# Symbol for the feasible set of portfolios in mean-variance analysis?

When we optimize some mean-variance efficient portfolio, it lies on the efficient frontier (blue line) which is considered superior to the feasible set of portfolios. The feasible set (red dots), on the other hand, is generated with random, rather than optimized, weight vectors.

Since there are tens of thousands of portfolios that lie within the feasible set, what is the convention in mean-variance analysis literature for symbolically expressing that a certain portfolio (weight vector) belongs to the feasible set? Is it:

$$w \in \mathcal{F}$$ where $$\mathcal{F}$$ is the feasible set?

• Please note that the feasible set is simply the set of all portfolio combinations such that $\sum_i w_i =1$. I do not know of any specific symbol for that,though. – Kermittfrog Oct 30 '20 at 13:20
• portfolio combinations that lie on the efficient frontier meet that criteria, so does that mean efficient portfolios (on the efficient frontier) are part of the feasible set? – develarist Oct 30 '20 at 14:28
• Your notation seems correct based on p.4 of this paper: sites.math.washington.edu/~burke/crs/408/fin-proj/mark1.pdf – CasusBelli Oct 30 '20 at 14:53