  Lead halide perovskites have recently been reported to demonstrate an
exceptionally high nonlinear (Kerr) refractive index n$_2$ of up to 10$^{-8}$
cm$^2$/W in CH$_3$NH$_3$PbBr$_3$. Other researchers however observe different,
substantially more conservative numbers. In order to resolve this disagreement
the nonlinear Kerr index of a bulk sample of lead halide perovskite was
measured directly by means of an interferometer. This approach has many
advantages as compared to the more standard z-scan technique. In particular
this method allows studying the induced changes to the refractive index in a
time-resolved manner, thus enabling to separate the different contributions to
$n_2$. The extracted n$_2$ values for CsPbBr$_3$ and MAPbBr$_3$ at $\lambda
\approx 1\mu m$ are $n_2=+2.1\times$ 10$^{-14}$ cm$^2$/W and $n_2=+6\times$
10$^{-15}$ cm$^2$/W respectively hence substantially lower than what has been
indicated in most of the previous reports implying the latter should be
regarded with a great care.
