Default Portfolio Problem

The default portfolio optimization problem has a risk and return proxy associated with a given problem, and a portfolio set that specifies portfolio weights to be nonnegative and to sum to 1. The lower bound combined with the budget constraint is sufficient to ensure that the portfolio set is nonempty, closed, and bounded. The default portfolio optimization problem characterizes a long-only investor who is fully invested in a collection of assets.

• For mean-variance portfolio optimization, it is sufficient to set up the default problem. After setting up the problem, data in the form of a mean and covariance of asset returns are then used to solve portfolio optimization problems.

• For conditional value-at-risk portfolio optimization, the default problem requires the additional specification of a probability level that must be set explicitly. Generally, “typical” values for this level are 0.90 or 0.95. After setting up the problem, data in the form of scenarios of asset returns are then used to solve portfolio optimization problems.

• For MAD portfolio optimization, it is sufficient to set up the default problem. After setting up the problem, data in the form of scenarios of asset returns are then used to solve portfolio optimization problems.