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(also from arXiv)

Abstract

Why do a market's prices move up or down? Claims about causes are made without actual information, and accepted or dismissed based upon poor or non-existent evidence. Here we investigate the price movements that ended with Apple stock closing at $500.00 on January 18, 2013. There is a ready explanation for this price movement: market manipulation by those who sold stock options, who stood to directly benefit from this closing price. Indeed, one web commentator predicted this otherwise unlikely event publicly. This explanation was subsequently dismissed by press articles that claim that stock prices end near such round numbers based upon legitimate hedging activity. But how can we know? We show that the accepted model that points to hedging as the driving cause of prices is not quantitatively consistent with the price movement on that day. The price moved upward too quickly over a period in which the hedgers position would require selling rather than buying. Under these conditions hedgers would have driven the price away from the strike price rather than toward it. We also show that a long published theory of the role of hedging is incomplete mathematically, and that the correct theory results in much weaker price movements. This evidence substantially weakens the case of those who claim hedging as cause of anomalous market price movements. The explanation that market manipulation is responsible for the final close cannot be dismissed based upon unsubstantiated, even invalid, hedging claims. Such proffered explanations shield potential illegal activity from further inquiry even though the claims behind those explanations have not been demonstrated.

Press Release: The $500.00 AAPL close: Manipulation or Hedging? A quantitative analysis.

CAMBRIDGE (Sep. 3) — On Friday, January 18th, 2013, Apple Inc.'s stock price closed the day's trading at exactly $500.00. Is the unlikelihood of closing on such a perfectly round number suspicious? While most press reporters brushed it off as an outlier amidst normal market activity, new calculations demonstrate that the deeper math behind the number simply does not add up. Researchers at the New England Complex Systems Institute are digging still deeper into the markets to understand how and why someone could cause Apple's stock to land at exactly $500.00 on one of the most auspicious dates on the options trading calendar.

In their report, "The $500.00 AAPL Close: Manipulation or Hedging? A Quantitative Analysis," Yavni Bar-Yam, Marcus de Aguiar, and Yaneer Bar-Yam investigate the very roots of why a market's prices move up and down, along with the actions, actors, and motivations behind these changes.

By carrying out sophisticated mathematical analyses, the researchers were able to disprove explanations relying on perfectly legitimate activity (called hedging).

"When we remove the explanation based upon legitimate activity, what's left is the likely intentional manipulation of market prices" said Yaneer Bar-Yam, one of the authors. "Insider trading and using fake news to manipulate markets is well known, but markets can be manipulated by directly selling and buying stock to move the price."

January 18, 2013 was a special date for those involved in the trading of options. Options are side-bets on stock price movements — they are contracts that give the purchaser the right to buy and sell stocks at pre-assigned prices. By closing at exactly $500.00 on Jan. 18, option contracts on $3.0 billion of Apple stock at that price simply expired worthless. The market makers who sold those options in the first place stood as the ones to gain from this, creating a financial incentive to manipulate prices. According to reports, the dominant market maker for AAPL options is Goldman Sachs (in separate news, Goldman Sachs recently suffered losses due to erroneous options trades).

"People often dismiss the possibility of a manipulation based upon the 'magic' of the market," Bar-Yam said. "Looking more carefully we can show that such explanations are not well founded."

How can we defeat market manipulation? The authors believe the answer lies in making the analysis of data a matter of public dialog, as well as eliminating incentives and mechanisms of manipulation. The findings in this paper are an important first step in this process.

FIG. 1 - Top Panel: Price of AAPL stock during Jan. 18, 2013 Bottom Panel: The amount of hedging needed by straddle owners. During the closing hour, the amount of hedging needed decreases and the stock must be sold which would drive the price down, away from the strike price rather than toward it. These results are counter to the claim that hedging is responsible for the closing strike price.

FIG. 3 - Simulation of the effect of hedging on prices including noise. Fifty instances are shown. Parameters are based on AAPL stocks on January 18, 2013, and noise consistent with the average intraday volatility in January.