  We consider the extreme value theory of a hyperbolic toral automorphism $T:
\mathbb{T}^2 \to \mathbb{T}^2$ showing that if a H\"older observation $\phi$
which is a function of a Euclidean-type distance to a non-periodic point
$\zeta$ is strictly maximized at $\zeta$ then the corresponding time series
$\{\phi\circ T^i\}$ exhibits extreme value statistics corresponding to an iid
sequence of random variables with the same distribution function as $\phi$ and
with extremal index one. If however $\phi$ is strictly maximized at a periodic
point $q$ then the corresponding time-series exhibits extreme value statistics
corresponding to an iid sequence of random variables with the same distribution
function as $\phi$ but with extremal index not equal to one. We give a formula
for the extremal index (which depends upon the metric used and the period of
$q$). These results imply that return times are Poisson to small balls centered
at non-periodic points and compound Poisson for small balls centered at
periodic points.
