Regardless of investors' personal preferences, all investors want to use the net present value method (NPV method) to judge whether to accept or abandon the same investment project.

Investors make two independent decisions:

1. Estimate the expected returns and differences of various securities or assets in the portfolio;

2. By calculating the covariance between the returns of various securities or assets, investors can calculate the effective set of risky assets.

Efficient set: when multiple securities form a portfolio, all portfolios are in a region, and investors should choose the boundary above the region anyway, which is the efficient set.

In all portfolios, there can be multiple expected returns corresponding to the same variance. Of course, investors want to maximize the expected return under the same variance, so there is a plan:

Maxe (s) s.t.var (s) = where k is a constant, where s stands for portfolio;

Similarly, in all portfolios, investors always want to minimize the risks they face in order to obtain the expected returns:

The minimum var(s) s.t. E(s)=k, where k is a constant.

There is no essential difference between the above two. From any of these schemes, we can get a set of data of all portfolios on the two-dimensional plane, which is the optimal portfolio, that is, the efficient set. Corresponding to the expected income that can be achieved, the combined variance on the effective set is the smallest; For the same variance, the portfolio on the efficient set has the largest expected return.