Positive feedback trading,institutional investors andsecurities price fluctuation

Yin HongBusiness School, East China Normal University,

Shanghai, People’s Republic of China

Abstract

Purpose – The purpose of this paper is to research and analyze the influence of institutional investorsin the present securities market due to behavior alienation with “running after rising and falling” and“herd behavior”.

Design/methodology/approach – A DeLong, Shleifer, Summers, and Waldmann (DSSW) modelwith positive feedback trading is established first to show the trading process, and these securitiesprices are calculated considering the investors’ emotion. Through numerical analysis, the influence ofinstitutional investors on securities price fluctuation is simulated. Further, the analysis of institutionalinvestors’ incomes is processed based on this model.

Findings – Through these analyses, the following conclusions are drawn: it lies on the scale of positivefeedback traders and their sensitivity to past market performances whether the institutional investorscan stabilize the market, and it is not necessary for the institutional investors to benefit frommanipulating the market due to the existence of noise trader risk, so the positive feedback traders maysurvive in the security market over the long term.

Originality/value – The DSSW model considering positive feedback trading, presented in the paper,is more effective in analyzing the relation among the behavior of institutional investors, securitiespricing and securities price fluctuation. The paper proposes some advice for policy decisions, which ishelpful for government and institutions to maintain the stability of securities markets.

Keywords China, Securities, Stock prices, Investors, Stakeholder analysis

Paper type Research paper

I. ForewordAs a result of policy orientation of “developing institutional investors in a supernormalway”, the number of institutional investors has risen sharply in China. But, practices of thesecurities market is opposition to what is expected, institutional investors have failed tostabilize the market and behavior characteristics of some institutional investors haveundergone serious variation and deformation. If so, then what on earth is the role ofinstitutional investors in the securities market where “herd behavior” and “positivefeedback strategy” are common, to make arbitrage – move price to fundamental value andstabilize the market, or to magnify positive feedback trading and non-stabilize the market?This has been a hot issue attracting attention from both management and academia.

Studies on this issue have come to quite differing results. Some scholars, representedby Sosin (1998), believe that rational institutional investors can find a timely irrational

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/2044-1398.htm

This research was supported by the National Social Science Foundation under grantno. 10CGL014 and Open Project of Hubei Province Key Laboratory of Systems Science inMetallurgical Process (Wuhan University of Science and Technology) under grant no. B201004.The author would like to thank Changbo Wang for his help.

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China Finance Review InternationalVol. 1 No. 2, 2011pp. 120-132q Emerald Group Publishing Limited2044-1398DOI 10.1108/20441391111100714

price in the market and take the opposite strategy to correct the mistaken price,which helps decrease fluctuations in the securities market. But the empirical studies(Dennis and Strickland, 2002) on mutual fund suggest that, due to the restriction ofperformance evaluation, institutional investors widely engage in herd behaviors andmomentum trading, and these irrational behaviors add to market fluctuations.

Besides, there are many literatures that study institutional behaviors and marketstabilization from the angle of positive feedback trading. Shleifer (2000) introduced arational arbitrageur into the model used to study positive feedback trading, andconsequently has discovered greater fluctuations in stock price. Some empirical studiesalso have found strong evidences to show that institutional investors who have takenpositive feedback trading strategies cause greater market fluctuations (Bennett et al.,2003; Sias, 2007). There are also scholars who hold the opposite opinions, like Gibson andSafieddine (2003) and Badrinath and Wahal (2002) who believe that, when positivefeedback effect causes price to deviate from its fundamental value, institutionalinvestors as rational arbitrageurs will take negative feedback strategies to correct suchdeviation, and as a result, positive feedback traders cannot benefit from trading and willeventually vanish from the market. Lakonishok et al. (1992) has thought thatinstitutional investors also have the possibility to take actively positive feedback tradingstrategies which do not necessarily bring the market more instability. The reason is thatinvestors actually need some time to digest information and then make an accordingreaction; therefore, for the market price to completely reflect the new information, aperiod of time is required; in this case, it may be rational for investors to take a positivefeedback trading strategy. Through empirical studies on institutional investors likemonetary fund and pension, Diebold and Kamil (2007) and Lipson and Puckett (2007)have found that institutional investors take negative feedback investment strategiesmore often than not, which helps reduce market fluctuations.

Therefore, it can be concluded that when market price is brought away fromfundamental value by positive feedback trading, the academia fall into two groupsholding different opinions upon the role of institutional investors: one group holds theopinion that rational arbitrage by institutional investors helps price return to value andstabilize the market, while the other group believes that behaviors of institutionalinvestors will magnify positive feedback trading in the market and make the situationworse. In view of this problem, this paper will build models and will try to reveal from theangle of normative analysis the logical relationship between behaviors of institutionalinvestors and securities price fluctuations in the presence of positive feedback trading.

DeLong et al. (1990a, b), Sentana and Wadhwani (1992) and Shleifer (2000)have conducted influential researches on positive feedback trading, but models built bythese scholars remain descriptive, failing to offer precise numerical solutions foraccurate quantization of the relations among positive feedback trading, behaviors ofinstitutional investors and assets price. The model built by Sentana is obviously flawedin that the proportion of rational traders or feedback traders may turn out to be negative.As for the noise trader model DeLong, Shleifer, Summers, and Waldmann (DSSW) builtby DeLong et al. on the pricing of risk assets, positive feedback trading is actuallyexcluded from consideration. We believe that in China’s securities market wherethe philosophy of “focus on hot spot and short-term speculation” is greatly welcomedand the blind “momentum strategy” wins popularity, such irrational positive feedbacktrading will impose certain impacts on institutional investors’ expected function

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of market stabilization. So, this paper has built a DSSW model taking into considerationof positive feedback trading to analyze the relationship between behaviors ofinstitutional investors and securities price fluctuations. By doing so, this paper has cometo some meaningful conclusions and has put forward corresponding policy suggestionsof practical significance for regulators to reasonably assess the role played byinstitutional investors and proceed to regulate their behaviors.

II. DSSW model considering positive feedback tradingA classic DSSW model is a stripped-down overlapping generation model, which iscomposed of two-term-surviving individuals. Such an economy consists of two kindsof assets: one is risk-free assets, for which fixed actual dividend income r is paid eachterm, and it is supplied in a completely elastic way at a fixed price one; the other is riskassets, and suppose it receives fixed dividend income r the same as that of risk-free asset.Supply of risk assets is not elastic and can be simplified as one unit. Pt represents themarket price of risk assets in term t.

The DSSW model consists of two types of investors: noise traders (marked by n)and sophisticated investors (marked by s) who have the ability of rational expectation.Suppose the proportion of noise traders is m (0 , m , 1), then the proportion ofsophisticated investors is 1 2 m, no difference in investors of the same type.Sophisticated investors can rationally expect the price of risk assets and know thedistribution of return on assets; however, the expectation of noise traders to the priceinvolves their mistaken view of the after-market. Suppose rt represents the mistakenevaluation of the expected price of risk assets in term t by young noise traders, thenrt . 0 (,0) indicates that noise traders hold the optimistic (pessimistic) motion forthe future price of assets.

Suppose individuals make no consumption when young and their investmentresource is exogenously given. When individuals become old, they sell their risk assetsto the younger generation at a price of Ptþ1 and use up all of their wealth. So the onlydecision they have to make is to select a portfolio when they are young to maximize theirsubjective expected utilities. Suppose for each individual, there exists a continuousabsolute risk aversion utility function: Ut ¼ 2e22gwt , where g stands for the absoluterisk aversion coefficient and wt the wealth realized by investors through investment interm t. This functions depends upon lt, the amount of risk assets held by investors,and Rt, excess return on unit risk asset, where Rt ¼ r þ Ptþ1 2 (1 þ r)Pt. Then, we canprove that Rt obeys normal distribution.

Therefore, sophisticated investors will choose to hold lst of risk assets to maximize

the following expression:

lst r þ Et½Ptþ1�2 ð1 þ rÞPtf g2 ðls

t Þ2gVARt½Rtþ1�; ð1Þ

where Et[ · ] and VARt[ · ], respectively, are the symbols of conditional expectation andconditional variance.

While noise traders tend to hold lnt of risk assets to maximize the following

expression:

lnt r þ Et½Ptþ1� þ rt 2 ð1 þ rÞPtf g2 ðln

t Þ2gVARt½Rtþ1�: ð2Þ

By equations (1) and (2), we get the demands for risk assets, respectively, bysophisticated traders and noise traders:

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lst ¼

r þ Et½Ptþ1�2 ð1 þ rÞPt

2gVARt½Ptþ1�; ð3Þ

lnt ¼

r þ Et½Ptþ1� þ rt 2 ð1 þ rÞPt

2gVARt½Ptþ1�: ð4Þ

With the market clearing condition: mlnt þ ð1 2 mÞls

t ¼ 1, we get the market clearingprice as:

Pt ¼1

1 þ rr þ Et½Ptþ1�2 2gVARt½Ptþ1� þ mrtf g: ð5Þ

Different from the classic DSSW model, we have supposed that a part of the noise traderswill take the momentum strategy, since the irrational investor’s sentiment (optimism orpessimism) for the after-market is easily guided by market trend. Considering that noisetraders taking positive feedback strategy make their prediction of the after-marketbased on the changes of assets price in the previous term, we represent the formationprocess of their sentiment (pt) by the formula below:

pt ¼ pt21 þ bðPt21 2 Pt22Þ; ð0 , b , 1Þ ð6Þ

This means that when positive feedback traders observe the security price rise in theprevious term (Pt21 . Pt22), they believe that such a rise will continue, and therefore, theybecome more optimistic about assets price in the coming term (pt . pt21), and vice versa.We can learn from formulas (4) and (6) that there is a proportional relationship betweennoise traders’ demand for risk assets and their sentiment, while their sentiment is again in aproportional relationship with price changes in the previous term. So we can conclude thatwhen Pt21 . Pt22, positive feedback traders become more optimistic about theafter-market and will purchase more risk assets proportionally; moreover, the higher theprice rise rate is, the more demand for assets. Therefore, b stands for sensitivity ofpositive feedback traders’ demand for risk assets to price changes in the previous term.The sentiment formation mode as shown in formula (6) suggests that traders may prefermaking adjustments to their judgment to the total denial of previous price prediction model.

Suppose the proportion of noise traders taking positive feedback strategy is d(0 , d , 1), leaving 1 2 d of the other noise traders. The latter are also those noisetraders defined and discussed in the DSSW model and their sentiment (represented by1t)totally come from their inner irrational turbulence. Suppose 1t(t ¼ 1, 2, . . .) obeys thenormal distribution with a mean of 1 * and a variance of s2

1 and they are mutualindependent in time. Based on these assumptions, we learn that the overall averagesentiments rt of noise traders actually consist of two parts: one part from thepsychological characteristics of noise traders following the market trend and the otherpart randomly generated from pure white noise process. So the sentiment formationmode can be specified below:

rt ¼ d pt21 þ bðPt21 2 Pt22Þ� �

þ ð1 2 dÞ1t: ð7Þ

The essential difference between our model and the DSSW model lies in that, due to a partof noise traders’ behavior characteristics of forecasting price based on previous marketperformance, the overall average sentiments of noise traders are no longer independent

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in time, but autocorrelative (obeying to the process of AR(1), see Appendix 1 for proof).Actually, the hypothesis of noise traders’ independent sentiments made by the DSSWmodel has long been under criticism from academia, and there is much empirical evidenceto show that sentiments of noise traders are autocorrelative in time (Sun, 2005). Theautocorrelation in our model stems from investors’ positive feedback trading behaviors.

III. Pricing of risk assetsAccording to formula (5), introduced by DeLong et al. (1990a) for pricing of risk assets,and formula (7), the formation process of average sentiments of noise traders given inthis paper, we obtain the formula of assets pricing considering positive feedbacktrading:

P 0t ¼ 1 þ

mðrt 2 r*Þ

1 þ r 2 w1þ

mr *

r2

2gm 2ð1 2 dÞ2s 21

rð1 þ r 2 w1Þ2; ð8Þ

where:

w1 ¼1

2ð1 þ rÞ2

1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1 þ rÞ2 2 4dbm

qis a constant. r * stands for the unconditional expectation of rt, indicating noise traders’average bullishness of the securities market, the expression of which, together withproof of formula (8) in Appendix 1.

If d ¼ 0, the price of risk assets in this paper is the same as that in the DSSW model:

Pt ¼ 1 þmð1t 2 1*Þ

1 þ rþ

m1*

r2

2gm 2s 21

rð1 þ rÞ2; ð9Þ

Comparing formula (8) with formula (9), we reach the following conclusions.First, when rt converges to 0, price of risk assets converges to its fundamental value

of one, no matter whether positive feedback traders appear or not.Second, the second term of formula (8) reflects the positive influence of noise traders’

current sentiments on the price of risk assets. Since m=ð1 þ r 2 w1Þ . m=ð1 þ rÞ, theinfluence of noise traders’ sentiments on assets price in our model is bigger than that inthe DSSW model. So we can conclude that when positive feedback trading occurs in themarket, institutional investors will enlarge the deviation of securities price from itsfundamental value, causing excessive market reaction.

One explanation is that in a wave of continuing bullishness, the continuing rise inassets price raises higher the sentiments of positive feedback traders (rt . r *), andwhen such a trend is detected by sophisticated investors, they will conclude that positivefeedback traders will increase their purchase in the coming term. With the aim ofarbitrage, they will buy heavily in the current term and push the price further from itsfundamental value. Even if sophisticated investors sell all their assets in the comingterm to rectify the price, due to high investment sentiments, positive feedback traderswill still buy in the risk assets, consequently making the price already raised drift furtherfrom the fundamental value. Therefore, it is the “arbitrage” committed by sophisticatedtraders and the “further price increment” given by positive feedback traders that areaccountable for worsened deviation of price from value.

Third, the third term in formula (8) suggests that the “price pressure” effect hasnothing to do with positive feedback trading and only depends upon the averagedsentiments of noise traders within a certain period of time.

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Fourth, the last term of formula (8) reflects the price compensation for noise traderrisk that sophisticated investors request, i.e. sophisticated investors will not hold theassets unless the falling of price can compensate for the extra risks brought to the marketby stochastic sentiments of noise traders. DeLong et al. thought that it is just such “riskcompensation” that makes noise traders “create their own space”. In the model in thispaper, risk compensation (or the living space of noise traders) requested by sophisticatedtraders may be smaller or bigger than that in the DSSW model. Whend, the proportion ofpositive feedback traders meets the condition below:

0 , d , 1 2bm

ð1 þ rÞ2; ð10Þ

risk compensation is smaller than that in the DSSW model. This is because, forinstitutional investors, changes in the investment sentiments of positive feedbacktraders are predictable, and noise trader risks only come from the remaining portionof noise traders whose sentiments cannot be foreseen. That is, when the positivefeedback trading of “follow bull market and beat bear market” exists widely in the stockmarket, the unpredictability faced by institutional investors is smaller than when noisetraders’ sentiments are totally random, and therefore requested risk compensation issmaller.

But, if b, m, and d are all big and enable the following relationship:

1 2bm

ð1 þ rÞ2, d , 1 ð11Þ

The result is to the contrary. We thus learn that when the scale (md) of positive feedbacktraders is bigger and their behaviors depend more upon previous market performance(b), institutional investors demand more risk compensation to hold the assets. This isbecause the presence of positive feedback trading causes rational arbitrageurs to enlargethe deviation of price from value, leading to more volatile prices; moreover, the widelypracticed “momentum strategy” easily gives birth to “the effect of sheep flock”, whichwill increase irrational fluctuations of price. As a result, sophisticated investorsfollowing the value investment idea will face more market risks and will, therefore,demand more risk compensation.

IV. Influence of institutional investors on price fluctuationWe can learn from the above analysis that the price of risk assets depends upon currentsentiments of noise traders, the “price pressure” effect and the “risk compensation”effect. If so, what is the role played by institutional investors in the presence of positivefeedback traders to stabilize the price or to add to price fluctuation? To answer thisquestion, we first need to analyze the fluctuation level in assets price when positivefeedback trading exists. We can obtain variance of Pt through formula (8):

VARt½Ptþ1� ¼mð1 2 dÞ

1 þ r 2 w1

� �2

s 21 : ð12Þ

The price fluctuation level in the DSSW model is m 2s21=ð1 þ rÞ2. A comparison tells us

that in the face of positive feedback traders, the influence of institutional investorson price fluctuation depends upon two aspects: on the one hand, since the sentiments ofpositive feedback traders are predictable, price uncertainty faced by institutional

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125

investors is much smaller than when the sentiments of noise traders are totally random,i.e. ð1 2 dÞ2s2

1 , s21, and therefore, price prediction can be more accurate and price

fluctuations are reduced. On the other hand, the presence of positive feedback tradingcauses rational arbitrageurs to widen the deviation of price from value, making the pricemore volatile (m=ð1 þ r 2 w1Þ . m=ð1 þ rÞ). Relative to the DSSW model, whetherfluctuations in assets price are increased or reduced depends upon the magnitude ofthese two aspects. It can be easily proven that when d meets condition (10), the force ofthe former aspect is bigger and consequently brings down price fluctuations, and if dmeets condition (11), price fluctuation is fueled.

The above analysis leads us to the following conclusions.First, the negative opinion to institutional investment held by DeLong et al. (1990b)

that “when there is positive feedback trading in the market, rational arbitrageurs do notact as a force to stabilize the market, but make the price drift further and cause more pricefluctuations through interaction with positive feedback traders” is true only undercertain market conditions, i.e. when the number of positive feedback traders reaches acertain level (big d) and they are more sensitive to past market performance (big b).

Second, an increment in the number of institutional investors facilitates institutionalinvestors’ role to stabilize the market, since when m decreases formula (10) is bettersatisfied.

Besides, we can obtain from formula (8) the covariance of assets price Pt:

CovðPt;Pt2kÞ ¼m 2wk

1

ð1 þ r 2 w1Þ2s 2r ; ðk ¼ 1; 2; . . .Þ ð13Þ

where s2r stands for the unconditional variance of rt, the expression of which can be

seen in Appendix 1. Owing to the hypothesis of “independent sentiments” in the DSSWmodel, prices become irrelevant. While in the model of this paper, the autocorrelationin time of noise traders’ sentiment rt gives assets price Pt a certain degree ofautocorrelation. We learn from formula (13) that there is a positive correlation betweenprices of the two terms, and the degree of positive correlation is weakened as lag timeincreases. What is more, when d and b, respectively, scale and degree of positivefeedback, increase, autocorrelation is enhanced. Stock price fluctuation also affectsthe magnitude of autocorrelation.

Let is go on to verifying the validation of conclusions reached by this paper throughnumerical simulation. We might as well set two groups of parameters:

(1) d ¼ 0.4, b ¼ 0.5, m ¼ 0.6, r ¼ 5 per cent; and

(2) d ¼ 0.7, b ¼ 0.65, m ¼ 0.6, r ¼ 5 per cent, and they can be easily verified assatisfying conditions (10) and (11).

Other parameters take the values below: p0 ¼ p1 ¼ 10 ¼ 11 ¼ 1* ¼ 0:1, s21 ¼ 0:01,

g ¼ 2. Shown in Figures 1 and 2 are, respectively, the prices of risk assets in our modeland the DSSW model, generated by the formula (A.10) in Appendix 1. Figure 1suggests that in a securities market where the positive feedback effect is not obvious,behaviors of institutional investors help suppress price fluctuations. When the numberof positive feedback traders reaches a certain level and feedback intensity is high,arbitrage committed by institutional investors magnifies positive feedback trading inthe market and consequently worsens securities price fluctuation.

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V. Benefit analysis of institutional investorsAccording to the model built by DeLong et al. (1990b), institutional investors buy in therisk assets to raise the volume when price is low, which makes traders following the“momentum strategy” be bullish and raise the stock price higher. During this process,the number of positive feedback traders is constantly on the rise, causing an excessivereaction that eventually raises the stock price to a high level. Then institutional investorssell their stock to maximize their benefits. During the stock price’s return to value,positive feedback traders suffer losses. Therefore, institutional investors can alwaysbenefit from rational arbitrage (negative feedback trading strategy) when there ispositive feedback trading in the market; meanwhile, they make the price more unstableand add to market fluctuations. But, we believe that, due to the existence of noise traderrisks, institutional investors do not always benefit from arbitrage, and they need certainmarket conditions to do so.

Suppose DRf2 s stands for the difference in excess income between positivefeedback traders and sophisticated traders in our model, it depends upon the differencein the amount of risk assets being held and excess income from unit risk asset, i.e:

DRf2s ¼ ðlft 2 ls

t ÞRt; ð14Þwhere:

lft 2 ls

t ¼pt

2gVARt½Rtþ1�

and Rt ¼ 2gVARt½Rtþ1�2 mrt þ ztþ1. ztþ1 are random disturbance terms, obedient tonormal distribution that has mean of zero (as proven in Appendix 2).

Figure 1.Situation where

institutional investorssuppress price fluctuation0

0.5

1

1.5

2

2.5

3

3.5

4

1 6 11 16 21 26 31 36 41 46

P'P

Figure 2.Situation where

institutional investorsworsen price fluctuation0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 6 11 16 21 26 31 36 41 46

P'P

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127

Therefore, difference in excess income between the two types of traders in term t is:

DRf2s ¼ pt 21

2gVARt½Rtþ1�mptrt 2 ptztþ1

� �; ð15Þ

With the above formula, we obtain the unconditional expected value of the difference inexcess income of the two types of traders:

E½DRf2s� ¼ p * 2ð1 þ r 2 w1Þ

2½s 2r þ dp *2 þ ð1 2 dÞp *1 *�

2gms 2r ð1 2 w2

1Þ; ð16Þ

where p* is the unconditional expectation of pt. When noise trading risk s 2r grows

bigger, the gap between excess income between the two types of traders is widenedmore. To simplify the analysis, let us suppose the mean of random sentiments of noisetraders is zero (1 * ¼ 0).

From formula (16), we learn that if d! 0, E½DRf2s� . 0 as long as:

p * .ð1 þ rÞ2

2gm; ð17Þ

This suggests that when there are fewer positive feedback traders in the market andthey remain highly optimistic about a bullish after-market for a certain period of time,the average income obtained by positive feedback traders may be higher than thatobtained by sophisticated traders.

From the above analysis, we draw the following two conclusions.First, positive feedback traders do not always suffer losses due to the presence of

noise trader risks, and may stand long in the market. Second, when the effect of positivefeedback is not obvious, rational arbitrage by institutional investors is not alwaysbeneficial.

The above conclusions stem from the fact that, when the population of positivefeedback traders is not numerous enough, the momentum effect will not be big enougheither, and there will not be enough resources available for institutional investors. Thekey to profit, for institutional investors, is to sell their assets at a high price in laterstages, and to make this possible, they have to buy risk assets in the earlier stage in away that can trigger a sufficient positive feedback effect and a certain degree of“follow-suit” in the market. When sentiments and group behaviors are stimulated in thelater stage and stock price is raised up, institutions sell the stock, bringing stock pricedown. But institutional investors do not necessarily benefit from this process. On the onehand, institutional investors will not wait and sell stock until the price is at the highestlevel for fear of noise trader risks, and to mitigate such risks, they tend to close positionwhen price is secondary high. On the other hand, even if they sell stock, the speed andmagnitude of the price fall may fall far short of their exceptions due to accumulatedbullish sentiments within a certain period of time and active entry of positive feedbacktraders in later stages. What is more, as long as investors’ sentiments are pushed toan excessively high level, that is, the overall average sentiments p* during the periodsatisfy formula (17), the expectation excess income obtained by positive feedbacktraders may exceed that obtained by sophisticated traders, i.e. higher than averagein the market. So we can conclude that positive feedback traders may survivein the market long term, no matter from the angle of simulation or elimination, andinstitutional investors do not always make successful arbitrage. This conclusion

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is consistent with that obtained by Hirshleifer et al. (2006), i.e. irrational investors takingthe positive feedback trading strategy are not always passive, and they may obtain moreexcess income than rational traders. In that case, under the action of the demonstrationeffect and regret aversion, institutional investors may prefer doing nothing to arbitrage.

VI. Conclusions and suggestionsBy considering positive feedback trading into the DSSW model, this paper has analyzedthe relationship among behaviors of institutional investors, pricing of risk assets andmarket fluctuation and has reached some meaningful conclusions:

. In a market where positive feedback trading is common with great feedbackintensity, institutional investors fail to stabilize the market, and on the contrary,they follow the trend to intensify positive feedback trading and fuel securitiesprice fluctuations. Increasing the number of institutional investors helps enhancetheir function to stabilize the market.

. Owing to the effect of positive feedback trading, a positive correlation is developedbetween prices of the two terms, and the stronger the scale and intensity ofpositive feedback are, the stronger the autocorrelation is. Autocorrelation is alsorelated to price fluctuation.

. In a market where positive feedback trading is not dominant, the existence ofnoise trader risks makes rational arbitrage by institutional investors not alwaysbeneficial. Moreover, irrational investors taking the positive feedback tradingstrategy do not always suffer losses and may survive in the market long term.

As to how we can enable institutional investors to function as they are supposed tofunction for the sake of a healthy securities market, we offer the following suggestions.

First, help minor investors build a proper value investment philosophy. China’ssecurities market is immature with short-term speculation widely favored. Under suchcircumstances, many minor retail investors tend to seek strong and beneficial stocks,totally neglecting poorly performing, but seriously undervalued stocks. Such a blindmomentum strategy inevitably generates positive feedback effect which, onceintensifying to a certain extent, causes institutional investors short-term arbitrage tomagnify positive feedback trading. As a result, institutional investors are not functioningto stabilize the market, but pushing the securities price further from its fundamentalvalue, making securities price fluctuation worse. Therefore, regulators should take theinitiative to change minor investors’ investment philosophy. On the other hand, currentcomments on the stock market focus more on technical analysis of stock prices than onfundamental issues like the financial position, operation status, and investment value oflisted firms. As a result, individual investors pay more attention to market trends, whichfacilitates transaction manipulation by institutional investors. Therefore, what weshould do is enhance guidance of public opinion and increase minor investors’ awarenessof risks, while putting under control stock comments that help institutions disseminatefalse information and mislead investors.

Second, create a sound institutional environment for institutional investors to stick tovalue investment. Current market practice shows that under the action of the sheep flockeffect, the positive feedback effect, and price pressure, most institutional investors tendto passively perform short-term holding for arbitrage purposes. Their preference forspeculation rather than long-term value investment can be explained by the fact that,

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with an immature capital market, a seriously defective governance framework for listedfirms and a flawed agency system, they find institutional loopholes for speculation thatwill bring them huge profits. Since institutional investors are also rational players ofprofit maximization and will not sacrifice their profits to stabilize the market, they willnot take market stabilization as their duty. Regulators need a sound and directive policyenvironment to support their rational behaviors. And to specify, we need to perfect theinvestment environment to guarantee their involvement in corporate governance,improve corporate performance and give play to the demonstration effect of valueinvestment.

Third, steadily expand the team of institutional investors. We need to traininstitutional investors, not only in number but also in quality and structure. Andcompetition among institutional investors should be enhanced through diversifieddevelopment to enable them to function as they are supposed to and to strengthen theirrisk-resisting capabilities. At the same time, market regulation should be intensified tosuppress market manipulation. To enable institutional investors to functional properly,we need a healthy institutional environment with sound legislation efforts, enhancedsuppression of fraud and manipulation, synchronous and effective regulation.

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Sosin, K., Rives, J. and West, J. (1998), “Unions and gender pay equity in academe: a study of US”,Institutions Feminist Economics, Vol. 4 No. 2, pp. 25-45.

Sun, B.B. (2005), “Study on noise traders’ sentiment evolution based on learning behavior”,Dissertation for Doctor, Fudan University, Shanghai, available at: www.cnki.net

Further reading

Chiyachantana, C., Jain, P., Jiang, C. and Wood, R. (2004), “International evidence on institutionaltrading behavior and price impact”, Journal of Finance, Vol. 59 No. 2, pp. 869-98.

Kim, S., Janet, R. and Janet, W. (1998), “Unions and gender pay equity in academe: a study of US”,Institutions Feminist Economics, Vol. 4 No. 2, pp. 25-45.

Rubin, A. and Smith, D.R. (2009), “Institutional ownership, volatility and dividends”, Journal ofBanking & Finance, Vol. 33 No. 4, pp. 627-39.

Shiller, R.J. (2002), From efficient market theory to behavioral finance, Cowles Foundationdiscussion paper 1385, Yale University, available at: http://ssrn.com/abstract¼349660

Appendix 1. Proof of risk assets pricing formula (8)Suppose noise traders’ sentiment rt obey the first-order autocorrelation process:

rt ¼ w0 þ w1rt21 þ ht; ðA:1Þ

where jw1j , 1, ht is obedient to white noise process with a mean of 0 and a variance of s 2h . The

unconditional expectation of rt is w0=1 2 w 1, conditional expectation is Et½rtþ1� ¼ w0 þ w1rt

and unconditional variance is s 2r ¼ s 2

h=ð1 2 w 21 Þ and conditional variance VARt½rtþ1� ¼ s 2

h .Suppose the price of risk assets is the one-variable linear function of noise traders’ sentiments

in current term:Pt ¼ a0 þ a1rt; ðA:2Þ

Then we obtain the conditional expectation and conditional variance of the price of risk assets:

Et½Ptþ1� ¼ a0 þ a1Et½rtþ1�; ðA:3Þ

VARt½Ptþ1� ¼ a 21 VARt½rtþ1� ¼ a 2

1 s2h : ðA:4Þ

By substituting equations (A.3) and (A.4) into formula (5), we obtain:

a0 ¼ 1 þmw0

rð1 þ r 2 w1Þ2

2g

r

m 2s 2h

ð1 þ r 2 w1Þ2

" #; ðA:5Þ

a1 ¼m

1 þ r 2 w1: ðA:6Þ

So Pt can be expressed by:

Pt ¼ 1 þmw0

rð1 þ r 2 w1Þ2

2gm 2s 2h

rð1 þ r 2 w1Þ2þ

mrt

ð1 þ r 2 w1Þ; ðA:7Þ

According to formula (6) that the formation process of positive feedback traders’ sentiments, weget:

pt ¼ ½ðp1 2 w1p0Þ þ ð1 2 dÞ10� þ ba1rt21; ðA:8Þ

Thereupon, we get the formation process of noise traders’ sentiments:

rt ¼ d½ðp1 2 w1p0Þ þ ð1 2 dÞ10� þ dba1rt21 þ ð1 2 dÞ1t; ðA:9Þ

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131

By comparing equations (A.1) and (A.8), we get:

w0 ¼ dðp1 2 w1p0Þ þ ð1 2 dÞð1 * 2 w110Þ

w1 ¼ dba1

ht ¼ ð1 2 dÞð1t 2 1 *Þ

8><>: ðA:10Þ

Substitute w1 into equation (A.5), we get the final expression of w1 as stated above. Substitute w0,w1 and ht into equation (A.1), we get the final expression of noise traders’ sentiments rt and theprice of risk assets:

Pt ¼ 1 þmð1 2 w1Þ

rð1 þ r 2 w1Þr * 2

2gm 2ð1 2 w 21 Þ

rð1 þ r 2 w1Þ2s2r þ

m

ð1 þ r 2 w1Þrt: ðA:11Þ

rt obeys AR(1), it can be easily proved that rt follows normal distribution and its mean r * isw0=ð1 2 w1Þ, its variance is:

s 2r ¼

ð1 2 dÞ2s 21

1 2 w 21

: ðA:12Þ

Appendix 2. Excess income Rt of unit risk asset and derivation of its varianceExcess income realizable by unit risk asset in term t can be expressed as:Rt ¼ r þ Ptþ1 2 (1 þ r)Pt. By substituting the price formula (A.10), we get:

Rt ¼2gm 2s 2

r

ð1 þ r 2 w1Þ22 mrt þ ztþ1; ðA:13Þ

where:

ztþ1 ¼m

1 þ r 2 w1htþ1;

obedient to normal distribution with a mean of zero. Then we get the conditional variance of Rt:

VARt½Rtþ1� ¼ m 2s 2r 1 þ

1 2 w 21

ð1 þ r 2 w1Þ2

� �; ðA:14Þ

The unconditional variance of Rt:

VAR½Rtþ1� ¼ VAR½Ptþ1� ¼m 2s 2

r

ð1 þ r 2 w1Þ2; ðA:15Þ

By substituting eqution (A.14) into formula (A.12), we get the expression of Rt.p * is the unconditional expectation of pt, and its relation with r * and 1 *:

r * ¼ dp * þ ð1 2 dÞ1 *

Therefore:

p * ¼dðp1 2 w1p0Þ þ ð1 2 dÞw1ð1 * 2 10Þ

dð1 2 w1Þ: ðA:16Þ

Corresponding authorYin Hong can be contacted at: hyin@jjx.ecnu.edu.cn

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