Markowitz Portfolio Theory

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Harry Markowitz introduced and later won the Nobel Prize for the Modern Portfolio Theory in his 1952 article and 1959 book. His theory attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets.

The mathematical formulation is the following.

We solve a quadratic programming problem to find the portfolios weights (ω’s) that maximize this objective function, where λ is the risk-adverse coefficient between 0 and ∞.

R^T w - \lambda \times w^T \Sigma w

One (unity) constraint is:

\sum_i w_i = 1

In additional, AlgoQuant lets you put any (reasonable) constraints on the ω’s as you like. For example, one common constraint is to disallow short selling. That is,

w_i \ge 0




An online demo is available.