org.akutan.blacklitterman
Class KrishnanMains

java.lang.Object
  org.akutan.blacklitterman.BlackLitterman
      org.akutan.blacklitterman.KrishnanMains

public class KrishnanMains
extends BlackLitterman

Provides test data and harness to reproduce the results from the Krishnan & Mains 2 factor Black-Litterman paper published in Risk magazine. Current status is that given the fact that the paper only provides summary statistics one can only start with those and run through the math.

Since:

March 10, 2007

Field Summary

Fields inherited from class org.akutan.blacklitterman.BlackLitterman

modifyVariance

Constructor Summary

KrishnanMains()

Method Summary

cern.colt.matrix.DoubleMatrix1D	getAdjustedPi_Risk() Returns the post factor Pi vector from the paper for checking to results.
cern.colt.matrix.DoubleMatrix1D	getAdjustedPi() Returns the post factor Pi vector from the paper for checking to results.
java.lang.String[]	getAssetNames() Returns the asset names used to test Krishnan-Mains
cern.colt.matrix.DoubleMatrix1D	getBetas_Risk() Returns the betas to the recession factor from the example in the Krishnan-Mains paper
cern.colt.matrix.DoubleMatrix1D	getBetas() Returns the betas to the recession factor from the example in the Krishnan-Mains paper
protected cern.colt.matrix.DoubleMatrix1D	getDelta(cern.colt.matrix.DoubleMatrix1D pi, cern.colt.matrix.DoubleMatrix2D V, cern.colt.matrix.DoubleMatrix1D w, cern.colt.matrix.DoubleMatrix2D rw, cern.colt.matrix.DoubleMatrix1D rF, cern.colt.matrix.DoubleMatrix2D beta) A first attempt at the multi-factor getDelta() method.
cern.colt.matrix.DoubleMatrix1D	getEquilibriumReturns_Risk() Returns the equilibrium returns from the paper
cern.colt.matrix.DoubleMatrix1D	getEquilibriumReturns() Returns the equilibrium returns from the paper
cern.colt.matrix.DoubleMatrix1D	getMarketWeights() Returns the market weights from the example shown in the Krishnan-Mains paper on 2 factor Black-Litterman.
cern.colt.matrix.DoubleMatrix1D	getReplWeights_Risk() Returns the weights of the replicating portfolio from the paper.
cern.colt.matrix.DoubleMatrix1D	getReplWeights() Returns the weights of the replicating portfolio from the paper.
cern.colt.matrix.DoubleMatrix2D	getTestV() Returns the covariance matrix for the example shown in the Krishnan & Mains paper on 2 factor Black-Litterman.
protected cern.colt.matrix.DoubleMatrix1D	getUpdatedPi(cern.colt.matrix.DoubleMatrix1D pi, cern.colt.matrix.DoubleMatrix2D beta, cern.colt.matrix.DoubleMatrix1D delta) Given a matrix of betas of the assets and factors, and the vector of deltas, computes a new adjusted vector of equilibrium asset returns.
static void	main(java.lang.String[] args) This program matches the results from the preliminary copy of the Krishnan and Mains paper which can be found on the internet.
protected static java.lang.String	print(java.text.DecimalFormat df, cern.colt.matrix.DoubleMatrix1D d) Helper function to return formatted print of vector
cern.colt.matrix.DoubleMatrix2D	transpose(cern.colt.matrix.DoubleMatrix1D d) Helper function to transpose a 1D matrix into a 2D matrix

Methods inherited from class org.akutan.blacklitterman.BlackLitterman

applyBL, applyBL, computeDelta, computeEr, computeImpliedWeights, computeInterval, computeKLIC, computeLambda, computeLambdaN, computePartialTevSensitities, computeTev, computeTevSensitities, computeV, getViewVariance, isModifyVariance, maxValue, mehalanobisDistance, overallProbability, reverseOptimize, sensitivities, setModifyVariance

Methods inherited from class java.lang.Object

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

Constructor Detail

KrishnanMains

public KrishnanMains()

Method Detail

getMarketWeights

public cern.colt.matrix.DoubleMatrix1D getMarketWeights()

Returns the market weights from the example shown in the Krishnan-Mains paper on 2 factor Black-Litterman.

Returns:

Vector of market weights for the assets.

getTestV

public cern.colt.matrix.DoubleMatrix2D getTestV()

Returns the covariance matrix for the example shown in the Krishnan & Mains paper on 2 factor Black-Litterman.

Returns:

Covariance matrix for the assets

getEquilibriumReturns

public cern.colt.matrix.DoubleMatrix1D getEquilibriumReturns()

Returns the equilibrium returns from the paper

Returns:

Vector of equilibrium returns from the example

getEquilibriumReturns_Risk

public cern.colt.matrix.DoubleMatrix1D getEquilibriumReturns_Risk()

Returns the equilibrium returns from the paper

Returns:

Vector of standard deviation of the returns for each asset from the paper.

getAssetNames

public java.lang.String[] getAssetNames()

Returns the asset names used to test Krishnan-Mains

Returns:

Array of the asset names

getBetas

public cern.colt.matrix.DoubleMatrix1D getBetas()

Returns the betas to the recession factor from the example in the Krishnan-Mains paper

Returns:

Vector of betas of the assets to the recession factor

getBetas_Risk

public cern.colt.matrix.DoubleMatrix1D getBetas_Risk()

Returns the betas to the recession factor from the example in the Krishnan-Mains paper

Returns:

The risk based on the betas (Check this TODO)

getAdjustedPi

public cern.colt.matrix.DoubleMatrix1D getAdjustedPi()

Returns the post factor Pi vector from the paper for checking to results.

Returns:

Adjusted returns (after adjustment for recession factor)

getAdjustedPi_Risk

public cern.colt.matrix.DoubleMatrix1D getAdjustedPi_Risk()

Returns the post factor Pi vector from the paper for checking to results.

Returns:

Vector of standard deviation of returns after adjusting for the recession factor.

getReplWeights

public cern.colt.matrix.DoubleMatrix1D getReplWeights()

Returns the weights of the replicating portfolio from the paper.

Returns:

Vector of weights of the recession factor replicating portfolio.

getReplWeights_Risk

public cern.colt.matrix.DoubleMatrix1D getReplWeights_Risk()

Returns the weights of the replicating portfolio from the paper.

Returns:

Returns the

transpose

public cern.colt.matrix.DoubleMatrix2D transpose(cern.colt.matrix.DoubleMatrix1D d)

Helper function to transpose a 1D matrix into a 2D matrix

Parameters:

d - input vector

Returns:

Matrix containing vector d in single row.

getDelta

protected cern.colt.matrix.DoubleMatrix1D getDelta(cern.colt.matrix.DoubleMatrix1D pi,
                                                   cern.colt.matrix.DoubleMatrix2D V,
                                                   cern.colt.matrix.DoubleMatrix1D w,
                                                   cern.colt.matrix.DoubleMatrix2D rw,
                                                   cern.colt.matrix.DoubleMatrix1D rF,
                                                   cern.colt.matrix.DoubleMatrix2D beta)

A first attempt at the multi-factor getDelta() method. I know that this returns the correct result for a second factor, but it probably doesn't work right for a third or higher factor. TODO Fix this so it is correct for three or more factors.

Parameters:

pi - Vector of Asset returns

V - Asset covariance matrix

w - Vector of equilibrium weights of the assets

rw - Matrix of replicating weights for each factor

rF - Vector of Factor returns

beta - Matrix of betas between the assets and the factors

Returns:

Vector of delta values for each factor (delta[0] is the standard Black-Litterman delta value).

getUpdatedPi

protected cern.colt.matrix.DoubleMatrix1D getUpdatedPi(cern.colt.matrix.DoubleMatrix1D pi,
                                                       cern.colt.matrix.DoubleMatrix2D beta,
                                                       cern.colt.matrix.DoubleMatrix1D delta)

Given a matrix of betas of the assets and factors, and the vector of deltas, computes a new adjusted vector of equilibrium asset returns. There might be a cleaner vector expression, but the iterative one works.

Parameters:

pi - Vector of asset returns

beta - Matrix of betas between the assets and the various factors

delta - Vector of delta values by factor (delta[0] = Black-Litterman delta)

Returns:

Updated vector of equilibrium asset returns after adjusting for the impact of the recession factor.

print

protected static java.lang.String print(java.text.DecimalFormat df,
                                        cern.colt.matrix.DoubleMatrix1D d)

Helper function to return formatted print of vector

Parameters:

df - Format to use for numbers

d - Vector to be formatted

Returns:

String version of the vector formatted as specified.

main

public static void main(java.lang.String[] args)

This program matches the results from the preliminary copy of the Krishnan and Mains paper which can be found on the internet.

Parameters:

args - Command line arguments (ignored).