Finding the auto-correlation function from PSD

I want to find the auto-correlation (AC) function of a signal by taking the inverse fourier transform of the power spectral density (PSD), but when I test my code on a sample signal the resulting AC function does not match with the AC I calcuate using the xcorr function. What is the reason of this difference? Should I calculate the PSD in a different way?

The signal is a noisy signal comprised of two sine signals (MATLAB example: https://www.mathworks.com/help/matlab/ref/fft.html) and my code is as following:

Fs = 1000; % Sampling frequency

T = 1/Fs; % Sampling period

L = 1500; % Length of signal

t = (0:L-1)*T; % Time vector

%Form a signal containing a 50 Hz sinusoid of amplitude 0.7 and a 120 Hz sinusoid of amplitude 1.

S = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);

%Corrupt the signal with zero-mean white noise with a variance of 4.

y = S + 2*randn(size(t));

%Auto correlation using matlab function:

[cor lag] = xcorr(y,y);

figure;

plot(lag(floor(length(cor)/2)+1:end),cor(floor(length(cor)/2)+1:end));

title('Auto Correlation')

% PSD

fy = fft(y);

nf = length(fy);

p2y = 1/(nf*Fs)*(abs(fy).^2);

p1y = p2y(1:nf/2+1);

p1y(2:end-1) = 2*p1y(2:end-1);

freqs = 0:Fs/nf:Fs/2;

figure;plot(freqs,p1y)

title('Power spectral density')

% PSD using the inverse fourier transform:

invCorr = abs(ifft(p2y));

figure;plot(invCorr);title('Estimated Auto Correlation from PSD')

~~~~~~~~~~~~~~ Results :

PSD:

AC from xcorr:

AC from PSD: