Let X₁ and X₂ be the returns of two securities with respective means m₁ and m₂, and variances σ²₁ and σ²₂ . We invest one unit of money: α in the first security and 1−α in the second. So, the investment return is the r.v. X = αX₁ +(1−α)X₂. Assume X₁ and X₂ to be independent.

(a) Find an α optimal under the mean-variance criterion (1.2.2).

(b) Consider two particular cases: m₁ = m₂ and k→∞.

(c) Find an α minimizing the variance of the investment return. Compare it with what you got before and the results of Exercise 3.61.