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Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%.

Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%.

a. What are the weights of A and B in the global minimum variance portfolio respectively?

Answer: You take standard deviation of A / total standard deviation. Then 1-A = Weight of B.

My question: Please explain how it is possible that one can calculate the portfolio weights using the standard deviation.

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