Exam 30: Portfolio Optimization with Negative Correlation: Finding Minimum Variance and Weight Allocation

Exhibit 7B.l USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The general equation for the weight of the first security to achieve the minimum variance (in a two stock portfolio) is given by: $\mathrm { W } _ { 1 } = \left[ \mathrm { E } \left( \sigma _ { 1 } \right) ^ { 2 } - \mathrm { r } _ { 1.2 } \mathrm { E } \left( \sigma _ { 1 } \right) \mathrm { E } \left( \sigma _ { 2 } \right) \right] \div \left[ \mathrm { E } \left( \sigma _ { 1 } \right) ^ { 2 } + \mathrm { E } \left( \sigma _ { 2 } \right) ^ { 2 } - 2 r _ { 1.2 } \mathrm { E } \left( \sigma _ { 1 } \right) \mathrm { E } \left( \sigma _ { 2 } \right) \right]$ -Refer to Exhibit 7B.1.What is the value of W₁ when r₁.₂ = -1 and E(s₁)= .10 and E(s₂)= .12?

Exhibit 7B.l USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The general equation for the weight of the first security to achieve the minimum variance (in a two stock portfolio) is given by: $\mathrm { W } _ { 1 } = \left[ \mathrm { E } \left( \sigma _ { 1 } \right) ^ { 2 } - \mathrm { r } _ { 1.2 } \mathrm { E } \left( \sigma _ { 1 } \right) \mathrm { E } \left( \sigma _ { 2 } \right) \right] \div \left[ \mathrm { E } \left( \sigma _ { 1 } \right) ^ { 2 } + \mathrm { E } \left( \sigma _ { 2 } \right) ^ { 2 } - 2 r _ { 1.2 } \mathrm { E } \left( \sigma _ { 1 } \right) \mathrm { E } \left( \sigma _ { 2 } \right) \right]$ -Refer to Exhibit 7B.1.Show the minimum portfolio variance for a portfolio of two risky assets when r₁.₂ = -1.