On the hellwig method of feasible portfolio construction

Abstract

The work feasible portfolio is built into the work, that is, the k-dimensional Q column vector with components q_i where q_i ≥ 0 for i=1,...,k and q₁+...+q_k=1. We define i=1,...,k in the following way:

$$q_1 = \frac{{r_i^2 }}{{1 - r_i^2 }}A^{ - 1} $$

, where:

$$r_i = r(R_i ,R_M ) {\text{and}} A = \sum\limits_{i = 1}^k {\frac{{r_i^2 }}{{1 - r_i^2 }}} $$

. It is indicated that if r_i<r_j, then q_i<q_j and, moreover, the q_i=t_ib ² _i relation occurs between q_i and b_i estimators of parameters of characteristic line:

$$R_i = \alpha _i + \beta _i R_M + e_i (i = 1,...,k)$$

, where t_i is a certain constant. The effective formulas for a profit rate and risk of the constructed feasible portfolio are given.