ANSWERS MAY BE CORRECT The expected return and standard deviation of a portfolio

Question

ANSWERS MAY BE CORRECT

The expected return and standard deviation of a portfolio that is 50 percent invested in 3 Doors, Inc., and 50 percent invested in Down Co. are the following: 3 Doors, Inc. DOwn Co. Expected return, E(R) standard deviation, 14% 57 128 34 What is the standard deviation if the correlation is +1? 0?-1? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Standard Deviation Correlation +1 Correlation 0 Correlation -1 45.50% 33.191% 11.50%

Explanation / Answer

Answer a.

Correlation, = +1

Weight of 3 Doors, Inc., wA = 50%
Weight of Down Co., wB = 50%
Standard Deviation of 3 Doors, Inc., A = 0.57
Standard Deviation of Down Co, B = 0.34

Variance of Portfolio = wA^2*A^2 + wB^2*B^2 + 2*wA*wB*A*B*
Variance of Portfolio = 0.50^2*0.57^2 + 0.50^2*0.34^2 + 2*0.50*0.50*0.57*0.34*1
Variance of Portfolio = 0.207025

Standard Deviation = (0.207025)^(1/2)
Standard Deviation = 0.455
Standard Deviation = 45.50%

Answer b.

Correlation, = 0

Weight of 3 Doors, Inc., wA = 50%
Weight of Down Co., wB = 50%
Standard Deviation of 3 Doors, Inc., A = 0.57
Standard Deviation of Down Co, B = 0.34

Variance of Portfolio = wA^2*A^2 + wB^2*B^2 + 2*wA*wB*A*B*
Variance of Portfolio = 0.50^2*0.57^2 + 0.50^2*0.34^2 + 2*0.50*0.50*0.57*0.34*0
Variance of Portfolio = 0.110125

Standard Deviation = (0.110125)^(1/2)
Standard Deviation = 0.3319
Standard Deviation = 33.19%

Answer c.

Correlation, = -1

Weight of 3 Doors, Inc., wA = 50%
Weight of Down Co., wB = 50%
Standard Deviation of 3 Doors, Inc., A = 0.57
Standard Deviation of Down Co, B = 0.34

Variance of Portfolio = wA^2*A^2 + wB^2*B^2 + 2*wA*wB*A*B*
Variance of Portfolio = 0.50^2*0.57^2 + 0.50^2*0.34^2 + 2*0.50*0.50*0.57*0.34*(-1)
Variance of Portfolio = 0.013225

Standard Deviation = (0.013225)^(1/2)
Standard Deviation = 0.1150
Standard Deviation = 11.50%

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