ConstrainedQuadraticPortfolioOptimiser
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Function Description
Returns a vector 
(and
three further values indicating the total asset weight, the return and the risk
of the portfolio in that order) that maximises the following investor utility
function subject to lower bound constraints of the form 
and 
further
(linear) constraints of the form and 
.
Here 
are
the portfolio weights (so typically we impose at least the following constraint
), 
is
the benchmark (or ‘minimum risk’ portfolio), 
is a
vector of assumed returns on each asset and 
is
the covariance matrix (
,
where 
is
the vector of risks on each asset class, here assumed to be characterised by
their volatilities, as this approach is merely a mean-variance one, and 
their
correlation matrix).
Constraints are coded -1 for 
, 0
for 
and
+1 for 
. For
example, if 
, 
and
the additional linear constraints are 
and 
then:
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Output type / Parameter details
Output type: Double()
| Parameter Name | Variable Type | Description |
| MinimumRiskPortfolio | Double() | Vector characterising the benchmark, i.e. minimum risk portfolio (n terms) |
| Lambda | Double | Risk aversion parameter |
| ForecastReturns | Double() | Vector of assumed returns from different assets (n terms) |
| ForecastRisks | Double() | Vector of assumed risks (volatilities) of different assets (n terms) |
| ForecastCorrelations | Double() | Array of assumed correlations between different assets (n x n terms) |
| LowerBounds | Double() | Vector containing the lower bounds on portfolio weights (n terms) |
| ConstraintMatrix | Double() | Array containing the constraint coefficients applicable to the problem (m x n terms) |
| ConstraintLimits | Double() | Vector containing the constraint limits applicable to the problem (m terms) |
| ConstraintTypes | Integer() | Vector containing constraint types (-ve is a less than constraint, 0 is an equals constraint and +ve is a greater than) (m terms) |
Links to:
-
Interactively run function
-
Interactive instructions
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Example calculation
-
Output type / Parameter details
-
Illustrative spreadsheet
-
Other Portfolio optimisation functions
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Computation units used
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