Skewness

The skewness of a distribution is a measure of the frequency with which large returns
in a particular direction occur. An asset which displays large negative returns more
frequently than large positive returns is said to have a return distribution skewed to
the left or to have a ‘fat left tail’. An asset which displays large positive returns more
frequently than large negative returns is said to have a return distribution skewed
to the right or to have a ‘fat right tail’. The normal distribution is symmetrical, that
is, its coefficient of skewness is exactly zero. Thus a significantly positive or negative
skewness coefficient is inconsistent with the assumption that returns are normal.
Figure 1.3 compares a skewed, but non-kurtotic, distribution with a normal
distribution with the same variance. Table 1.1 presents estimates of the kurtosis and
skewness of some widely traded assets. All the assets displayed have significant
positive or negative skewness, and most also have a coefficient of kurtosis significantly
greater than 3.0.
The exchange rates of the Mexican peso and Thai baht vis-a` -vis the dollar have
the largest coefficients of kurtosis. They are examples of intermittently fixed exchange
rates, which are kept within very narrow fluctuation limits by the monetary authorities.
Typically, fixed exchange rates are a temporary phenomenon, lasting decades in
rare cases, but only a few years in most. When a fixed exchange rate can no longer
be sustained, the rate is either adjusted to new fixed level (for example, the European
Monetary System in the 1980s and 1990s and the Bretton Woods system until 1971)
or permitted to ‘float’, that is, find a free-market price (for example, most emerging
market currencies). In either case, the return pattern of the currency is one of
extremely low returns during the fixed-rate period and extremely large positive or
negative returns when the fixed rate is abandoned, leading to extremely high kurtosis.
The return patterns of intermittently pegged exchange rates also diminishes the
forecasting power of forward exchange rates for these currencies, a phenomenon
known as regime-switching or the peso problem. The term ‘peso problem’ has its
origin in experience with spot and forward rates on the Mexican peso in the 1970s.
Observers were puzzled by the fact that forward rates for years ‘predicted’ a significant
short-term depreciation of the peso vis-a` -vis the US dollar, although the peso–dollar
exchange rate was fixed. One proposed solution was that the exchange rate peg was
not perfectly credible, so market participants expected a switch to a new, lower value
of the peso with a positive probability. In the event, the peso has in fact been
periodically permitted to float, invariably depreciating sharply.