Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return of 10% and a standard deviation of return of 30%. The weight of security B in the minimum-variance portfolio is?

40%

Explanation:

Here, We have two perfectly negatively correlated risky securities.

So, the minimum variance portfolio will be the portfolio with zero variance.

so, x(A)=σ(B)/(σA)+σ(B)) and x(B)=σ(A)/(σ(A)+σ(B))

therefore, x(B)=20/(20+30)

x(B)=20/50

x(B)=2/5 = 40%

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