RDP 9501: Modern Approaches to Asset Price Formation: A Survey of Recent Theoretical Literature 3. Fads, Irrational Bubbles, and Noise Traders
March 1995
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In this strand of the literature, there are at least some investors and traders whose sentiment and expectations are driven by extraneous or nonfundamental factors such as fads, fashions, rumours and “noise”. The participation of such a group of investors can disrupt and destabilise speculative asset markets; they may generate excessive volatility in asset prices and contribute to the more severe episodes of financial market instability, colourfully described by some as “speculative manias”, “frenzies”, “irrational speculative bubbles”, “panics” and “crashes”.^{[18]}
The view that prices in speculative asset markets might at times be influenced by irrational investor behaviour, while not new^{[19]}, first found influence with the contributions of Robert J. Shiller. Building on his earlier empirical work dealing with “excessive” volatility in stock prices, Shiller (1984) and (1989) emphasised the importance of mass psychology in financial markets, in particular the role played by investors' susceptibility to “fashions” and “fads”. According to Shiller, changing fashions, fads, and erratic and capricious shifts in investor sentiment, have been the chief causes of mispricings of assets.
This theory of asset price dynamics is now simply referred to as the “fads” model of asset prices. A fad is defined as any departure of asset prices from their fundamental values due to socially, or psychologically, induced changes in market sentiment and opinion. Unlike a rational speculative bubble, however, in these models the asset price does not deviate from its fundamental value in an explosive manner.
To help understand the dynamics of fads, Shiller finds useful mathematical models of epidemics and contagion which some sociologists have employed in their analysis of the spread of news and rumour. Such diffusion models describe how a fad develops by specifying an “infection rate” – the rate at which interest in a fad spreads among a population – and a “removal rate” – the rate at which interest dissipates. Other variables, such as the number of “carriers” and the size of the “susceptible” population, are also relevant. Thus, Shiller states: “A fad is a bubble if the contagion of the fad occurs through price; people are attracted by observed price increases. Observing past price increases means observing other people becoming wealthy who invested heavily in the asset, and this observation might interest or excite other potential investors”.^{[20]}
Shiller dismisses one critique of fads advanced by proponents of the EMH. These proponents argue that the actions of rational arbitrageurs will negate the influence of fads by exploiting large, riskless profit opportunities associated with them. According to Shiller, this argument reflects a misunderstanding of the relationship between the ability to forecast asset returns and market efficiency. While market efficiency implies that changes in asset prices cannot be forecast, the inability of investors to forecast asset prices does not necessarily imply market efficiency (in the sense that observed prices will always equal their intrinsic values). Shiller concludes that, if the future path of a fad is unpredictable, even rational investors would be unable to profit from the discrepancy between observed asset prices and their fundamental values.
Following Summers (1986) formalisation of Shiller's “fad” concept, a fad in an asset price may be represented by the following expression:
where x_{t} is the log of the asset price at time t; is the fundamental value of the asset at time t (given by equation (3) above); F_{t} is the fad in the asset price; λ is a parameter measuring the rate of decay of the fad; and ε_{t} is a stochastic disturbance term with zero mean.
In this approach, the asset price is modelled as the sum of a random walk (the fundamental component) and a fad component which, while it is assumed to persist, is not assumed to diverge indefinitely (i.e 0 ≤ λ <1).^{[21]} Shiller (1984) and Summers (1986) observe that, with such a specification, inability to forecast asset returns over the short run and large departures of prices from their fundamentals would not be inconsistent. This is because the fad component, F_{t}, would follow a stochastic process similar to a random walk, while retaining the property of mean reversion.
3.1 The NoiseTrader Approach
Friedman's (1953) contribution, referred to in the Introduction, contained the central tenet of the EMH that rational speculation will stabilise asset prices and drive out irrational or destabilising speculation. Recent contributions have subjected this view to a forceful attack, notably within the “noise trader” approach. Seminal and representative papers include De Long, Shleifer, Summers and Waldman (1990a, 1990b, 1991); Cutler, Poterba, and Summers (1990, 1991); and Shleifer and Summers (1990). The noisetrader approach is gaining wider acceptance in the economics and finance literature.
Two propositions lie at the core of the noisetrader framework:

the coexistence of heterogeneous investors and traders
The noise traders approach explicitly acknowledges the interaction of two qualitatively distinct categories of trader/investor. One category comprises traditional rational speculators, also referred to as “arbitrageurs”, “smart money” or “fundamentalist” traders. These are sophisticated investors whose opinions and trading decisions are based on economic fundamentals and who strive to digest all relevant economic information when making investment decisions. They are also assumed to be risk averse and have relatively short trading horizons.
Trading decisions of the other category of investors – “noisetraders”^{[22]} – display a degree of irrationality. This category of “unsophisticated” investors is not as well informed as rational investors and is highly susceptible to fads, rumours and other extraneous information (“noise”). Attitudes of noise traders are thus highly correlated and their opinions cannot be fully justified by economic fundamentals. Their activity can therefore generate shifts in aggregate demand for the asset which cannot be fully explained in terms of the fundamentals.

arbitrage limitations
In the noisetrader model, the degree of arbitrage activity undertaken by rational investors is limited, and unable fully to counteract demand shifts generated by noise traders. In these models rational investors are typically assumed to be risk averse, in relation to:
 fundamental risk, i.e. the risk of loss due to unexpected changes in an asset's fundamentals. For example, after evaluating relevant information, a rational investor may be convinced that an asset is definitely “overvalued” today. The investor may be reluctant to sell heavily at that price, however, because of the risk that fundamentals will move against him. Unanticipated information reflecting favourably on the asset may be released in future periods, raising the fundamental value and thereby generating a loss on the trade undertaken today.
 noise trader risk, i.e. the possibility of erratic shifts in asset demand due to the unpredictable and capricious nature of noise trader expectations. This can increase uncertainty about the future price of an asset, thereby adding to risk borne by rational arbitrageurs. For example, suppose that, due to noisetrader demand, an asset is considerably undervalued relative to its fundamentals. Arbitrageurs contemplating buying the asset cannot ignore the possibility that, by the time they have to liquidate their positions, noise traders will have become even more “bearish” and pushed the price even lower. This would clearly limit the size of the initial position that a riskaverse rational investor would be prepared to take.
 uncertainty about fundamentals, i.e. individual rational investors may be uncertain about whether an observed movement in an asset price is due to changes in noise trader demand or to new information about fundamentals. Perfect arbitrage presumes that rational investors know with certainty the fundamental value of an asset and can accurately determine whether it is undervalued or overvalued. A more realistic view is that rational investors do not have absolute confidence in their estimates of the fundamental value, or their ability to discern even significant mispricings of assets.^{[23]}
The limited appetite of rational speculators for arbitrage also reflects the assumption that rational speculators have shortterm investment horizons. Two reasons are advanced for this assumption:^{[24]}
 the performance of most portfolio and pension fund managers' is evaluated over a relatively short term. Funds managers therefore have a strong incentive to focus on factors affecting the shortterm performance of a portfolio. Factors bearing on the fund's longerterm performance will tend to have less importance.
 capital market imperfections reflecting, say, asymmetric information, may limit the borrowing capacity of rational speculators. Limited access to capital and other such credit restrictions, might mean that longterm arbitrage positions cannot be maintained indefinitely or would be very expensive compared with shortterm arbitrage opportunities.
The noisetrader approach is a more realistic description of asset markets than earlier models of asset pricing since a group of irrational investors coexists with a group of rational investors, and the arbitrage activities of the latter are limited. This implies that arbitrage activity by rational speculators might not be sufficient to eliminate fully the influence of noise traders, but can nonetheless move asset prices at least partially towards their fundamental values.
3.2 Destabilising Rational Speculation
A variation of the noise trader approach describes situations in which trading by rational speculators might actually exacerbate price movements arising from the activities of noise traders. De Long, Shleifer, Summers and Waldman (1990b) demonstrate how rational speculators will find it in their interest to exploit the presence of positive feedback elements in the market. In this case, activity by rational investors might induce deviations of asset prices from their fundamental values beyond those due to the activity of noise traders. Contrary to the conclusion of Friedman (1953), rational speculation could have a destabilising impact on asset prices.
Positive feedback strategies involve purchasing an asset after it has appreciated in value or selling it after it has depreciated. Trading activity based on this strategy is quite common in asset markets, and may be prompted by a number of investment approaches, including “chartism” and technical analysis, “stoploss” orders, portfolio insurance and extrapolative price expectations.^{[25]} Positive feedback effectively reinforces and perpetuates the direction of asset price movements and generates “momentum”. De Long et al. (1990b) demonstrate that such momentum will be exploited by profitmaximising rational speculators, thereby accentuating asset price volatility.
The way in which interaction between sophisticated rational speculators and unsophisticated positive feedback traders (essentially noise traders) can generate asset price instability can be illustrated by the following scenario. Suppose that sophisticated rational speculators receive some “bad” news about an asset's fundamentals. Recognising that any fundamentalbased selling that they might undertake today will cause positivefeedback selling of the asset tomorrow, sophisticated speculators may initially sell excessively large amounts of the asset causing its price to fall by far more than is warranted by the deterioration in fundamentals. Positive feedback traders might then observe the large price fall and react by also selling the asset, causing its price to fall yet further. Rational speculators can then close their short positions to realise a profit.
In summary, unfavourable news which would have dictated some fall in an asset's intrinsic price, would – as a result of sales by rational speculators anticipating positivefeedback trading – lead to a substantially larger fall in the asset price than could be justified by the fundamentals. Rather than offsetting noise trader behaviour, the behaviour of rational speculators would magnify its impact, at least in the short term.
Advocates of the EMH claim that, by virtue of their trading behaviour, noise traders will incur large losses and be forced to exit the market. The presence of noise traders will therefore only have a very marginal influence on asset prices. In response, proponents of the noise trader approach advance several reasons for the survival and persistence of noise traders:
 noise traders tend to make erroneous assessments about an asset's return and its riskiness (i.e. they tend to overestimate returns and/or underestimate risk). They are therefore likely to be more “bullish”, on average, than rational speculators, and willing, on average, to bear more risk. Since asset markets compensate investors who take on more risk with higher rates of return, it is possible that expected returns to noise traders will be higher than those of rational speculators, even though they would, on average, be purchasing overpriced assets and selling underpriced ones. This reward might not necessarily reflect the bearing of “fundamental risk”; the higher return to noise traders might simply reflect compensation for accepting more of the risk which they themselves have introduced.^{[26]}
 successful noise traders, and the strategies they employ, will attract new traders adopting similar strategies. These recruits might erroneously attribute the higher average returns earned by noise traders to skill, rather than greater risktaking and luck.
 there is a continual influx of new traders and investors in asset markets. A sizeable proportion of these are likely to embrace unsophisticated investment strategies, including noise trading. Furthermore, noise traders who incur losses and are forced to exit the market, may save and return to the market at a later point in time, still adhering to their noisetrader strategies.
The longrun viability of noise traders, and their impact, cannot therefore easily be dismissed. Their presence can be an important factor in the dynamics of asset prices, not only in the short run but also over longer periods of time.
Footnotes
See Kindleberger (1989) and also Malkiel (1990). [18]
Nurkse (1944) for example, maintained that the documented excessive volatility and instability of currencies during the interwar period of the 1920s and 1930s was due primarily to irrational destabilising currency speculation. He argued that as a consequence of irrational and extrapolative expectations on the part of currency speculators, small fluctuations in the exchange rate would induce large and selfreinforcing movements of the currency in the same direction. Speculation in foreign currency markets was thus perceived by Nurske as a destabilising influence, accentuating and prolonging what otherwise would be small and shortterm fluctuations of a currency around its longrun equilibrium value. See also Keynes' (1936) incisive and pertinent observations on the nature of speculative activity and of financial markets in general, in Chapter 12 of The General Theory. [19]
Shiller (1989, p. 56). [20]
Note that, if λ = the fad component will be identical to a rational speculative bubble leading to the asset price diverging explosively from its fundamental value. [21]
The introduction of this term into the literature is attributed to Black (1986) and Kyle (1985). Black (1986) defines “noise” as essentially the antithesis of information: “Noise trading is trading on noise as if it were information. People who trade on noise are willing to trade even though from an objective point of view they would be better off not trading. Perhaps they think the noise they are trading on is information. Or perhaps they just like to trade.” Black (1986, p. 531). [22]
In light of the large number of alternative and empirically unsuccessful models of exchange rate determination, this problem of accurately assessing fundamental value is particularly acute in the foreign currency market. Witness, for example, the negative assessment by Meese (1990, p. 118): “The proportion of (monthly or quarterly) exchange rate changes that current models can explain is essentially zero. … The economics profession has not yet reached a consensus on the appropriate set of fundamental factors to include in an exchange rate equation”. [23]
Tuckman and Vila (1992) show that holding costs or unit time costs can also discourage the maintenance of longterm arbitrage positions by rational risk averse traders. [24]
Contributions by Frankel and Froot (1986, 1988 and 1990b) on the formation of actual
expectations in the foreign exchange market are indicative of the substantial presence
of positive feedback trading. Based on extensive survey data of investors expectations
on the US dollar and the Japanese yen, Frankel and Froot document how over the “short
term”(1, 2, and 4weeks ahead) expectations are extrapolative i.e. exhibit
significant “bandwagon” tendencies. On the other hand, over the “long
term”(3, 6 and 12 months ahead) expectations were heavily influenced by currency
fundamentals. Examination of forecasts and recommendations of leading exchange rate
forecasting services during mid 1980s, when the US dollar was generally perceived to be
overvalued, supported this conclusion. The typical forecaster maintained that the dollar
was overpriced relative to its fundamentals and was expected to depreciate within a 12
month period, but was still issuing “buy” recommendations for the currency
over the short term.
Allen and Taylor (1990) document that the formation of short term exchange rate
expectations is heavily influenced by chartist/technical analysis. Survey evidence
compiled from major participants in the London foreign exchange market revealed that 90
per cent of the respondents used some form of technical analysis in assessing the future
direction of the exchange rate over the short run. For horizons of a one year and
longer, 85 per cent of respondents viewed fundamentals as being considerably more
important.
[25]
De Long et al. (1990a, p. 74). [26]