tech.nmfin.portfoliooptimization.markowitz

Class MarkowitzByCLM

java.lang.Object

tech.nmfin.portfoliooptimization.markowitz.MarkowitzByQP

tech.nmfin.portfoliooptimization.markowitz.MarkowitzByCLM

public class MarkowitzByCLM
extends MarkowitzByQP

Solves for the optimal weights in the Markowitz formulation by critical line method. That is, \[ \begin{aligned} w_{\mathrm{eff}} &= \operatorname*{arg\,min}_{w} \left\{q\,w^{\mathsf T}Vw-w^{\mathsf T}r\right\},\\ \text{subject to}\quad &w^{\mathsf T}\mathbf{1}=1,\quad w_{\mathrm{lower}}\le w\le w_{\mathrm{upper}}. \end{aligned} \]

Constructor Summary

Constructors

Constructor and Description
MarkowitzByCLM(Vector r, Matrix V) Solves w_eff = argmin {q * (w' V w) - w'r}, w'1 = 1, w ≥ 0.
MarkowitzByCLM(Vector r, Matrix V, Vector w_lower, Vector w_upper) Solves w_eff = argmin {q * (w' V w) - w'r}, w'1 = 1, w ≥ w_lower, w ≤ w_upper.
MarkowitzByCLM(Vector r, Matrix V, Vector w_lower, Vector w_upper, double benchmarkRate) Constructs a Markowitz portfolio from expected future returns and future covariance for a given benchmark rate, with lower and upper limits on asset weights.

Method Summary

Modifier and Type	Method and Description
protected Vector	getOptimalW(double q) Solves w_eff = argmin {q * (w' Σ w) - w'r}.

Methods inherited from class tech.nmfin.portfoliooptimization.markowitz.MarkowitzByQP

fw, getOptimalRiskAversionCoefficient, getOptimalRiskAversionCoefficient, getOptimalWeights, getRiskAversionCoefficientForTargetReturn, getRiskAversionCoefficientForTargetVariance, setRiskAversionCoefficient

Methods inherited from class java.lang.Object

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

Constructor Detail

MarkowitzByCLM

public MarkowitzByCLM(Vector r,
                      Matrix V)

Solves w_eff = argmin {q * (w' V w) - w'r}, w'1 = 1, w ≥ 0.

Parameters:

r - the expected returns

V - the covariance matrix

MarkowitzByCLM

public MarkowitzByCLM(Vector r,
                      Matrix V,
                      Vector w_lower,
                      Vector w_upper)

Solves w_eff = argmin {q * (w' V w) - w'r}, w'1 = 1, w ≥ w_lower, w ≤ w_upper.

Parameters:

r - the expected returns

V - the covariance matrix

w_lower - the lower limits for weights

w_upper - the upper limits for weights

MarkowitzByCLM

public MarkowitzByCLM(Vector r,
                      Matrix V,
                      Vector w_lower,
                      Vector w_upper,
                      double benchmarkRate)

Constructs a Markowitz portfolio from expected future returns and future covariance for a given benchmark rate, with lower and upper limits on asset weights.

Parameters:

r - expected future returns of assets

V - future covariance of assets

w_lower - the lower limits for weights

w_upper - the upper limits for weights

benchmarkRate - the benchmark rate used to compute Sharpe ratio

Method Detail

getOptimalW

protected Vector getOptimalW(double q)
                      throws Exception

Description copied from class: MarkowitzByQP

Solves w_eff = argmin {q * (w' Σ w) - w'r}.

Overrides:

getOptimalW in class MarkowitzByQP

Parameters:

q - the risk-aversion coefficient

Returns:

the optimal weights w_eff

Throws:

QPInfeasible - when the underlying quadratic programming problem is infeasible

Exception