Covariance Estimation

Question

Covariance estimate $\frac{1}{n}\sum_ix_ix^T$. From the result it seems the estimate is very poor? This contradicts LLN so I'm wondering if there's something wrong the way I did this simulation?

M = 5;
N = 9999;
Y = zeros(N,M);
A = rand(M,M);
Sigma = A*A';

for i = 1:N
    [S,V,U] = svd(Sigma);
    X = rand(M,1);
    Y(i,1:M) = S*sqrt(V)*X;
end

sum = 0;
for i = 1:N
   X = Y(i,:);
   sum = sum + X'*X;
end
Sigma_hat = sum/N;
diff = (Sigma - Sigma_hat)./Sigma;

and get

diff =

0.8696    0.8621    0.6979    0.8151    0.7628
0.8621    0.8705    0.6561    0.8067    0.7515
0.6979    0.6561    0.3176    0.4588    0.3674
0.8151    0.8067    0.4588    0.7772    0.6885
0.7628    0.7515    0.3674    0.6885    0.5767