Positive feedback trading, institutional investors and securities price fluctuation

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  • Positive feedback trading,institutional investors andsecurities price fluctuation

    Yin HongBusiness School, East China Normal University,

    Shanghai, Peoples Republic of China


    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 andherd 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


    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.



    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 Chinas 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

    Positive feedbacktrading


  • 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 Pt1 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 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 r Pt1 2 (1 r)Pt. Then, we canprove that Rt obeys normal distribution.

    Therefore, sophisticated investors will choose to hold lst of risk assets to maximizethe following expression:

    lst r EtPt12 1 rPtf g2 lst 2gVARtRt1; 1where 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 followingexpression:

    lnt r EtPt1 rt 2 1 rPtf g2 lnt 2gVARtRt1: 2By equations (1) and (2), we get the demands for risk assets, respectively, bysophisticated traders and noise traders:



  • lst r EtPt12 1 rPt

    2gVARtPt1 ; 3

    lnt r EtPt1 rt 2 1 rPt

    2gVARtPt1 : 4

    With the market clearing condition: mlnt 1 2 mlst 1, we get the market clearingprice as:

    Pt 11 r r EtPt12 2gVARtPt1 mrtf g: 5

    Different from the classic DSSW model, we have supposed that a part of the noise traderswill take the momentum strategy, since the irrational investors 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 pt21 bPt21 2 Pt22; 0 , b , 1 6

    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 1, 2, . . .) obeys thenormal distribution with a mean of 1 * and a variance of s21 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 d pt21 bPt21 2 Pt22 1 2 d1t: 7

    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

    Positive feedbacktrading


  • 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 1 mrt 2 r*1 r 2 w1

    mr *


    2gm 21 2 d2s 21r1 r 2 w12

    ; 8where:

    w1 121 r2 1


    ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 r2 2 4dbm

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

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

    Pt 1 m1t 2 1*

    1 r m1*


    2gm 2s 21r1 r2 ; 9

    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 pric...


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