Sometimes, you may want to validate either your inputs to, or outputs from, a portfolio optimization problem. Although most error checking that occurs during the problem setup phase catches most difficulties with a portfolio optimization problem, the processes to validate portfolio sets and portfolios are time consuming and are best done offline. So, the portfolio optimization tools have specialized functions to validate portfolio sets and portfolios. For information on the workflow when using Portfolio objects, see Portfolio Object Workflow.

Since it is necessary and sufficient that your portfolio set
must be a nonempty, closed, and bounded set to have a valid portfolio
optimization problem, the `estimateBounds`

function
lets you examine your portfolio set to determine if it is nonempty
and, if nonempty, whether it is bounded. Suppose that you have the
following portfolio set which is an empty set because the initial
portfolio at `0`

is too far from a portfolio that
satisfies the budget and turnover constraint:

p = Portfolio('NumAssets', 3, 'Budget', 1); p = setTurnover(p, 0.3, 0);

If a portfolio set is empty, `estimateBounds`

returns `NaN`

bounds
and sets the `isbounded`

flag to `[]`

:

[lb, ub, isbounded] = estimateBounds(p)

lb = NaN NaN NaN ub = NaN NaN NaN isbounded = []

Suppose that you create an unbounded portfolio set as follows:

p = Portfolio('AInequality', [1 -1; 1 1 ], 'bInequality', 0); [lb, ub, isbounded] = estimateBounds(p)

lb = -Inf -Inf ub = 1.0e-08 * -0.3712 Inf isbounded = logical 0

`estimateBounds`

returns (possibly
infinite) bounds and sets the `isbounded`

flag to
`false`

. The result shows which assets are unbounded so that
you can apply bound constraints as necessary.Finally, suppose that you created a portfolio set that is both nonempty and bounded. `estimateBounds`

not only validates
the set, but also obtains tighter bounds which are useful if you are concerned with
the actual range of portfolio choices for individual assets in your portfolio
set:

p = Portfolio; p = setBudget(p, 1,1); p = setBounds(p, [ -0.1; 0.2; 0.3; 0.2 ], [ 0.5; 0.3; 0.9; 0.8 ]); [lb, ub, isbounded] = estimateBounds(p)

lb = -0.1000 0.2000 0.3000 0.2000 ub = 0.3000 0.3000 0.7000 0.6000 isbounded = logical 1

In this example, all but the second asset has tighter upper bounds than the input upper bound implies.

Given a portfolio set specified in a Portfolio object, you often
want to check if specific portfolios are feasible with respect to
the portfolio set. This can occur with, for example, initial portfolios
and with portfolios obtained from other procedures. The `checkFeasibility`

function determines
whether a collection of portfolios is feasible. Suppose that you perform
the following portfolio optimization and want to determine if the
resultant efficient portfolios are feasible relative to a modified
problem.

First, set up a problem in the Portfolio object `p`

,
estimate efficient portfolios in `pwgt`

, and then
confirm that these portfolios are feasible relative to the initial
problem:

m = [ 0.05; 0.1; 0.12; 0.18 ]; C = [ 0.0064 0.00408 0.00192 0; 0.00408 0.0289 0.0204 0.0119; 0.00192 0.0204 0.0576 0.0336; 0 0.0119 0.0336 0.1225 ]; p = Portfolio; p = setAssetMoments(p, m, C); p = setDefaultConstraints(p); pwgt = estimateFrontier(p); checkFeasibility(p, pwgt)

ans = 1 1 1 1 1 1 1 1 1 1

Next, set up a different portfolio problem that starts with the initial problem with an additional a turnover constraint and an equally weighted initial portfolio:

q = setTurnover(p, 0.3, 0.25); checkFeasibility(q, pwgt)

ans = 0 0 0 1 1 0 0 0 0 0

`q`

.
Solving the second problem using `checkFeasibility`

demonstrates
that the efficient portfolio for Portfolio object `q`

is
feasible relative to the initial problem:qwgt = estimateFrontier(q); checkFeasibility(p, qwgt)

ans = 1 1 1 1 1 1 1 1 1 1

`Portfolio`

| `checkFeasibility`

| `estimateBounds`

- Creating the Portfolio Object
- Working with Portfolio Constraints Using Defaults
- Estimate Efficient Portfolios for Entire Efficient Frontier for Portfolio Object
- Estimate Efficient Frontiers for Portfolio Object
- Asset Allocation Case Study
- Portfolio Optimization Examples