org.ojalgo.finance.portfolio

Class MarkowitzModel

java.lang.Object

org.ojalgo.finance.portfolio.FinancePortfolio

org.ojalgo.finance.portfolio.MarkowitzModel

All Implemented Interfaces:

Comparable<FinancePortfolio>, FinancePortfolio.Context

public final class MarkowitzModel
extends FinancePortfolio

The Markowitz model, in this class, is defined as:

min (RAF/2) [w]^T[C][w] - [w]^T[r]
subject to |[w]| = 1

RAF stands for Risk Aversion Factor. Instead of specifying a desired risk or return level you specify a level of risk aversion that is used to balance the risk and return.

The expected returns for each of the assets must be excess returns. Otherwise this formulation is wrong.

The total weights of all assets will always be 100%, but shorting can be allowed or not according to your preference. ( setShortingAllowed(boolean) ) In addition you may set lower and upper limits on any individual asset. ( setLowerLimit(int, BigDecimal) and setUpperLimit(int, BigDecimal) )

Risk-free asset: That means there is no excess return and zero variance. Don't (try to) include a risk-free asset here.

Do not worry about the minus sign in front of the return part of the objective function - it is handled/negated for you. When you're asked to supply the expected excess returns you should supply precisely that.

Basic usage instructions

After you've instantiated the MarkowitzModel you need to do one of three different things:

1. setRiskAversion(Number) unless this was already set in the MarketEquilibrium or FinancePortfolio.Context used to instantiate the MarkowitzModel
2. setTargetReturn(BigDecimal)
3. setTargetVariance(BigDecimal)

Optionally you may setLowerLimit(int, BigDecimal), setUpperLimit(int, BigDecimal) or setShortingAllowed(boolean).

To get the optimal asset weighs you simply call getWeights() or getAssetWeights().

If the results are not what you expect the first thing you should try is to turn on optimisation model validation: model.optimisation().validate(true);

Author:

apete

Nested Class Summary

Nested classes/interfaces inherited from class org.ojalgo.finance.portfolio.FinancePortfolio

FinancePortfolio.Context

Field Summary

Fields inherited from class org.ojalgo.finance.portfolio.FinancePortfolio

MATRIX_FACTORY

Constructor Summary

Constructors

Constructor and Description
MarkowitzModel(BasicMatrix covarianceMatrix, BasicMatrix expectedExcessReturns)
MarkowitzModel(FinancePortfolio.Context portfolioContext)
MarkowitzModel(MarketEquilibrium marketEquilibrium, BasicMatrix expectedExcessReturns)

Method Summary

Modifier and Type	Method and Description
org.ojalgo.finance.portfolio.LowerUpper	addConstraint(BigDecimal lowerLimit, BigDecimal upperLimit, int... assetIndeces) Will add a constraint on the sum of the asset weights specified by the asset indices.
protected BasicMatrix	calculateAssetReturns()
protected BasicMatrix	calculateAssetReturns(BasicMatrix aWeightsVctr)
protected BasicMatrix	calculateAssetWeights() Constrained optimisation.
protected BasicMatrix	calculateAssetWeights(BasicMatrix aReturnsVctr)
protected Scalar<?>	calculatePortfolioReturn(BasicMatrix aWeightsVctr, BasicMatrix aReturnsVctr)
double	calculatePortfolioReturn(FinancePortfolio weightsPortfolio)
protected Scalar<?>	calculatePortfolioVariance(BasicMatrix aWeightsVctr)
double	calculatePortfolioVariance(FinancePortfolio weightsPortfolio)
protected void	calibrate(BasicMatrix aWeightsVctr, BasicMatrix aReturnsVctr)
void	clearAllConstraints()
BasicMatrix	getAssetReturns()
BasicMatrix	getAssetVolatilities()
BasicMatrix	getAssetWeights()
BasicMatrix	getCorrelations()
BasicMatrix	getCovariances()
MarketEquilibrium	getMarketEquilibrium()
double	getMeanReturn() The mean/expected return of this instrument.
double	getReturnVariance() The instrument's return variance.
Scalar<?>	getRiskAversion()
String[]	getSymbols()
List<BigDecimal>	getWeights() This method returns a list of the weights of the Portfolio's contained assets.
protected BasicMatrix	handle(Optimisation.Result optimisationResult)
boolean	isShortingAllowed()
org.ojalgo.finance.portfolio.OptimisedPortfolio.Optimiser	optimiser()
protected void	reset()
void	setLowerLimit(int assetIndex, BigDecimal lowerLimit)
void	setRiskAversion(Number factor)
void	setShortingAllowed(boolean allowed)
void	setTargetReturn(BigDecimal targetReturn) Will set the target return to whatever you input and the target variance to null.
void	setTargetVariance(BigDecimal targetVariance) Will set the target variance to whatever you input and the target return to null.
void	setUpperLimit(int assetIndex, BigDecimal upperLimit)
int	size()
List<SimpleAsset>	toSimpleAssets()
SimplePortfolio	toSimplePortfolio()
String	toString()

Methods inherited from class org.ojalgo.finance.portfolio.FinancePortfolio

compareTo, forecast, getConformance, getLossProbability, getLossProbability, getSharpeRatio, getSharpeRatio, getValueAtRisk, getValueAtRisk95, getVolatility, normalise, normalise

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

MarkowitzModel

public MarkowitzModel(BasicMatrix covarianceMatrix,
                      BasicMatrix expectedExcessReturns)

MarkowitzModel

public MarkowitzModel(FinancePortfolio.Context portfolioContext)

MarkowitzModel

public MarkowitzModel(MarketEquilibrium marketEquilibrium,
                      BasicMatrix expectedExcessReturns)

Method Detail

addConstraint

public org.ojalgo.finance.portfolio.LowerUpper addConstraint(BigDecimal lowerLimit,
                                                             BigDecimal upperLimit,
                                                             int... assetIndeces)

Will add a constraint on the sum of the asset weights specified by the asset indices. Either (but not both) of the limits may be null.

clearAllConstraints

public final void clearAllConstraints()

setLowerLimit

public final void setLowerLimit(int assetIndex,
                                BigDecimal lowerLimit)

setTargetReturn

public final void setTargetReturn(BigDecimal targetReturn)

Will set the target return to whatever you input and the target variance to null.

Setting the target return implies that you disregard the risk aversion factor and want the minimum risk portfolio with return that is equal to or as close to the target as possible.

There is a performance penalty for setting a target return as the underlying optimisation model has to be solved several (many) times with different pararmeters (different risk aversion factors).

Setting a target return (or variance) is not recommnded. It's much better to simply modify the risk aversion factor.

See Also:

setTargetVariance(BigDecimal)

setTargetVariance

public final void setTargetVariance(BigDecimal targetVariance)

Will set the target variance to whatever you input and the target return to null.

Setting the target variance implies that you disregard the risk aversion factor and want the maximum return portfolio with risk that is equal to or as close to the target as possible.

There is a performance penalty for setting a target variance as the underlying optimisation model has to be solved several (many) times with different pararmeters (different risk aversion factors).

Setting a target variance is not recommnded. It's much better to modify the risk aversion factor.

See Also:

setTargetReturn(BigDecimal)

setUpperLimit

public final void setUpperLimit(int assetIndex,
                                BigDecimal upperLimit)

toString

public String toString()

calculateAssetWeights

protected BasicMatrix calculateAssetWeights()

Constrained optimisation.

reset

protected void reset()

isShortingAllowed

public final boolean isShortingAllowed()

optimiser

public org.ojalgo.finance.portfolio.OptimisedPortfolio.Optimiser optimiser()

setShortingAllowed

public final void setShortingAllowed(boolean allowed)

calculateAssetReturns

protected final BasicMatrix calculateAssetReturns()

handle

protected final BasicMatrix handle(Optimisation.Result optimisationResult)

calculatePortfolioReturn

public final double calculatePortfolioReturn(FinancePortfolio weightsPortfolio)

Specified by:

calculatePortfolioReturn in interface FinancePortfolio.Context

calculatePortfolioVariance

public final double calculatePortfolioVariance(FinancePortfolio weightsPortfolio)

Specified by:

calculatePortfolioVariance in interface FinancePortfolio.Context

getAssetReturns

public final BasicMatrix getAssetReturns()

Specified by:

getAssetReturns in interface FinancePortfolio.Context

getAssetVolatilities

public final BasicMatrix getAssetVolatilities()

Specified by:

getAssetVolatilities in interface FinancePortfolio.Context

getAssetWeights

public final BasicMatrix getAssetWeights()

getCorrelations

public final BasicMatrix getCorrelations()

Specified by:

getCorrelations in interface FinancePortfolio.Context

getCovariances

public final BasicMatrix getCovariances()

Specified by:

getCovariances in interface FinancePortfolio.Context

getMarketEquilibrium

public final MarketEquilibrium getMarketEquilibrium()

getMeanReturn

public final double getMeanReturn()

Description copied from class: FinancePortfolio

The mean/expected return of this instrument. May return either the absolute or excess return of the instrument. The context in which an instance is used should make it clear which. return.

Specified by:

getMeanReturn in class FinancePortfolio

getReturnVariance

public final double getReturnVariance()

Description copied from class: FinancePortfolio

The instrument's return variance. Subclasses must override either FinancePortfolio.getReturnVariance() or FinancePortfolio.getVolatility().

Overrides:

getReturnVariance in class FinancePortfolio

getRiskAversion

public final Scalar<?> getRiskAversion()

getSymbols

public final String[] getSymbols()

getWeights

public final List<BigDecimal> getWeights()

Description copied from class: FinancePortfolio

This method returns a list of the weights of the Portfolio's contained assets. An asset weight is NOT restricted to being a share/percentage - it can be anything. Most subclasses do however assume that the list of asset weights are shares/percentages that sum up to 100%. Calling FinancePortfolio.normalise() will transform any set of weights to that form.

Specified by:

getWeights in class FinancePortfolio

setRiskAversion

public final void setRiskAversion(Number factor)

size

public int size()

Specified by:

size in interface FinancePortfolio.Context

toSimpleAssets

public final List<SimpleAsset> toSimpleAssets()

toSimplePortfolio

public final SimplePortfolio toSimplePortfolio()

calculateAssetReturns

protected final BasicMatrix calculateAssetReturns(BasicMatrix aWeightsVctr)

calculateAssetWeights

protected final BasicMatrix calculateAssetWeights(BasicMatrix aReturnsVctr)

calculatePortfolioReturn

protected final Scalar<?> calculatePortfolioReturn(BasicMatrix aWeightsVctr,
                                                   BasicMatrix aReturnsVctr)

calculatePortfolioVariance

protected final Scalar<?> calculatePortfolioVariance(BasicMatrix aWeightsVctr)

calibrate

protected final void calibrate(BasicMatrix aWeightsVctr,
                               BasicMatrix aReturnsVctr)