  We prove the power law decay $p(t,x) \sim t^{-\phi(x,b)/2}$ in which $p(t,x)$
is the probability that the fraction of time up to $t$ in which a random walk
$S$ of i.i.d. zero-mean increments taking finitely many values, is
non-negative, exceeds $x$ throughout $s \in [1,t]$. Here $\phi(x,b)=
\mathbb{P}(\text{L\'evy}(1/2,\kappa(x,b))<0)$ for $\kappa(x,b) =
  \frac{\sqrt{1-x} b - \sqrt{1+x}}{\sqrt{1-x} b + \sqrt{1+x}}$ and $b=b_S \geq
0$ measuring the asymptotic asymmetry between positive and negative excursions
of the walk (with $b_s=1$ for symmetric increments).
