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Show the weights necessary to create a risk-free portfolio from 2 stocks when the correlation coefficient...

Show the weights necessary to create a risk-free portfolio from 2 stocks when the correlation coefficient between these 2 stocks is -1.

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Answer #1

For creating risk free portfolio standard deviation should be equal to 0
Weight of Stock A + Weight of Stock B = 1
Weight of Stock B = 1 - Weight of Stock A
Standard Deviation = ((Weight of A * Standard Deviation of A)2 + (weight of B* standard Deviation of B)2 + 2* Weight of A * Standard Deviation of A * weight of B * standard Deviation of B * correlation)0.5
When correlation = -1
Then Standard Deviation = (Weight of A * Standard Deviation of A - Weight of B * Standard Deviation of B) = 0
weight A * Standard Deviation of A = Weight B * Standard Deviation B

Weight A = Standard Deviation B/( Standard Deviation of A + Standard Deviation B)
Weight B = Standard Deviation A/( Standard Deviation of A + Standard Deviation B)

Please Discuss in case of Doubt

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