验证疯狂的投资组合

Since it is necessary and sufficient that your MAD portfolio set must be a nonempty, closed, and bounded set to have a valid portfolio optimization problem, the估计函数使您可以检查投资组合设置以确定它是否是非发行的，并且，如果非发行，是否是有限的。假设您有以下MAD投资组合集，这是一个空集，因为初始投资组合在0is too far from a portfolio that satisfies the budget and turnover constraint:

p =投资组合（'NumAssets', 3,'预算'，1）;p = setturnover（p，0.3，0）;

If a MAD portfolio set is empty,估计returnsNaN边界并设置isboundedflag to[]:

[LB，UB，ISBOUNDED] =估计值（P）

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

假设您创建一个无限的MAD投资组合集，如下所示：

p =投资组合（'AInequality', [1 -1; 1 1 ],“ binequality', 0); [lb, ub, isbounded] = estimateBounds(p)

lb = -Inf -Inf ub = 1.0e-008 * -0.3712 Inf isbounded = 0

Finally, suppose that you created a投资组合既非空和有限的对象。估计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:

p = portfoliomad;p = setBudget（p，1,1）;p = setBounds（p，[-0.1; 0.2; 0.3; 0.2]，[0.5; 0.3; 0.9; 0.9; 0.8]）;[LB，UB，ISBOUNDED] =估计值（P）

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

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

Validating MAD Portfolios

Given a MAD portfolio set specified in a投资组合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. ThecheckFeasibilityfunction 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投资组合objectp，估计有效的投资组合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 ]; m = m/12; C = C/12; AssetScenarios = mvnrnd(m, C, 20000); p = PortfolioMAD; p = setScenarios(p, AssetScenarios); 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 1 1 1 0 0 0 0 0

qwgt = estimateFrontier(q); checkFeasibility(p, qwgt)

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