Vectorizing tensor-matrix product - for-loop is faster??

Hi All. I am trying to calculate a tensor-matrix inner product in the following code. I need

 K(i,a,k,b) = C(i,J,k,L)*N(a,J)*N(b,L) where we sum over repeated indices.

I did it using for-loop and using reshape() and shiftdim() and timed both versions. I get for-loop to be faster.

clear;clc;
% Inner-product test
C = rand(2,2,2,2);
N = rand(3,2);

tic;
% Using for-loop
K_for = zeros(2,3,2,3);
for i=1:2
    for a=1:3
        for k=1:2
            for b=1:3
                for J=1:2
                    for L=1:2
                        K_for(i,a,k,b) = K_for(i,a,k,b) +...
                            C(i,J,k,L)*N(a,J)*N(b,L);
                    end
                end
            end           
        end
    end
end
toc;

tic;
% Using permute and reshape
[n1,n2,n3,n4] = size(C);
[a,b] = size(N);
K = reshape(C,n1*n2*n3,n4)*N.';
K = reshape(K,[n1,n2,n3,a]);
K = shiftdim(K,2);
K = reshape(K,n3*a*n1,n2)*N.';
K = reshape(K,[n3,a,n1,a]);
K = shiftdim(K,2);

toc;

My tic-toc outputs are:

 Elapsed time is 0.000035 seconds. <-- For for-loop version
 Elapsed time is 0.009384 seconds. <-- For vectorized version

Is there a more efficient way of vectorizing inner products?

Regards,

 Amit