Problems with regstats: more predictor variables than observations

Hello, I have some problems with the calculation of the parameters of a regression. More precisely, I have a sample of N observations (monthly observations) and K assets (the last one is the market) and I need to find the alpha and beta (as the CAPM do:(Rportfolio-Rfree_risk)=(Rmarket-Rfree_risk)beta) for each period (hence, I need to have N alphas and N betas). I have written this function:

function [Alpha,Beta,EqReturns,EqVarCovar]=CAPM(RetMarket,RetAssets,VarMarket)
  for k=1:size(RetAssets,1);
    for i=1:size(RetAssets,2);
      out(k,:)=regstats(RetAssets(k,i),RetMarket(k,:),'linear',{'beta','r','rsquare'});
      Alpha(i,k)=out(k,:).beta(1);
      Beta(i,k)=out(k,:).beta(2);
      R2(i,k)=out(k,:).rsquare;
      Resid(k,i)=out(k,:).r;
      EqRet(i,k)=out(k,:).beta(2)*(RetMarket(k,:));
    end
    EqReturns(k,i)=eqret(i,k)';
    EqVarCovar(:,:,k)=Beta(:,k)*(Beta(:,k)')*VarCovarMarket(k,:)+diag(diag(cov(Resid(k,:))));
  end;
end

where RetMarket is Nx1, RetAssets is NxK and VarMarket is Nx1.

Is there someone who can explain me where is my error?? Thanks!!!

Answer 1

[dpb]

In

out(k,:)=regstats(RetAssets(k,i),RetMarket(k,:),'linear',{'beta','r','rsquare'});

RetAssets(k,i) is always only a single point and RetMarket(k,:) is also if size(RetMarket) is Nx1 as stated.

To fit a linear regression you'll have to have at least two points for the x and y vectors. In general, of course, one would have at least one extra DOF and generally quite a few more than that.

It's not clear what you would mean for each period; at first I thought you were likely meaning a regression for each of the k "assets" but then you explicitly state N sets of coefficients so I'm at a loss what that would be (unless it's a point-to-point return as compared to the previous month, maybe??? If that were so, it's just a ratio of the two successive values for percentage but if is actually a regression it'd be the specific line between the two point values).