naivemv.m

Numerical Methods In_Finance And Economics Matlab Source Code

function [PRisk, PRoR, PWts] = NaiveMV(ERet, ECov, NPts)
ERet = ERet(:);      % makes sure it is a column vector
NAssets = length(ERet);  % get number of assets
% vector of lower bounds on weights
V0 = zeros(NAssets, 1);
% row vector of ones
V1 = ones(1, NAssets);
% set medium scale option
options = optimset('LargeScale', 'off');
% Find the maximum expected return 
MaxReturnWeights = linprog(-ERet, [], [], V1, 1, V0);
MaxReturn = MaxReturnWeights' * ERet;
% Find the minimum variance return
MinVarWeights = quadprog(ECov,V0,[],[],V1,1,V0,[],[],options);
MinVarReturn = MinVarWeights' * ERet;
MinVarStd = sqrt(MinVarWeights' * ECov * MinVarWeights);
% check if there is only one efficient portfolio     
if MaxReturn > MinVarReturn 
	   RTarget = linspace(MinVarReturn, MaxReturn, NPts);
	   NumFrontPoints = NPts;
else
      RTarget = MaxReturn;
      NumFrontPoints = 1;
end
% Store first portfolio		
PRoR = zeros(NumFrontPoints, 1);
PRisk = zeros(NumFrontPoints, 1);
PWts = zeros(NumFrontPoints, NAssets);
PRoR(1) = MinVarReturn;
PRisk(1) = MinVarStd; 
PWts(1,:) = MinVarWeights(:)';
% trace frontier by changing target return
VConstr = ERet';
A = [V1 ; VConstr ];
B = [1 ; 0];
for point = 2:NumFrontPoints
	B(2) = RTarget(point);
	Weights = quadprog(ECov,V0,[],[],A,B,V0,[],[],options);
	PRoR(point) = dot(Weights, ERet);
	PRisk(point) = sqrt(Weights'*ECov*Weights);
	PWts(point, :) = Weights(:)';
end