# Why is the variance of ACF of white noise 1/T

In many books, articles and comments on this website I read that the variance of the autocorrelation of a white noise process is $\frac{1}{T}$ when T is sufficiently large. Often this characteristic is used to calculate the confidence bounds in an ACF plot, where the bounds are calculated by: $b = \pm 1.96 \frac{1}{\sqrt{T}}$, which is the confidence interval of a normally distributed value having zero mean and variance $\frac{1}{T}$.

The question is where the $\frac{1}{T}$ is coming from. Why is the variance of the autocorrelation $r_h$ of a white noise process equal to $\frac{1}{T}$?