addition to the funds A and B in the previous question,now you decide to include fund C to your portfolio. Its expectedreturn is 10%, its variance 0.0625, its correlation with A is0.1050 and its correlation with B is 0.07. You want to achieve anexpected return of 16% on your portfolio, with the minimum possiblerisk (measured by the standard deviation). Derive analytically(that is, without the help of solver, but through calculus) theweights of such desired portfolio, and its standard deviation.

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Given Returns Variance Std Weights A 20 03600 06 wA B 15 01200 034641 wB C 10 00625 025 wC Correlations AB BC AC 0084 007 0105 Let wA wB and wC be the weights of each Mutual Fund in the portfolio Portfolio variance V is given by V wA2A2 wB2B2 wC2C2 2wAwBCovarianceAB See Answer

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Problem 3: You have access to two investmentopportunities. Mutual Fund A, which promises 20% expected returnwith a variance of 0.36, and Mutual Fund B, which promises 15%expected return with a variance 0f 0.12. The correlation betweenthe two is 0.084.2. In addition to the funds A and B in the previous question,now you decide to include fund C to your portfolio. Its expectedreturn is 10%, its variance 0.0625, its correlation with A is0.1050 and its correlation with B is 0.07. You want to achieve anexpected return of 16% on your portfolio, with the minimum possiblerisk (measured by the standard deviation). Derive analytically(that is, without the help of solver, but through calculus) theweights of such desired portfolio, and its standard deviation.