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Journal of Financial Risk Management 2013. Vol.2, No.4, 87-91 Published Online December 2013 in SciRes (http://www.scirp.org/journal/jfrm) http://dx.doi.org/10.4236/jfrm.2013.24015 Open Access 87 The Herd Behavior of Risk-Averse Investor Based on Information Cost Guangming Deng College of Science, Guilin Univ ersity of Technology, Guilin, China Email: dgm@glut.edu. cn Received November 11th, 2013; revise d D e cember 11th, 2013; accepted December 18th, 2013 Copyright © 2013 Guangming Deng. This is an open access article distributed under the Creative Commons At- tribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, the traditional model of herd behavior was improved and extended. The herd behavior of risk-averse investor based on information cost was studied in the financial market. By refining the con- cept of Bayes equilibrium and the analysis of the behavior of investors, it was discovered that the herd behavior of the second risk-averse investor did not produce until the first risk-averse investors chose to buy information. Keywords: Risk Avoidance; Information Cost; Herd Behavior Introduction Herding behavior of financial markets refers that the majority of individual investors tend to take the same or similar invest- ment strategy with the others when making investment deci- sions. Causes of herd behavior include information asymmetry, the concern for the reputation and rewards programs (Sharma & Bikhchandani, 2000), where the information asymmetry caused by the spread of information is an important reason for herd behavior. Banerjee (1992) was first proposed based on asym- metric information model of herd behavior. Bikhchandani, Hir- shleifer and Welch (1992,1998) also studied the relevant herd behavior model, although both models are different, they all believe that information diffusion is the cause of herd behavior. As BHW model assumes that investors can get free private information, Cui Wei (2008) for the real market, raised the cost of herd behavior based on the information model, However, BHW model also assumes that investors are risk neutral, in which most investors in financial markets do not match the characteristics of risk aversion. In this paper, BHW model was further extension studied, and we analyzed the risk-averse in- vestor herd behavior based on information costs, and by refin- ing the concept and inductive method of Bayesian risk aversion of investors so as to get the optimal decision-making behavior. The Model of Risk-Averse Investor Herd Behavior Based on the Information Cost In this paper, the traditional basis of BHW model, the intro- duction of investor risk aversion in financial markets and the presence of the characteristics of information costs, with a negative exponential utility function is the risk aversion of in- vestors, the cost of herd behavior based on the information model. Basic model assumptions are as follows: 1) The investment result 1,1vV 1 in the beginning is determined randomly. represents investment result is well and represents investment result is bad. is equally likely to take on the values of and . v 1 v v 1 1 c 2) Each of the investors chooses whether to buy private sig- nal before making a decision. Let i denote the cost that in- vestment purchase information, assuming . c i01 i 3) Let 1,1 i sS 1s denote that private signal investor receives. i denotes a good signal, denotes a bad signal. Conditions in the investment result, the investor’s pri- vate signal is independent. 1s 4) i p stands for the accuracy of the investor i acquires private signal, it is a function of the information cost , de- i c noted as i ppci and 11 2i p . Accuracy refers to the probability of signal correct on the conditions given investment, and 0pc , 1 02 p . It is assumed that the information cost can be observed. The following investors can infer signal accuracy according to information cost the previous investors paid for. 5) 0,1 i aA 1adenotes the investment decisions of inves- tors. stands for the decision to invest and 1a for decision not to invest. 6) The information set of investor is observed in front of all his investment decisions i 12 1ii of investors and their private information. Section of the public belief ,,haa i,a 1 ii , that investment in the historical conditions , we get the probability of good investment results. Pv h i h7) Investors using negative exponential utility function, the choice to buy private information, risk aversion returns to in- vestors depends on information costs, investment decisions and investment results , defined as follows: ,,e ii i i uacv c i va In the case of uncertain future, investors expected return is conditional expectation of ,, iii uacv under the condition of the information set. G. M. DENG ,, , 1,,, 1,,, iii ii ii iiiii ii iiiii Eu acvhs PshEu acvhs PshEu acvhs 1 1 where 1, 0 ,, e,, 1 ii iii vii ii ca Eua c vEhsca 1 1 e, 1, e1, e vii ii ii Ehs Pv hsPvhs Without purchasing information, the risk aversion of inves- tors expected return is: 1, 0 , e, 1 i N ii ivii a Eu avhEha e1e1 e1 e ee e vii i ii i EhPvh Pvh e Risk-Averse Investors Decision Analysis After comparing the purchase information and do not pur- chase information expected return, risk averse investors before deciding whether to buy information. This section uses the Bayesian algorithm and the inductive method to analyze inves- tors optimal information cost and make the optimal investment decisions to maximize the expected return. The First Risk Averse Investor’s Investment Decisions A1 In order to analyze the first investor risk aversion A1 invest- ment decisions, you first need to discuss the situation given information costs, and then further discuss the best information costs. Case Given Information Costs Information costs are assumed, the signal accuracy is. Ac- cording to Bayes rule, in the purchase of information, the first investor risk aversion investment results A1 update their beliefs as: 11 11 11 11 1 11 1 1, 1 ,11 1 ,111,1 11 1,11 Pv hs Phs v Pv Phs v PvPhs vPv pc Pv hspc (1) If you get a good signal A1, then A1 investment results are good update belief; if A1 get is bad signal, then the result is good for investors A1 updated belief. A1 in getting a good sig- nal and bad signal to make investment decisions after the ex- pected benefits are: 11 1 11 11 1 1 11 1 11 1 1 1 11 1, ,,1 e,1 1, 1e 1,1e e1 e v Eu acvhs Ehsc Pv hs Pv hsc pcpc c 1 (2) 111 11 11 1 1 11 1 11 1 1 1 11 1, ,,1 e,1 1,1 e 1,1 e 1e e v Eu acvhs Ehsc Pv hs Pv hsc pc pcc 1 (3) There 111 11111 111 ,, ,10,, ,1 E uacvhsEua cvhsc So ended the first A1 in investor risk aversion will not be a bad signal for investment. Proposition 1 Assume 1 11 2pc , then 111 111 ,,, 11Eu acvhsc . Proposition 1 is true can guarantee a good signal was ob- served after the first risk averse investor must invest A1. Oth- erwise, regardless of the resultin g signal A1 is good or bad, A1 will not invest, so that investors behind the A1 will not be able to grasp the behavior of their access to real information. The second risk averse investors A2 and A1 will face the same situ- ation, so A2 would not choose to invest, and after that all in- vestors will not invest. Thus, if Proposition 1 is false, no one making investment decisions, and no one involved in the deci- sion-making model. Proposition 1 is equivalent to 1 1e ee pc Intuitively, since investors are risk averse, the accuracy of the signal must be larger to ensure investors. In the case of Proposition 1 is true, A1 will make investment decisions according to its private signal, that is, while getting good signal 11s , A1 decided to invest in 11a ; For the bad signal 11s , A1 decided not to invest 10a . A1 in getting a good signal and bad signal the expected benefits re- spectively is: 111 11 1 1 11 11 111 111 ,,, 1 e1 e eee ,, ,1 1 Eu acvhs pcpc c pc c Eu acvhsc 1 (4) Open Access 88 G. M. DENG The first risk aversion investor, the probability of obtaining good signals and bad A1 were 50%, therefore, A1 expected return after purchase information is: 11111 11 11111 1 11 ,, , 1,,,1 1 1 22 ee e1 22 Eu acvhs PshEu acvhs c c pc c If A1 chooses not to purchase information, the A1 fo ment results for the good faith is the public belief, i.e. 11 11111 11 1, ,,1 1 eee PshEu acvhs pc (5) r invest- 1 1 2 , the A1 earnings should be: 11 1 ee 11 ,e1 N Eu avh 22 2 ee 2 4 Thus, when 11111111 ,,Euacvh , , N sEu avh Namely, 11 11 1 1 ee e1 ee2 22 ee ee 20 2 21 0 ee2 pc c pc c c pc 4 . The first risk averse investors A1 is willing to buy private information. Lemma 1 Assum 0pc, ee 1 4 p (ee 0, 4 c ), if and only if 21 :0 ee2 c cpc , the first risk aversion inves inform. Proposition 2 , s. t. tor A1 purchasesation Assume c 21 0 ee2 c pc ， and ee ee 0,c , 1 44 p . Under the conditions in Lemma 1, Proposition 2 is true guarantee of a risk averse investor A1 never buys a private e. If A1 is not purchasing information, then the result is investment belief is 0.5, the probability of investment is 0.5. So, A1 investment decisions investors will not give back any of the information transmitted, the second investor risk aversion and A1 A2 facing the same situationmpathy, A2, and behind all investors will not buy information, which model lo messag good for , e ses significance Optimal Cost of Information While purchasing information, A1 faced with the expected return on the following maximization problem: 1 11 1 0,1,0 ee 2pc c 1 1 1 21 max :ee 2 21 s.t.: c c pc c pc ( 6) A1 Optimal information cost * 1 c meet * 1 2 pc ee , or * 11pc and * 1 ee 04 c . At the same time, the optim investmeal nt decision A1 is make decisions according to their private signals, namely when the it gains signal * 11s , A1 decidto invest ed * 11a ; when it gets bad ed not to invest. The Second Investor Risk Aversion A2 Investment Decisions signal, A1 decid The second risk averse investors A2 according to the optimal information cost * 1 c of A1, can be speculated that A1 signal accuracy. First, assume that A1 decided to invest * 11a, this that the A1 has good signal s mean *1s. So A2 in t 1h t results, a e purchase lso is the information, update beliefs about investmen second period public faith 2 : ** 1 ase if exp 22 11 * 111 1e Pv hPv apc pc (7) ee So, in the absence of purchnormation, the second risk avoidance investors A2 the optimal decision is a choice, and A2 after investment earnings areected to be: * 22 21 1,e ee1 N Eu avhpc Then, the second risk aversion investor A2 in bu mation and not to buy the expected return of the comparison. If th ying infor- e given information for cost, when the A2 is a good sign, she updated belief as the result of the investment: 22 1, 1Pvh s 22 * 12 ** 12 21 ,1 1 1 1. 2 12 Ph svPv pc pc pcpcpcpc 22 22 * 12 ** 212 1 ,1 11,1 11 11 Phs vPvPhs vPv pc pc pc pcpcpc . Open Access 89 G. M. DENG Open Access 90 A2, therefore, decided to invest in. When the A2 is bad signal, she updated belief as the result of the investment: 22 22 22 22 ** 12 12 ** ** 12 1 21 21 ,11 1 1, 1,11 1,111 11 2 11 Ph svPv Pvh sPh svPvPh svPv pc pcpc pc pcpcpcpc pc pcpcpc . 2 When * 12 pc pc, the value is more than 1 2, A2 decided to invest in; Otherwise, not investment. d bad, respectively is: The second risk aversion investor A2, the probability of obtaining good signals an ** 221221 ** 22 1212 11 2 12 Pshpcpcpcpc Pshpcpcpc pc After the purchase information, A2 expected return is: 222222 2222222222222 ,, ,1,, ,11,, ,1EuacvhsPshEuacvhsPshEu acvhs where 1 1 222 222222222 ,, ,1e,11,1 e1,1Eu acvhsEhscPvhsPvhs2 ** 1212 1 12 22 22 e e1 e 11 c pc pcpcpcc Ps hPs h v 22 Eu a 2 222 ,,,1 1cvhs c When * 12 p cpc, that is, the second risk aversion investor A2 signal is not the first risk aversion investor A1ignal accu- rately s * 222 2212 ,,,eeeEu acvhspcc . * 12 ee e p cc A2 buys private information after the expected return , less than expected earnings of not to buy pri- vate information * 22 21 ,ee N Eu avhpce . A2 will not buy private information, therefore, A2 will fully believe that the signal1 and follow A1 investment decisions. A * 1 pc pc, When 2 ** 12 22 2e eeepcpccc Only when ** 1212 1 1 222 22222222 22 22 1 ,, ,1e1e11 11 1e1 pc pcpcpc Eu acvhsPshcPshc Ps hPsh pc p 22222 222 ,, ,, N Eu acvhsEuavh , that is ** 1212222 2eee1e102eee1e 100pc pcpcpcccc , t deci- sions. Obviously, A2 buate information conditions cannot be met. So when The second risk avoidance investors A2 will buy private information, and according to its private signal making investmen y priv * 12 pc pc estor A1 bought th , A2 will not purchase information. Synthetically the above two kinds of circumstances, if the first risk aversion inve most accurate information and investment, then the second risk aversion investor A2 will follow A1 investment decisions. Next, the discussion on the first risk-averse investors A1 do not invest. If the A1 is not investment so that she will get the bad signal A similar analysis can get the condition of second risk averse investors A2 bue information is: * 10a, y privat * 11s . ** 11 22 2ee1e 10pcpcpcpcc 2 e Also shows that A2 can be not buy private information, A2 will follow A1’s decision and choose not to invest, the expected re to turn A2. 222 0, N Eu avh 1 . G. M. DENG whether the f formation A2 can take full advantage of A Investment Decision No.N Risk Averse Investors in AN ehavior if the second risk averse investors A2 not buy private information and imitate A1, A2 e purchase of pri- make the same deci- irst risk averse investors ill not buy private information. T Therefore,irst risk averse investors whether A1 investment, second risk averse investors A2 will not purchase information, private in 1 buy, and follow A1’s investment decision. We can use similar methods to analysis behind all the risk averse investors. Investment b bhavior cannot risk on the back of the investors to avoid any information reveals the role of. Then, the third risk averse in- vestors A3 is facing the same situa tion and A2, A3 and A2 will make the same decision, which mimics the first risk averse investors A1 investment behavior without the vate information. Next, A4, A5… AN will sion. So, all investors are behind the f follow A1 behavior, and w herefore, information diffusion and herding from second risk averse investors A2 began. Conclusion This paper, based on the BHW model, considering the char- acteristics of investors in financial markets, risk aversion, and the introduction of information cost, discusses the risk investors herd behavior based on information cost. Through the research of risk averse investors found, only the first risk averse inves- tors are willing to buy information, the optimal information cost is * 1 c, and meet: * 1 2 ee pc or and * 11pc * 1 ee 04 c Starting from the second risk ainvestor, all the risk aversion of investors behind will not purchase information, version and follow the first risk aversion of iavior. In addition, the information cost and risk aversion of investors decision- to happen. Acknowledgements This work was jointly supported by tal Social Sci- ence Fund (No.1 V. (1992) A simple model of herd behavior [J]. The Quarterly Journal of Economics. 107, 797-817. http://dx.doi.org/10 nvestors beh making model, information diffusion and herd behavior will occur, and from the second risk avoidance investors are starting he Nation 3BTJ009), and the Guangxi Key Laboratory of Spatial Information and Geomatics (No.1207115-27). REFERENCES Sharma, S., & Bikhchandani, S. (2000). 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