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%

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20

answer; a set of mutual funds with similar risk characteristics to your mutual fund;