3 Two-Period Model: Mean-Variance Approach

Abstract

The minimum–variance portfolio is the portfolio of risky assets with the minimal portfolio variance:

$$\displaystyle(\lambda _1^{MV}, \lambda _2^{MV}) = \arg \min _{\lambda } \;\sigma _\lambda ^2, \quad \text{ s.t. } 0 \le \lambda _1, \, 0 \le \lambda _2, \, \lambda _1+\lambda _2=1,$$

where the variance of portfolio λ is

$$\displaystyle\sigma _\lambda ^2 = \sigma ^2(\lambda _1 R_1+ \lambda _2 R_2) = \lambda ^T COV \lambda .$$