Volatility is considered the most accurate measure of risk and, by extension, of return, its flip side. The higher the volatility, the greater the risk – and reward. That volatility increases in the transition from bull to bear markets seems to support this theory for pets. But how to account for volatility to rise in fall handbags? In the depths of the bear phase, volatility and risk increase while returns evaporate – even taking short-selling into account.

“The Economist” has recently proposed yet another dimension of risk:

“The Chicago Board Options Exchange VIX Index, a measure of traders’ expectations of price gyrations, in July reached levels not seen since the 1987 crash, and hit it again (two weeks ago) … In the last five years, volatility spikes have become ever more frequent, from the Asian crisis of 1997 to World Trade Center attacks. In addition, it is not just price gyrations that have increased, but the volatility of volatility itself. The markets, as Apparently they now have a dimension of risk. ”

Call-writing has increased dramatically, as players, fund managers, institutional investors and try to Eke a return run wild and to protect their stock portfolios decline. Naked strategies – options contracts of sale or purchase in the absence of an investment portfolio of underlying assets – translate into trading of volatility itself and, therefore, risk. Short-selling and spread-betting funds join single stock futures in profiting from the cheap.

Market – also known as beta or systematic – risk and volatility reflect 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 an equal number of Nobel laureates and controversies. The hesitation of security prices is often measured by a coefficient of variation within the formula of Black-Scholes published in 1973. The implied volatility is defined as the standard deviation of the returns of an asset. The value of an option increases with volatility. The higher the volatility the greater the possibility of an option during his life of being “in the money” – convertible to the underlying asset at a nice profit.

Without digging too deeply into the model, this mathematical expression works well and not when the trends miserably when the markets change sign. There is disagreement among scholars and practitioners if you need to make better use of historical data or current market prices – which include expectations – to estimate the volatility of prices and 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 estimates of future volatility because changing market conditions cause volatility (a) vary through time stochastically, and historical volatility can not adapt to changing market conditions more quickly. The folly of this thesis is that stochastic volatility contradicts the assumption required by the BS model – if volatility changes stochastically over time, the Black-Scholes is no longer the correct pricing formula and an implied volatility derived from the formula of Black-Scholes is not provides new information. ”

Black-Scholes is thought deficient on other issues as well. The implied volatility of options on the same stock tend to vary, defying the formula postulated that an individual stock may be associated with only one value of implied volatility. The model assumes a certain – geometric Brownian – distribution of stock prices that has been shown not to apply to U.S. markets, among others.

Studies have exposed serious departure from the price process fundamental to Black-Scholes: skewness, excess kurtosis (ie, concentration of prices around the mean), serial correlation, and time varying volatility. Black-Scholes tackles stochastic volatility bad. 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 formula for setting prices.

Volatility also decreases in administered markets and over different spans of time. On the contrary, the received wisdom of the random walk model, most investment vehicles sport different volatility over different time horizons. The volatility is especially high when the supply and inelastic demand and are subject to large random shocks. This is why the prices of industrial products are less volatile than the prices of shares, or commodities.

But because the stocks are volatile exchange rates and to start? Why not follow a smooth evolutionary path in line with, for example, inflation, interest rates or, or productivity, or net gain?

To begin with, because economic fundamentals fluctuate – sometimes as wildly as shares. The Fed has cut interest rates 11 times in the last 12 months to 1.75 percent – its lowest level in 40 years. Inflation gyrated from double digit to a single number in the space of two decades. This uncertainty is, inevitably, incorporated in the price signal.

Moreover, because of delays 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, he 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 example, the axes of interest rates and the causes for the depreciation of the currency. The rational outcome should have been a panic sale of bonds denominated in the currency collapse. But the devaluation is so excessive that people reasonably expect a return – namely, an appreciation of the currency – and purchase bonds rather than dispose of them.

Yet, even Dornbusch ignored the fact that some twirls prices have nothing to do with political or economic, or with the emergence of new information – and much to do with mass psychology. How else can you account for the crash of October 1987? This goes to the heart of the undecided debate between technical and fundamental analysts.

As Robert Shiller has demonstrated in his tomes “market volatility” and “irrational exuberance”, the volatility of stock prices exceeds the predictions arising from any of the efficient market hypothesis, or to discount the flow of future dividends, or profits . However, this result is very controversial.

Some studies of researchers such as Stephen LeRoy and Richard Porter offer support – other, no less heavy, scholarships by the likes of Eugene Fama, Kenneth French, James Poterba, Allan Kleidon, and William Schwert deny that – mainly by attacking Shiller’s assumptions underlying and simplifications. Everyone – proponents and opponents, and – admit that stock returns does not change with time, although for different reasons.

Volatility is a form of market inefficiency. This is a reaction to incomplete information (eg, uncertainty). Excessive volatility is irrational. The confluence of mass greed, fears of mass, mass and disagreement regarding the preferred mode of reaction to public and private information – yields price fluctuations.

Changes in volatility – as manifested in options and futures premiums – are good predictors of shifts in sentiment and the beginning of new trends. Some traders are contrarians. When the VIX or the NASDAQ Volatility indices are high – which means an oversold market – they buy and when the indices are low, they sell.

Chaikin’s Volatility Indicator, a popular timing tool, seems to couple market tops with increased indecisiveness and nervousness, ie, with greater volatility. Market funds – boring, cyclical, affairs – usually suppress volatility. Interestingly, Chaikin disputed this interpretation. He believes that volatility increases near the bottom, reflecting panic selling – and decreases near the top, when investors are in full agreement regarding the direction of the market.

But most market players follow the trend. They sell when the VIX is high and, therefore, portends a declining market. A bullish consensus is indicated by low volatility. Thus, low VIX readings signal the time to buy. If this is more than superstition or a mere gut reaction remains to be seen.

And ‘the work of theoreticians of finance. Alas, I am consumed by mutual rubbishing and dogmatic thinking. The few that wander out of the ivory tower and actually bother to ask what the players and I do not believe – and why – are much derided. It is a sad scene, devoid of volatile creativity.

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