Question

Derive the weights in stocks x + y that would result in the lowest risk portfolio that could be created with them. I'm not sure if more info is needed to answer this question

Answer 1

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

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

Please Discuss in case of Doubt

Best of Luck. God Bless
Please Rate Well