You have $50,000 to invest in three stocks. Let Ri be the random variable representing the annual return on $1 invested in stock i. For example, if Ri = 0.12, then $1 invested in stock i at the beginning of a year is worth $1.12 at the end of the year. The means are E(R1) = 0.17, E(R2) = 0.15, and E(R3) = 0.12. The variances are Var R1 = 0.25, Var R2 = 0.18, and Var R3 = 0.14. The correlations are r12 = 0.6, r13 = 0.9, and r23 = 0.7. Determine the minimum-variance portfolio that attains a mean annual return of at least 0.14. If needed, round your answers to three decimal digits.Investment decision Stock 1Stock 2Stock 3Fractions to invest

The question can be solved using Excel solver. Objective: To find a minimum variance (minimum risk) portfolio using the given information. Given information: Stock Expected return Variance Stock 1 0.17 0.25 Stock 2 0.15 0.18 Stock 3 0.12 0.14 Correlation: Stock Correlation Stock 1 and stock 2 0.6 Stock 1 and stock 3 0.9 Stock 2 and stock 3 0.7 Correlation between stock 3 and 1 will be the same as the correlation between 1 and 3. Similarly, for each such combinations, the correlation will be the same. We need to calculate covariance for each stock combination. Covariance stock 1 and stock 2 = Correlation between stock 1 and stock 2 ×Standard deviation of stock 1 ×Standard deviation of stock 2 The covariance table will be as follows. Covariance Stock 1 Stock 2 Stock 3 Stock 1 0.50*0.50 0.6*0.5*0.42 0.9*0.5*0.37 Stock 2 0.6*0.5*0.42 0.42*0.42 0.7*0.42*0.37 Stock 3 0.9*0.5*0.37 0.7*0.42*0.37 0.37*0.37 Data in Excel: Formulas used: Please note: After entering the formula in Cell B23, press Ctrl+Shift+Enter. Solver parameters. Output: Minimum portfolio variance = 0.141 Fractions to invest Stock 1: 0.110 Stock 2: 0.483 Stock 3: 0.407

Answered: You have $50,000 to invest in three…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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You have $50,000 to invest in three stocks. Let R_i be the random variable representing the annual return on $1 invested in stock i. For example, if R_i = 0.12, then $1 invested in stock i at the beginning of a year is worth $1.12 at the end of the year. The means are E(R₁) = 0.17, E(R₂) = 0.15, and E(R₃) = 0.12. The variances are Var R₁ = 0.25, Var R₂ = 0.18, and Var R₃ = 0.14. The correlations are r₁₂ = 0.6, r₁₃ = 0.9, and r₂₃ = 0.7. Determine the minimum-variance portfolio that attains a mean annual return of at least 0.14. If needed, round your answers to three decimal digits.

Investment decision
	Stock 1	Stock 2	Stock 3
Fractions to invest

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