Portfolio Optimisation using a mean/ mean absolute deviation model (linear program)

4 次查看（过去 30 天）
Daniel
Daniel 2013-8-4
回答： Alejandra Pena-Ordieres 2024-9-10
Hey everybody, I am new to Matlab. I have recently used quadprog for the standard mean-variance model to optimise a portfolio. I want to try several models and am currently trying to model the linear program -> mean / mean absolute deviation. Mathematically speaking :
[URL=http://www.pic-upload.de/view-20298258/Screen-Shot-2013-08-05-at-01.05.47.png.html][IMG]http://www10.pic-upload.de/thumb/05.08.13/3hz1okoiiv24.png[/IMG][/URL]
in case that didn't work :
http://www.pic-upload.de/view-20298258/Screen-Shot-2013-08-05-at-01.05.47.png.html
S = 872 observations I have for 9 stocks. delta is the target return.
% This script will calculate and plot the efficient frontier for a % mean - mean absolute deviation model in the Konno context.
% Take sample 'Sample' and calculate the mad -> transpose PeriodMAD
% and store variable in the workspace
PeriodMAD = mad(Sample);
PeriodMAD = PeriodMAD';
assignin('base','PeriodMAD',PeriodMAD);
% get number of Assets ( i am using 9 stocks)
nAssets = numel(PeriodMAD);
% Set the first targetreturn
targetreturn = 0.000001;
% Not sure if that is right -> allow none of the MAD values to lower than
% 0
nonnegativityMAD = zeros(nAssets, 1);
% Conformity with the linproq notation
f = PeriodMAD;
% Set some restrictions -> as shown in the graphic I have provided. NOt
% sure if I set them up correctly to be honest.
% PeriodDeviations includes nothing more than Observation at time(i) -
% mean of the asset (PeriodDeviations -> (9,1) vector)
% PeriodReturns -> ln returns for the observations 782 -> vector (9,1)
Aeq = [ PeriodDeviations
-PeriodDeviations
-PeriodMAD
-PeriodReturns ];
Beq = [ PeriodMAD
-PeriodMAD
nonnegativityMAD
-targetreturn];
% Set lower and upper boundaries for the weights -> 0<= x <= 1
lb = zeros(nAssets,1);
ub = ones(nAssets, 1);
% Copied that line from the quadprog example given on the internet
% changed interior-point-convex to interior-point
options = optimset('Algorithm','interior-point');
options = optimset(options,'Display','iter','TolFun',1e-10);
for i=1:100000;
x = linprog ( f,[],[],Aeq,Beq,lb,ub,[], options );
% Not sure if that is correct. Store respective mean in Output(1,i)
% do the same for the portfolio MAD -> is that correct?
% This is a modified "Sharpe- Ratio" or Konno Ratio. the quotient of
% the former two variables
% Finally store the weights x in Output as well -> 9 variables
% therefore Output(5,i) to Output(13,i)
Output(1,i) = x' * PeriodReturns;
Output(2,i) = x' * PeriodMAD;
Output(3,i) = (Output(1,i)/Output(2,i));
Output(5,i) = x(1,1);
Output(6,i) = x(2,1);
Output(7,i) = x(3,1);
Output(8,i) = x(4,1);
Output(9,i) = x(5,1);
Output(10,i) = x(6,1);
Output(11,i) = x(7,1);
Output(12,i) = x(8,1);
Output(13,i) = x(9,1);
% now increment targetreturn -> repeat the entire process as long as
% linprog finds a solutions (converges to a solution) otherwise
% stop/break
targetreturn = targetreturn + 0.000001;
if(exitflag == 1)
continue
else
break
end
end
% Find highest KonnoRatio - Quotient of Returns/Risk stored as
% maxKonnoRatio then find position in Output
maxKonnoRatio = max(Output(3,:));
[row col] = find(maxKonnoRatio == Output(3,:));
% finally create and display an array that contains all the information
% for the optimal allocation.
OptimalAll = [ Output(1,col)
Output(2,col)
Output(3,col)
0
Output(5,col)
Output(6,col)
Output(7,col)
Output(8,col)
Output(9,col) ]
% and hopefully draw the efficient frontier
plot(Output(2,i),Output(1,i))
I am stuck. I have modified so much stuff already and I keep getting error messages. currently this is the most recent one :
EDU>> MAD Error using linprog (line 231) The number of rows in Aeq must be the same as the number of elements of beq.
Error in MAD (line 37) x = linprog ( f,[],[],Aeq,Beq,lb,ub,[], options );
EDU>> MAD Error: File: MAD.m Line: 108 Column: 32 Unbalanced or unexpected parenthesis or bracket.
EDU>>
if you could please help me. Am I at least close to a proper solution ? Btw. : I will annualise those daily data observations - as soon as I can solve the basic problem.
I would be very grateful for some advice and/or help. Thank you so much!
Daniel

请先登录，再回答此问题。

回答（2 个）

Shashank Prasanna
Beq should be a column vector, but in your the above example it seems to be a row vector.
Beq = Beq(:); % Forces it to be a column vector
Take a look at the documentation of linprog for more information on how Aeq and Beq should be specified.
Equality constraints should be of the form:
Aeq*w = Beq, where
Aeq -> m x n
Beq -> m x 1
w -> n x 1
w is the weights you are trying to solve for.
Alejandra Pena-Ordieres
You can use the PortfolioMAD functionality to compute optimal portfolios using the mean-absolute devaition as the risk measure.
To get started with the PortfolioMAD object, see the examples in Creating the PortfolioMAD Object.

类别

在 Help Center 和 File Exchange 中查找有关 Portfolio Optimization and Asset Allocation 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by