  Financial volatility obeys two fascinating empirical regularities that apply
to various assets, on various markets, and on various time scales: it is
fat-tailed (more precisely power-law distributed) and it tends to be clustered
in time. Many interesting models have been proposed to account for these
regularities, notably agent-based models, which mimic the two empirical laws
through a complex mix of nonlinear mechanisms such as traders' switching
between trading strategies in highly nonlinear way. This paper explains the two
regularities simply in terms of traders' attitudes towards news, an explanation
that follows almost by definition of the traditional dichotomy of financial
market participants, investors versus speculators, whose behaviors are reduced
to their simplest forms. Long-run investors' valuations of an asset are assumed
to follow a news-driven random walk, thus capturing the investors' persistent,
long memory of fundamental news. Short-term speculators' anticipated returns,
on the other hand, are assumed to follow a news-driven autoregressive process,
capturing their shorter memory of fundamental news, and, by the same token, the
feedback intrinsic to the short-sighted, trend-following (or herding) mindset
of speculators. These simple, linear, models of traders' expectations, it is
shown, explain the two financial regularities in a generic and robust way.
Rational expectations, the dominant model of traders' expectations, is not
assumed here, owing to the famous no-speculation, no-trade results
