The frequency axis for the PSD of a signal

Suppose I have the signal x that contains N samples, and I take the FFT of this signal and rearrange the frequency components to have the 0 frequency componenet to the center

X = fftshift(fft(x));

and then calculate the PSD of the signal as

psd = (1/(fs*N))*abs(X).^2;

where fs is the sampling frequency, what is the exact frequency axis that corresponds to psd in this case? If I defined it as

freq = -fs/2:fs/N:fs/2;

it would be 1 element greater than the size of psd, but if I define it as

freq = -fs/2+fs/N:fs/N:fs/2;

it will be of the same size as psd.

Is the second definition accurate? If yes, why the negative frequencies don't extend to -fs/2 as it's the case for the positive frequencies?