CVAR Optimisation - Portfolio Weights and Iterations

Good Afternoon,

I'm trying to do a CVAR optimisation on 6 stock tickers and have no problems retrieving the data. However, my code seems to have the following issues:

1) Produces strange portfolio weights

2) Hits the iteration limit which I understand is 1000 . Is this normal?

I'm new to Matlab so would really appreciate guidance from more experienced users.

Linus

c = yahoo; ClosePriceBXMT = fetch(c,'BXMT','Close','08/01/15','08/25/10'); ClosePriceSTWD = fetch(c,'STWD','Close','08/01/15','08/25/10'); ClosePriceCLNY = fetch(c,'CLNY','Close','08/01/15','08/25/10'); ClosePriceSTAR = fetch(c,'STAR','Close','08/01/15','08/25/10'); ClosePriceRWT = fetch(c,'RWT','Close','08/01/15','08/25/10'); ClosePriceNRF = fetch(c,'NRF','Close','08/01/15','08/25/10');

pricematrix= [ClosePriceBXMT(:,2) ClosePriceSTWD(:,2) ClosePriceCLNY(:,2) ClosePriceSTAR(:,2) ClosePriceRWT(:,2) ClosePriceNRF(:,2)];

ScenRets = price2ret(pricematrix);

close(c);

%The code estimates the portfolio CVaR and the asset weights

%INPUTS: %The data matrix (historical returns or simulation) ScenRets size JxnAssets % the confidence level beta (scalar, between 0.9 and 0.999, usually o.95 or % 0.99) %the Upper Bounds for the weights in order to inforce diversification %R0 the portfolio target return [J, nAssets]=size(ScenRets); i=1:nAssets; beta=0.95; %change it if you want but stay between 0.9 and 0.999 UB=0.25; %the upper bound to force diversification, positive between (0,1) R0=0.03; %the target return ShortP=0; %If ShortP=1 allow for short positions, else if ShortP=0 only long positions are allowed %function to be minimized %w(31)=VaR objfun=@(w) w(nAssets+1)+(1/J)*(1/(1-beta))*sum(max(-w(i)*ScenRets(:,i)'-w(nAssets+1),0)); % initial guess w0=[(1/nAssets)*ones(1,nAssets)]; VaR0=abs(quantile(ScenRets*w0',1-beta)); % the initial guess for VaR is the %HS VaR of the equally weighted portfolio w0=[w0 VaR0]; % the (linear) equalities and unequalities matrixes A=[-mean(ScenRets) 0]; if ShortP==0 A=[A; -eye(nAssets) zeros(nAssets,1)]; A=[A; eye(nAssets) zeros(nAssets,1)]; b=[-R0 zeros(1,nAssets) UB*ones(1,nAssets)]; elseif ShortP==1 A=[A; -eye(nAssets) zeros(nAssets,1)]; A=[A; eye(nAssets) zeros(nAssets,1)]; b=[-R0 -LB*ones(1,nAssets) UB*ones(1,nAssets)]; elseif ShortP~=0|ShortP~=1 error('Input ShortP=1 (line14) if you allow short positions and 0 else!!')

end b=b'; Aeq=[ ones(1,nAssets) 0]; beq=[1];

options=optimset('LargeScale','off');

options=optimset(options,'MaxFunEvals',100000); [w,fval,exitflag,output]=fmincon(objfun,w0,A,b,Aeq,beq,[],[],[],options) portfWeights=zeros(1, nAssets); for i=1:nAssets % clear rounding errors if w(i)<0.0001 w(i)=0; end % save results to the workfile portfWeights(1,i)=w(i); end Risk=zeros(1,2); Risk(1,1)=w(nAssets+1); %Remember that w(31)= portfolio VaR Risk(1,2)=fval;

Answer 1

[Johan Löfberg]

CVar from data is linear programming representable, so trying to to solve it as a non-smooth nonlinear program using a nonlinear solver is not a good idea. Just google cvar linear program and you will find a lot of material on how to solve these models.