Pricing persistence is described in chaos theory as the Joseph effect, drawn from the familiar biblical story of Joseph interpreting the pharaoh’s dream to mean seven years of feast followed by seven years of famine. The presence of this phenomenon in public capital markets is exhibited by bull markets and bear markets in that identifiable trends emerge and endure for significant time periods.
Pricing discontinuity is described in chaos theory as the Noah effect, taken from the biblical story of the Flood. Public capital markets exhibit the Noah effect in price changes. For example, suppose IBM opens at 50 and closes at 30. That does not necessarily mean that during some point in the trading day an investor could have traded IBM at 40 (or any other price between 50 and 30). Rather, the price of a stockmoves discontinuously in the sense that at one moment it may be trading at 45 and at the next it cannot be sold for more than 35.
The alternating presence of price persistence (the Joseph effect) and price discontinuity (the Noah effect) shows that chronological time—a linear concept—is not the most precise temporal measure of public capital market phenomena. When discontinuous pricing— the Noah effect—dominates a market, wide swings occur and market pricing is relatively unstable because intrinsic time and trading activity outpace chronological time and information gathering. When price persistence—the Joseph effect—dominates a market, pricing is relatively stable because intrinsic time is approximately equal to or slower than chronological time.
The speed of intrinsic time may differ from that of chronological time. Price changes would then move ahead of information changes. Investors and other market participants conform perfectly neither to the linear assumption of homogeneous expectations nor to the ubiquitous irrationality of noise theory.
Instead, investors have heterogeneous expectations that may or may not be rational and that may be defined according to a number of variables. Chief among them are investor time horizons that range from the very short term (for day traders and minute traders and market makers, say) to the very long term (for central banks, say).
The range of different time dimensions contributes to the Joseph and Noah effects, persistence, discontinuity, and premature and delayed adjustments to information. Short-term traders react more quickly to new information; long-term investors react more slowly.
Therefore, information changes will not produce proportionate price changes. Indeed, volatility will increase when there are greater numbers of short-term traders (day traders) than long-term traders.
Changes that are produced constitute new information, producing another round of price changes again defined according to a range of discrete time dimensions. Adding further complexity to this mix of investor heterogeneity and time dimensions is the increasingly global nature of financial markets: News itself is dynamic, traveling around the world, usually in 24-hour cycles, and impacting Tokyo, then London/Frankfurt, then New York, and around again.
In this reality, it seems implausible to claim instantaneous, unbiased market adjustment to new information and it is not necessary to attribute all market preadjustment or readjustment to irrational noise trading. Incremental information changes in a perfect market would be expected to produce proportionate price changes.
But informational changes produce disproportionate changes. In terms of chaotic dynamics, these disproportionate changes may be seen as a result of initial measurement error that (as in the hockey puckexample and the butterfly effect generally) leads to exponentially greater price changes over time.
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