Fmincon - Value-at-Risk Minimization - Incorrect values returned

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Edouard
Edouard 2014-1-22
回答： Moad 2014-2-18
Hi all,
I'm having troubles using fmincon. A little help would be reaally appreciated.
So i'm trying to minimize the following function (Semi-Parametric Conditional Value-at-Risk) over w, the weight between two assets return series :
function adjcvar=adjcvar(rets,alpha,w)
%Portfolio return
rp=w*rets(:,1)+(1-w)*rets(:,2);
%Mean return and StDev
mu=mean(rp);
sig=std(rp);
%Skewness and Kurtosis
S=skewness(rp);
K=kurtosis(rp);
%Standard Normal inverse cumulative distribution function
z=norminv(alpha,0,1);
%Estimated Quantile adjusted for Skewness and Kurtosis
Q=z+(z^2 - 1)*S/6+(z^3 -3*z)*(K-3)/24 - (2*z^3 - 5*z)*(S*diag(S))/36;
%Adjusted Value-at-Risk
adjvar=min(mu+sig*diag(Q),0);
%Adjusted Conditional VaR
adjcvar=mean(rp(rp<=adjvar));
Fmincon is used as follows:
[w]=fmincon(@(w)adjcvar([ret.mscimin,static.vsfret],alpha,w),w0w,[],[],[],[],lbw,ubw,[],options);
with
options = optimset('Display','notify','Algorithm','active-set');
lbw=0; %Upper-bound
ubw=1; %Lower-bound
w0w=0.5; %Starting Value
What happens is that if I set w0w, the starting value, between 0 and 0.61, fmincon returns w=0. If i set w0w at 0.62 or above, fmincon returns w=1.
I know empirically that the right weight is around 0.61-0.62.
Fmincon returns the following message:
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the function tolerance,
and constraints were satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
Active inequalities (to within options.TolCon = 1e-006):
lower upper ineqlin ineqnonlin
1
I'm quite new to fmincon and don't really understand why itjust goes to the upper or lower boundary and stops.
Thanks for reading and any advice you could give.
Have a nice day.
Edouard

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采纳的回答

Amit
Amit 2014-1-22
This is a single variable minimization. You should try fminbnd instead of fmincon.
Also, try plotting adjcvar([ret.mscimin,static.vsfret],alpha,w) for w values between 0 and 1 and see is the difference in sizes.
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Edouard
Edouard 2014-1-22
Thank you so much, fminbnd works way better!
Actually, in the sample I work on mu+sig*diag(Q) is never greater than zero, such that the min(x,0) is always at x within the boudaries set for w.
The function is a nice, smooth bell.
Finally, and you might find this ridiculous, I'm mnimizing CVaR whereas CVaR is a negative value.
Hence I changed adjcvar to abs (mean(rp(rp<=adjvar))) and it works fine.
Note that fmincon returns a close but different value than fminbnd (0.6144 against 0.6183).
Anyway, thanks to you both.
Matt J
Matt J 2014-1-22
编辑：Matt J 2014-1-22
Actually, in the sample I work on mu+sig*diag(Q) is never greater than zero, such that the min(x,0) is always at x within the boudaries set for w.
That doesn't eliminate the hazards of non-smoothness. FMINCON doesn't confine itself to the bounds during its search. Not by default anyway. Moreover, min(x,0) is only smooth where x is strictly less than zero, and it's not clear whether your bounds would guarantee that, even if obeyed.
Note that fmincon returns a close but different value than fminbnd (0.6144 against 0.6183).
That could be a matter of the stopping tolerances you've chosen in each.

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更多回答（1 个）

Moad
Moad 2014-2-18
Hello Sir can u provide a code of minimazing Value at Risk with the fmincon
i actualy want to minimize portfolio Parametric VaR for many assest returns
thank you very much

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