Use the following information to calculate the expected return and standard deviation of a portfolio that is 60 percent invested in 3 Doors, Inc., and 40 percent invested in Down Co.: (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

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Tundexi Tundexi · Answer 1 · 2020-11-03T03:43:22+01:00

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3 Doors, Inc. Down Co.

Expected return, E (R) 16% 11%

Standard deviation, s 49 34.5

What is the standard deviation if the correlation is +1? 0? -1? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Portfolio Variance = wA^2*σA^2 + wB^2*σB^2 + 2*wA*WB* σA* σB* ρAB

For correlation = 1

Portfolio Variance = 0.6^2*0.49^2 + 0.4^2*0.345^2 + 2*0.4*0.6*0.49*0.345*1

Portfolio Variance = 0.1866

Portfolio Standard deviation = [tex]\sqrt{0.1866}[/tex]

Portfolio Standard deviation = 0.4320

Portfolio Standard deviation = 43.2%

For correlation = 0

Portfolio Variance = 0.6^2*0.49^2 + 0.4^2*0.345^2 + 2*0.4*0.6*0.49*0.345*0

Portfolio Variance = 0.10548

Portfolio Standard deviation = [tex]\sqrt{0.10548}[/tex]

Portfolio Standard deviation = 0.3248

Portfolio Standard deviation = 32.48%

For correlation = -1

Portfolio Variance = 0.6^2*0.492 + 0.4^2*0.345^2 + 2*0.4*0.6*0.49*0.345*(-1)

Portfolio Variance = 0.0243

Portfolio Standard deviation = [tex]\sqrt{0.0243}[/tex]

Portfolio Standard deviation = 0.156

Portfolio Standard deviation = 15.6%