Capitalistic Musings | Page 6

institutional
investors try to eke an extra return out of the wild ride and to protect
their dwindling equity portfolios. Naked strategies - selling options
contracts or buying them in the absence of an investment portfolio of
underlying assets - translate into the trading of volatility itself and,
hence, of risk. Short-selling and spread-betting funds join single stock
futures in profiting from the downside.
Market - also known as beta or systematic - risk and volatility reflect
underlying problems with the economy as a whole and with corporate
governance: lack of transparency, bad loans, default rates, uncertainty,
illiquidity, external shocks, and other negative externalities. The
behavior of a specific security reveals additional, idiosyncratic, risks,
known as alpha.
Quantifying volatility has yielded an equal number of Nobel prizes and
controversies. The vacillation of security prices is often measured by a
coefficient of variation within the Black-Scholes formula published in
1973. Volatility is implicitly defined as the standard deviation of the
yield of an asset. The value of an option increases with volatility. The
higher the volatility the greater the option's chance during its life to be
"in the money" - convertible to the underlying asset at a handsome
profit.
Without delving too deeply into the model, this mathematical
expression works well during trends and fails miserably when the
markets change sign.
There is disagreement among scholars and traders whether one should
better use historical data or current market prices - which include
expectations - to estimate volatility and to price options correctly.
From "The Econometrics of Financial Markets" by John Campbell,
Andrew Lo, and Craig MacKinlay, Princeton University Press, 1997:
"Consider the argument that implied volatilities are better forecasts of
future volatility because changing market conditions cause volatilities
(to) vary through time stochastically, and historical volatilities cannot
adjust to changing market conditions as rapidly. The folly of this
argument lies in the fact that stochastic volatility contradicts the
assumption required by the B-S model - if volatilities do change
stochastically through time, the Black-Scholes formula is no longer the
correct pricing formula and an implied volatility derived from the

Black-Scholes formula provides no new information."
Black-Scholes is thought deficient on other issues as well. The implied
volatilities of different options on the same stock tend to vary, defying
the formula's postulate that a single stock can be associated with only
one value of implied volatility. The model assumes a certain -
geometric Brownian - distribution of stock prices that has been shown
to not apply to US markets, among others.
Studies have exposed serious departures from the price process
fundamental to Black-Scholes: skewness, excess kurtosis (i.e.,
concentration of prices around the mean), serial correlation, and time
varying volatilities. Black-Scholes tackles stochastic volatility poorly.
The formula also unrealistically assumes that the market dickers
continuously, ignoring transaction costs and institutional constraints.
No wonder that traders use Black-Scholes as a heuristic rather than a
price-setting formula.
Volatility also decreases in administered markets and over different
spans of time. As opposed to the received wisdom of the random walk
model, most investment vehicles sport different volatilities over
different time horizons. Volatility is especially high when both supply
and demand are inelastic and liable to large, random shocks. This is
why the prices of industrial goods are less volatile than the prices of
shares, or commodities.
But why are stocks and exchange rates volatile to start with? Why don't
they follow a smooth evolutionary path in line, say, with inflation, or
interest rates, or productivity, or net earnings?
To start with, because economic fundamentals fluctuate - sometimes as
wildly as shares. The Fed has cut interest rates 11 times in the past 12
months down to 1.75 percent - the lowest level in 40 years. Inflation
gyrated from double digits to a single digit in the space of two decades.
This uncertainty is, inevitably, incorporated in the price signal.
Moreover, because of time lags in the dissemination of data and its
assimilation in the prevailing operational model of the economy -
prices tend to overshoot both ways. The economist Rudiger Dornbusch,
who died last month, studied in his seminal paper, "Expectations and
Exchange Rate Dynamics", published in 1975, the apparently irrational
ebb and flow of floating currencies.
His conclusion was that markets overshoot in response to surprising

changes in economic variables. A sudden increase in the money supply,
for instance, axes interest rates and causes the currency to depreciate.
The rational outcome should have been a panic sale of obligations
denominated in the collapsing currency. But the devaluation is so
excessive that people reasonably expect a rebound - i.e., an
appreciation of the currency - and purchase bonds rather than dispose
of them.
Yet, even Dornbusch ignored the fact that some price twirls have
nothing to do with economic policies or realities, or with the emergence
of new