exit flag -2

Hi, I have the following code which returns exit flag -2. I've tried using different algorithms and different initial starting values. But I'm not sure what to do next. Thanks!

for iPt = 1:nFrontierPts %This is only looping over the FX overlay - I'm adding the exogenous portfolio at the final step
             %Max iter and funevals small while debugging - need to increase to deal with exit flag 0

                 %Currency Specific Frontier
                 options = optimoptions(@fmincon,'Algorithm','interior-point','MaxIter',1000,'MaxFunEvals',10000);
                 targetVar_cs = minVar_cs + (iPt-1)*VarIncr_cs; 
                 [tempWts_cs,FVAL_cs,EXITFLAG_cs,OUTPUT_cs] =fmincon(@(w) ERObjective(w,ExpFXret_cs_t),w0_cs,[],[],[],[],LB_cs,UB_cs, @(w) nonlcon2(w,targetVar_cs,teCap,AssetReturns(t-59:t,1),csAssetReturns(t-59:t,2:7),equRet(t-59:t),covCap),options);                  
                % [tempWts_cs,FVAL_cs,EXITFLAG_cs,OUTPUT_cs] =fmincon(@(w) ERObjective(w,ExpFXret_cs_t),w0_cs,[],[],[],[],LB_cs,UB_cs, @(w) nonlcon2(w,targetVar_cs,100,AssetReturns(t-59:t,1),csAssetReturns(t-59:t,2:7),equRet(t-59:t),100),options);                  

                 if EXITFLAG_cs ==-2
                      w0_cs = UB_cs';
                      options = optimoptions(@fmincon,'Algorithm','sqp','MaxIter',1000,'MaxFunEvals',10000);
                      [tempWts_cs,FVAL_cs,EXITFLAG_cs,OUTPUT_cs] =fmincon(@(w) ERObjective(w,ExpFXret_cs_t),w0_cs,[],[],[],[],LB_cs,UB_cs, @(w) nonlcon2(w,targetVar_cs,teCap,AssetReturns(t-59:t,1),csAssetReturns(t-59:t,2:7),equRet(t-59:t),covCap),options);                  
                         if EXITFLAG_cs==-2
                              options = optimoptions(@fmincon,'Algorithm','active-set','MaxIter',1000,'MaxFunEvals',10000);
                              [tempWts_cs,FVAL_cs,EXITFLAG_cs,OUTPUT_cs] =fmincon(@(w) ERObjective(w,ExpFXret_cs_t),w0_cs,[],[],[],[],LB_cs,UB_cs, @(w) nonlcon2(w,targetVar_cs,teCap,AssetReturns(t-59:t,1),csAssetReturns(t-59:t,2:7),equRet(t-59:t),covCap),options);                  
                         end
                             if EXITFLAG_cs==-2

                                 for ct = 1:10
                                      w0_cs = UB_cs'*rand(1);
                                      options = optimoptions(@fmincon,'Algorithm','active-set','MaxIter',1000,'MaxFunEvals',10000);
                                      [tempWts_cs,FVAL_cs,EXITFLAG_cs,OUTPUT_cs] =fmincon(@(w) ERObjective(w,ExpFXret_cs_t),w0_cs,[],[],[],[],LB_cs,UB_cs, @(w) nonlcon2(w,targetVar_cs,teCap,AssetReturns(t-59:t,1),csAssetReturns(t-59:t,2:7),equRet(t-59:t),covCap),options);                  

                                      if EXITFLAG_cs ~= -2
                                          break;     
                                      end    
                                 end
                             end
                 end  
  end

I'm not sure what else to do next. Thanks!

[Walter Roberson]

(exit flag 2 is "No feasible point was found.")

Probably your non-linear constraints are difficult to satisfy.

It is not easy for us to give more advice without the initial values and code for ERObjective and nonlcon2

[DrLoz]

Hi Walter, does this help?

function [c, ceq] = nonlcon2(w,volcap,teCap,Aud6040ret,FXret,equRet,covCap)
% nonlcon1: add TE constraint
% nonlcon2: add equity beta/correlation constraint 

ret_w = Aud6040ret+FXret*w;
covMat=cov(equRet,FXret*w)*12;

%Inequality Constraints (Less than zero)
c(1)      = std(ret_w)*sqrt(12) - volcap; %Vol to be less than 60/40 with country specific hedging strategy
c(2) = std(FXret*w)*sqrt(12) - teCap; %Tracking error to exogenous 60/40 asset allocation constraint
c(3) = covMat(1,2) - covCap; %Covariance of FX overlay to be less than covariance of FX exposure resulting from benchmark hedging strategy
% c = [];   
%Equality Constraint 
ceq = [];
% ceq = std(ret_w)*sqrt(12) - volcap;
%ceq(1)   = (BondRisk-EqRisk)*PctRisk;
end

function [fval] = ERObjective(w,ExpRet)

fval   = -ExpRet*w;

[Walter Roberson]

So for initial values I should use

nFrontierPts = 1;
minVar_cs = rand();
VarIncr_cs = rand();
w0_cs = rand(6,1);  %60x6 array * w must be size 60x1
ExpFXret_cs_t = rand(1, 6); %ExpRet * w must be scalar, and w is 6 x 1 so this must be 1 x 6
LB_cs = randn(1, 6);
UB_cs = abs(LB_cs) + rand(1, 6);
targetVar_cs = rand();
teCap = rand();
max_ass = 70;
t = randi([60 max_ass-1]);
AssetReturns = rand(max_ass, 7);
csAssetReturns = rand(max_ass, 7);
equRet = rand(1, max_ass);
covCap = rand();

?

[DrLoz]

THese are my initial values and bounds:

nFrontierPts =

      20

minVar_cs =

     7.4804e-07

VarIncr_cs =

    -3.9370e-08

w0_cs =

     1.0e-05 *

      0.4445
      0.1251
      0.2048
      0.5538
      0.1801
      0.1973

ExpFXret_cs_t =

     -0.0180   -0.0639   -0.0391   -0.0144   -0.0444   -0.0405

LB_cs =

       0     0     0     0     0     0

UB_cs =

      0.2743    0.0897    0.0599    0.0316    0.0162    0.0104

targetVar_cs =

     7.4804e-07

teCap =

      0.0239

covCap =

     -0.0021

[Walter Roberson]

.. That's a question. You said nothing about the sizes or ranges of the various arrays, so I had to analyze the code to figure out what the sizes should be, but I have no information about the ranges. And I don't really expect random values to correlate well.

[DrLoz]

And I think it should be ok to use rand for the others

[DrLoz]

Yes I posted the answer to the question above once I realized! Also, will it help if I paste the actual data for AssetReturns and equRet?

[DrLoz]

Here is the data

[Walter Roberson]

Your tolerances are really tight, and it is doubtful that they can be reached.

By substituting symbolic values for w in your nonlinear constraint, you get the constraints (approximated)

3.464101615137755*(0.01694915254237288*abs(0.02886816362771872*W1 - 0.03919406352959544*W2 - 0.01471540136021817*W3 + 0.001764295435917194*W4 + 0.02169337934246846*W5 + 0.003808776033319812*W6 - 0.007810693788828932)^2 + 0.01694915254237288*abs(0.02855036042080595*W1 + 0.05246672670654582*W2 + 0.01344316226620105*W3 + 0.05689676429094718*W4 + 0.02513266972362289*W5 + 0.01493600721644268*W6 + 0.006573339283632679)^2 + 0.01694915254237288*abs(0.1008818933232127*W1 + 0.03363397981747138*W2 + 0.09193710929326652*W3 + 0.06260122318826636*W4 + 0.0314784317932701*W5 - 0.01638339436670971*W6 - 0.0362581320732622)^2 + 0.01694915254237288*abs(0.009944527705669346*W1 + 0.004801202173645304*W2 + 0.03746771896868998*W3 + 0.04024934172509101*W4 - 0.009168549520271511*W5 + 0.07719767506189507*W6 - 0.01752969683179822)^2 + 0.01694915254237288*abs(0.001443991565420401*W1 + 0.009336049413569379*W2 + 0.01642127430543069*W3 - 0.01760146926307485*W4 + 0.06357473155100584*W5 + 0.02317444687843411*W6 - 0.009756550245816604)^2 + 0.01694915254237288*abs(0.06386285687709857*W1 + 0.03216806993093482*W2 + 0.03733988696681619*W3 + 0.05808236721427315*W4 + 0.03579942317781597*W5 - 0.004628231701378556*W6 - 0.02568921578155649)^2 + 0.01694915254237288*abs(0.1637096021144607*W1 + 0.06431269847065455*W2 + 0.232211118801498*W3 + 0.06894874064470538*W4 + 0.0386202329205308*W5 + 0.1252409436547383*W6 - 0.09657637505125539)^2 + 0.01694915254237288*abs(0.070467758765154*W1 + 0.005039429448805956*W2 + 0.08544372221730149*W3 + 0.02197201985753841*W4 + 0.0259575410724639*W5 + 0.0005507631252086938*W6 - 0.03480264849756702)^2 + 0.01694915254237288*abs(0.00009767920594915454*W1 - 0.002344294880547639*W2 + 0.03711707855930765*W3 + 0.00483001928496737*W4 - 0.004560979806947093*W5 + 0.0007797227047124304*W6 - 0.004590387658694567)^2 + 0.01694915254237288*abs(0.01069903165890184*W1 - 0.01591310058623983*W2 + 0.03116878745387571*W3 + 0.02216149003455678*W4 + 0.01005456699799805*W5 + 0.004097689286192633*W6 + 0.002063401415436799)^2 + 0.01694915254237288*abs(0.001360938054981699*W2 - 0.004697382636704596*W1 + 0.00796215864036113*W3 - 0.02769392943175905*W4 - 0.02065530264663334*W5 + 0.00009188255972420641*W6 + 0.03210173899669516)^2 + 0.01694915254237288*abs(0.02147919509426887*W1 + 0.04967523403587983*W2 + 0.004574993153138882*W3 + 0.02089555764946435*W4 + 0.008364072833520079*W5 + 0.05465864399232639*W6 - 0.0173887004394178)^2 + 0.01694915254237288*abs(0.01053879537020961*W2 - 0.01335690571895142*W1 + 0.02128161380304675*W3 + 0.009715067362178451*W4 - 0.00409195917243104*W5 - 0.01744772201190397*W6 + 0.0125760864740233)^2 + 0.01694915254237288*abs(0.004613012626886746*W1 + 0.01279167251159617*W2 - 0.02261524565034841*W3 + 0.004714555441240696*W4 - 0.01146464856401379*W5 + 0.009068086926069481*W6 + 0.005816171087468841)^2 + 0.01694915254237288*abs(0.008714953183499454*W1 + 0.02467649678914332*W2 - 0.002113740479597927*W3 + 0.05293642609160639*W4 - 0.008093406863126714*W5 + 0.02478805726830163*W6 - 0.01200860133889904)^2 + 0.01694915254237288*abs(0.009356529420095148*W2 - 0.01842066629845896*W1 - 0.04097180554439187*W3 + 0.0008109601687445696*W4 + 0.01593669157010873*W5 - 0.03990493268042156*W6 + 0.007767448121098935)^2 + 0.01694915254237288*abs(0.03675987811621339*W1 + 0.0267677261170123*W2 + 0.03299204879710223*W3 + 0.02015164250031051*W4 + 0.01844290288900468*W5 + 0.02171165920971024*W6 - 0.02863963427756737)^2 + 0.01694915254237288*abs(0.01970217439079637*W1 - 0.01153316632893588*W2 + 0.04586317454692194*W3 + 0.01086909741888479*W4 + 0.002600131096182242*W5 - 0.008331068828564873*W6 - 0.02599386882117953)^2 + 0.01694915254237288*abs(0.01738464430445396*W1 + 0.008138446520113994*W2 + 0.01841051171356863*W3 - 0.0003549281839545818*W4 - 0.01241626814822922*W5 + 0.005290320568326172*W6 - 0.01532518460600704)^2 + 0.01694915254237288*abs(0.0007080707274939128*W1 + 0.01571896844807583*W2 - 0.01164908599804523*W3 + 0.01034580887364392*W4 - 0.02739758150760346*W5 + 0.01741575509731348*W6 - 0.04891144590277257)^2 + 0.01694915254237288*abs(0.02413262620627333*W1 - 0.02064897381491306*W2 - 0.05103433808968146*W3 + 0.01026435982902011*W4 + 0.02607308067454012*W5 - 0.008873788536872977*W6 + 0.01768482292562261)^2 + 0.01694915254237288*abs(0.06651952597416343*W1 - 0.03541481294911939*W2 + 0.018732931926384*W3 + 0.1152631439344755*W4 + 0.05049041486163024*W5 - 0.06304357864392114*W6 - 0.007451690392748649)^2 + 0.01694915254237288*abs(0.02153799254550616*W1 + 0.04422940792410311*W2 + 0.01373271323502815*W3 + 0.03590135205744508*W4 + 0.03824231158959929*W5 + 0.03943289428943315*W6 + 0.01259271173448739)^2 + 0.01694915254237288*abs(0.0717409791567266*W1 + 0.004668159722943009*W2 + 0.05347797804619644*W3 + 0.0195776598052941*W4 + 0.03936132432209754*W5 + 0.04133345983698927*W6 - 0.03090593363542517)^2 + 0.01694915254237288*abs(0.09657826715945107*W1 + 0.01571544797081934*W2 + 0.100432340144781*W3 + 0.09617273145565445*W4 + 0.08725383366515311*W5 + 0.01209452300468334*W6 - 0.03844215465488828)^2 + 0.01694915254237288*abs(0.008205755614250419*W1 + 0.02451384853872283*W2 - 0.04554785127616386*W3 + 0.02571331112252121*W4 + 0.01012366048490227*W5 + 0.01770004250771912*W6 + 0.01405875797119326)^2 + 0.01694915254237288*abs(0.04730605195656722*W1 + 0.02231075431262044*W2 + 0.07019703195027168*W3 + 0.0251992351735952*W4 + 0.03169533687847153*W5 + 0.02766700002858129*W6 - 0.01179722528059325)^2 + 0.01694915254237288*abs(0.01990904417022955*W1 + 0.01257948064757184*W2 - 0.001553445057516832*W3 + 0.02060348454891173*W4 + 0.01637651213666353*W5 - 0.009213775962750019*W6 - 0.01531287918276451)^2 + 0.01694915254237288*abs(0.07675846419670106*W1 + 0.02997639671899546*W2 + 0.09506455291229428*W3 + 0.07392825387771304*W4 + 0.06492076833202558*W5 + 0.055292815255988*W6 - 0.04147173977469168)^2 + 0.01694915254237288*abs(0.04445628667505274*W1 + 0.0451927398822294*W2 + 0.04536829115820803*W3 + 0.009528929502412544*W4 - 0.01117507648879752*W5 + 0.04994402302580141*W6 - 0.04582373592017678)^2 + 0.01694915254237288*abs(0.03511086104418825*W1 + 0.01222483262253007*W2 + 0.01519705758928299*W3 + 0.03005925775667203*W4 + 0.02017964095510976*W5 + 0.0009838003227123286*W6 + 0.009305891398178395)^2 + 0.01694915254237288*abs(0.03167144235429219*W1 + 0.01501248308608252*W2 + 0.01854407487268968*W3 + 0.01379518151441924*W4 - 0.04571970230315487*W5 + 0.01967977718481455*W6 - 0.04516663450600488)^2 + 0.01694915254237288*abs(0.02062678364226011*W1 + 0.0287471584998519*W2 + 0.07316802271921027*W3 + 0.02157885454130878*W4 - 0.01425129164017187*W5 + 0.00614409706634094*W6 - 0.033947254887092)^2 + 0.01694915254237288*abs(0.09291853992042099*W1 + 0.03564336641889741*W2 + 0.07895923204055603*W3 + 0.01542179478356823*W4 + 0.05557052912962496*W5 + 0.03951972740886073*W6 + 0.02060317154796509)^2 + 0.01694915254237288*abs(0.03068083387529287*W1 + 0.004481926838663865*W2 + 0.02259161346734443*W3 + 0.01795008279303581*W4 + 0.006191976388562455*W5 + 0.03983644146444127*W6 - 0.006569421445265661)^2 + 0.01694915254237288*abs(0.05852351269317634*W1 + 0.01141742941119108*W2 + 0.03895911804021065*W3 + 0.0134632636713636*W4 + 0.03190474502824164*W5 + 0.0005404305666641333*W6 - 0.007143288844499157)^2 + 0.01694915254237288*abs(0.007351466116568027*W2 - 0.002744092368167093*W1 + 0.08070136826717774*W3 + 0.009656192658019171*W4 + 0.0344816366307748*W5 + 0.007520494113197044*W6 + 0.04505940766613334)^2 + 0.01694915254237288*abs(0.01774539921618855*W1 - 0.001038117044324529*W2 - 0.02430172683174207*W3 + 0.01339682855518195*W4 + 0.02356065275932056*W5 - 0.02453008372812855*W6 + 0.05433962935367405)^2 + 0.01694915254237288*abs(0.01422999148685899*W1 + 0.00811154474464739*W2 + 0.0229023186701592*W3 - 0.01773257107535245*W4 + 0.02939326454724505*W5 + 0.008614005424517005*W6 + 0.01455559199487116)^2 + 0.01694915254237288*abs(0.07988302531680714*W1 + 0.04255412700524384*W2 + 0.09958224847621659*W3 + 0.06213093505626047*W4 + 0.07864722184644252*W5 + 0.05701718833217712*W6 - 0.06581721877353225)^2 + 0.01694915254237288*abs(0.03976964395545513*W1 + 0.04171074031032727*W2 + 0.0147283638633409*W3 + 0.04806033319211359*W4 + 0.03062828804891377*W5 + 0.03767065691454358*W6 + 0.009119733703566463)^2 + 0.01694915254237288*abs(0.02187649009169988*W2 - 0.0008708627629635442*W1 + 0.000645029398526988*W3 + 0.02056945797945245*W4 + 0.001368802453779746*W5 + 0.01084112710461711*W6 + 0.01390151494002642)^2 + 0.01694915254237288*abs(0.09883784473949696*W1 + 0.02786747463804919*W2 + 0.06881421102385962*W3 + 0.001787444081364078*W4 + 0.007431345470142618*W5 + 0.03417390687223425*W6 - 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0.0021 - 0.009297155142165595*W2 - 0.02916361600811235*W3 - 0.01287926224525597*W4 - 0.006723535156931461*W5 - 0.0138267870327616*W6 - 0.02357251266548311*W1 <= 0

In the first and second of those, you are adding a number of non-negative terms -- terms forced to be non-negative by the various abs() and ^2 . Then at the end you subtract 0.00000074804 from the first (which is your targetVar_cs) and 0.0239 from the second (which is your teCap). The first of those is going to be difficult to satisfy.

The third constraint puts some lower bounds on variables. If you make it the equality, you can solve for W1, and substitute into the first constraint. Once done, you can use repeated solving of the derivatives for 0 to find a set of values that (hopefully) minimizes the first constraint. If my calculations are correct, then about 0.08-ish is the minima -- but I need to cross-check that. If that is correct, then it is not possible to satisfy the constraint -- though possibly you could do better than 0.08-ish. I need to keep testing.

[DrLoz]

Thanks so much Walter! It will take me a little while to understand what you've written!!!

[Walter Roberson]

With further testing, I find that within the bounds you have established, it is difficult for c(1) of your nonlinear bounds to be smaller than about 0.06960, but for nonlinear constraints, all of the c values must be <= 0.

At the moment the smallest c(1) in my tests is found at [0.27095896530759056, 0.0879588055366868626, 0.0567802973620968668, 0.0280586544904970411, 0.0012036650345792555, 0.00935621223782138849] where it has a value of 0.0696019946898777109 . This is about 10^5 times larger than the cutoff you are asking for.

[DrLoz]

Oh rats! Ok thanks so much Walter! You've saved me probably a whole day (or more if I'm honest) of wasted effort trying different optimsations and starting points etc!!

[Walter Roberson]

If you leave the lower bound at 0 but remove the upper bound, then you can do a bit better. I am not sure yet how much better you can do.

[DrLoz]

Okay thanks. I'll give that a go....

[Walter Roberson]

Not a lot better. The c(1) value still does not get below about 0.0662 (needs to be negative or 0).

I guess negative porfolio ratings are not acceptable? I think you can reach the constraints with negative portfolios ;-)

[DrLoz]

haha! Actually, the weights are for an overlay so they potentially can go negative.. If I let the lower bound go negative do you think that would help?

[Walter Roberson]

Ah, when I permit negatives as well, I still can't get c(1) below about 0.06065 in the range I tried (out to -10000). It is looking as if there might simply be no position at all that satisfies c(1) .

[DrLoz]

ok thanks for all your help Walter. I will have to try something else! You've saved me loads of time though. I really appreciate the help. :o)

[Walter Roberson]

Out to -100000 finds the same thing.

[DrLoz]

oh... I guess this is not looking promising at all... thanks Walter.

[Walter Roberson]

Okay, I will look at it when I am able. I have some dental work when in the morning, so I am not sure whether I will feel up to doing anything for a couple of days.