Volatility and Risk: The Roller Coaster Market

By: Dr. Sam Vaknin

Also published by United Press International (UPI)

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Volatility is considered the most accurate measure of risk and, by extension, of return, its flip side. The higher the volatility, the higher the risk - and the reward. That volatility increases in the transition from bull to bear markets seems to support this pet theory. But how to account for surging volatility in plummeting bourses? At 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's VIX index, a measure of traders' expectations of share price gyrations, in July reached levels not seen since the 1987 crash, and shot up again (two weeks ago)... Over the past five years, volatility spikes have become ever more frequent, from the Asian crisis in 1997 right up to the World Trade Centre attacks. Moreover, it is not just price gyrations that have increased, but the volatility of volatility itself. The markets, it seems, now have an added dimension of risk."

Call-writing has soared as punters, fund managers, and 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 information - and a lot to do with mass psychology. How else can we 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 yielded by any efficient market hypothesis, or by discounted streams of future dividends, or earnings. Yet, this finding is hotly disputed.

Some scholarly studies of researchers such as Stephen LeRoy and Richard Porter offer support - other, no less weighty, scholarship by the likes of Eugene Fama, Kenneth French, James Poterba, Allan Kleidon, and William Schwert negate it - mainly by attacking Shiller's underlying assumptions and simplifications. Everyone - opponents and proponents alike - admit that stock returns do change with time, though for different reasons.

Volatility is a form of market inefficiency. It is a reaction to incomplete information (i.e., uncertainty). Excessive volatility is irrational. The confluence of mass greed, mass fears, and mass disagreement as to 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 inception of new trends. Some traders are contrarians. When the VIX or the NASDAQ Volatility indices are high - signifying 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, i.e., with enhanced volatility. Market bottoms - boring, cyclical, affairs - usually suppress volatility. Interestingly, Chaikin himself disputes this interpretation. He believes that volatility increases near the bottom, reflecting panic selling - and decreases near the top, when investors are in full accord as to market direction.

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

It is the work of theoreticians of finance. Alas, they are consumed by mutual rubbishing and dogmatic thinking. The few that wander out of the ivory tower and actually bother to ask economic players what they think and do - and why - are much derided. It is a dismal scene, devoid of volatile creativity.

A Note on Short Selling and Volatility

Short selling involves the sale of securities borrowed from brokers who, in turn, usually borrow them from third party investors. The short seller pays a negotiated fee for the privilege and has to "cover" her position: to re-acquire the securities she had sold and return them to the lender (again via the broker). This allows her to bet on the decline of stocks she deems overvalued and to benefit if she is proven right: she sells the securities at a high price and re-acquires them once their prices have, indeed, tanked.

A study titled "A Close Look at Short Selling on NASDAQ", authored by James Angel of Georgetown University - Department of Finance and Stephen E. Christophe  and Michael G. Ferri of George Mason University - School of Management, and published in the Financial Analysts Journal, Vol. 59, No. 6, pp. 66-74, November/December 2003, yielded some surprising findings:

"(1) overall, 1 of every 42 trades involves a short sale; (2) short selling is more common among stocks with high returns than stocks with weaker performance; (3) actively traded stocks experience more short sales than stocks of limited trading volume; (4) short selling varies directly with share price volatility; (5) short selling does not appear to be systematically different on various days of the week; and (6) days of high short selling precede days of unusually low returns."

Many economists insist that short selling is a mechanism which stabilizes stock markets, reduces volatility, and creates
incentives to correctly price securities. This sentiment is increasingly more common even among hitherto skeptical economists in developing countries.

In an interview he granted to Financialexpress.com in January 2007, Marti G Subrahmanyam, the Indian-born Charles E Merrill professor of Finance and Economics in the Stern School of Business at New York University had this to say:

"Q: Should short-selling be allowed?

A: Such kind of restrictions would only magnify the volatility and crisis. If a person who is bearish on the market and is not allowed to short sell, the market cannot discount the true sentiment and when more and more negative information pour in, the market suddenly slips down heavily."

But not everyone agrees. In a paper titled "The Impact of Short Selling on the Price-Volume Relationship: Evidence from Hong Kong", the authors, Michael D. McKenzie or RMIT University - School of Economics and Finance and Olan T. Henry of the University of Melbourne - Department of Economics, unequivocally state:

"The results suggest (i) that the market displays greater volatility following a period of short selling and (ii) that asymmetric responses to positive and negative innovations to returns appear to be exacerbated by short selling."

Similar evidence emerged from Australia. In a paper titled "Short Sales Are Almost Instantaneously Bad News: Evidence from the Australian Stock Exchange", the authors, Michael J. Aitken, Alex Frino, Michael S. McCorry, and Peter L. Swan of the University of Sydney and Barclays Global Investors, investigated "the market reaction to short sales on an intraday basis in a market setting where short sales are transparent immediately following execution."

They found "a mean reassessment of stock value following short sales of up to −0.20 percent with adverse information impounded within fifteen minutes or twenty trades. Short sales executed near the end of the financial year and those related to arbitrage and hedging activities are associated with a smaller price reaction; trades near information events precipitate larger price reactions. The evidence is generally weaker for short sales executed using limit orders relative to market orders." Transparent short sales, in other words, increase the volatility of shorted stocks.

Studies of the German DAX, conducted in 1996-8 by Alexander Kempf, Chairman of the Departments of Finance in the University of Cologne and, subsequently, at the University of Mannheim, found that mispricing of stocks increases with the introduction of arbitrage trading techniques. "Overall, the empirical evidence suggests that short selling restrictions and early unwinding opportunities are very influential factors for the behavior of the mispricing." - Concluded the author.

Charles M. Jones and Owen A. Lamont, who studied the 1926-33 bubble in the USA, flatly state: "Stocks can be overpriced when short sale constraints bind." (NBER Working Paper No. 8494, issued in October 2001). Similarly, in a January 2006 study titled "The Effect of Short Sales Constraints on SEO Pricing", the authors, Charlie Charoenwong and David K. Ding of the Ping Wang Division of Banking and Finance at the Nanyang Business School of the Nanyang Technological University Singapore, summarized by saying:

"The (short selling) Rule’s restrictions on informed trading appear to cause overpricing of stocks for which traders have access to private adverse information, which increases the pressure to sell on the offer day."

In a March 2004 paper titled "Options and the Bubble", Robert H. Battalio and Paul H. Schultz of University of Notre Dame - Department of Finance and Business Economics contradict earlier (2003) findings by Ofek and Richardson and correctly note:

"Many believe that a bubble was behind the high prices of Internet stocks in 1999-2000, and that short-sale restrictions prevented rational investors from driving Internet stock prices to reasonable levels. Using intraday options data from the peak of the Internet bubble, we find no evidence that short-sale restrictions affected Internet stock prices. Investors could also cheaply short synthetically using options. Option strategies could also permit investors to mitigate synchronization risk. During this time, information was discovered in the options market and transmitted to the stock market, suggesting that the bubble could have been burst by options trading."

But these findings, of course, would not apply to markets with non-efficient, illiquid, or non-existent options exchanges - in short, they are inapplicable to the vast majority of stock exchanges, even in the USA.

A much larger study, based on data from 111 countries with a stock exchange market was published in December 2003. Titled "The World Price of Short Selling" and written by Anchada Charoenrook of Vanderbilt University - Owen Graduate School of Management and Hazem Daouk of Cornell University - Department of Applied Economics and Management, its conclusions are equally emphatic:

"We find that there is no difference in the level of skewness and coskewness of returns, probability of a crash occurring, or the frequency of crashes, when short-selling is possible and when it is not. When short-selling is possible, volatility of aggregate stock returns is lower. When short-selling is possible, liquidity is higher consistent with predictions by Diamond and Verrecchia (1987). Lastly, we find that when countries change from a regime where short-selling is not possible to where it is possible, the stock price increases implying that the cost of capital is lower. Collectively, the empirical evidence suggests that short-sale constraints reduce market quality."

But the picture may not be as uniform as this study implies.

Within the framework of Regulation SHO, a revamp of short sales rules effected in 2004, the US Securities and Exchange Commission (SEC) lifted, in May 2005, all restrictions on the short selling of 1000 stocks. In September 2006, according to Associated Press, many of its economists (though not all of them) concluded that:

"Order routing, short-selling mechanics and intraday market volatility has been affected by the experiment, with volatility increasing for smaller stocks and declining for larger stocks. Market quality and liquidity don't appear to have been harmed."

Subsequently, the aforementioned conclusions notwithstanding, the SEC recommended to remove all restrictions on stocks of all sizes and to incorporate this mini-revolution in its July 2007 regulation NMS for broker-dealers. Short selling seems to have finally hit the mainstream.

Volatility and Price Discovery

Three of the most important functions of free markets are: price discovery, the provision of liquidity, and capital allocation. Honest and transparent dealings between willing buyers and sellers are thought to result in liquid and efficient marketplaces. Prices are determined, second by second, in a process of public negotiation, taking old and emergent information about risks and returns into account. Capital is allocated to the highest bidder, who, presumably, can make the most profit on it. And every seller finds a buyer and vice versa.

It is an open question whether frictionless markets are more efficient. Traders and investors need time to digest new information; incorporate it in models and theories regarding the markets and specific securities; map out the full implications of recent developments; and decide how to act. We call this time lapse "friction" and it guarantees that players and agents act more or less rationally and consistently. In a frictionless market, panics, crashes, and bubbles are far more likely, rendering it less efficient, not more so.

The current global crisis is not only about the failure of a few investment banks (in the USA) and retail banks (in Europe). The very concept of free markets seems to have gone bankrupt. This was implicitly acknowledged by governments as they rushed to nationalize banks and entire financial systems.

In the last 14 months (August 2007 to October 2008), markets repeatedly failed to price assets correctly. From commodities to stocks, from derivatives to houses, and from currencies to art prices gyrate erratically and irrationally all over the charts. The markets are helpless and profoundly dysfunctional: no one seems to know what is the "correct" price for oil, shares, housing, gold, or anything else for that matter. Disagreements between buyers and sellers regarding the "right" prices are so unbridgeable and so frequent that price volatility (as measured, for instance, by the VIX index) has increased to an all time high. Speculators have benefited from unprecedented opportunities for arbitrage. Mathematical-economic models of risk, diversification, portfolio management and insurance have proven to be useless.

Inevitably, liquidity has dried up. Entire markets vanished literally overnight: collateralized debt obligations and swaps (CDOs and CDSs), munis (municipal bonds), commercial paper, mortgage derivatives, interbank lending. Attempts by central banks to inject liquidity into a moribund system have largely floundered and proved futile.

Finally, markets have consistently failed to allocate capital efficiently and to put it to the most-profitable use. In the last decade or so, business firms (mainly in the USA) have destroyed more economic value than they have created. This net destruction of assets, both tangible and intangible, retarded wealth formation. In some respects, the West - and especially the United States - are poorer now than they were in 1988. This monumental waste of capital was a result of the policies of free and easy money adopted by the world's central banks since 2001. Easy come, easy go, I guess.

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