Extrapolative expectation model

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Contents

Introduction

1. Event Study

1.1 Data

1.2 The check of the existence of the bubble

1.3 The check for bubble driven by investors with extrapolative expectations

2. Adjusted weights of value and growth signals

2.1 New model of expectation formation

2.2 Empirical analysis

Conclusion

List of references

Appendix



Introduction

Financial bubbles have triggered off the disturbances in the economies across the world. Tulip Mania (1637), South Sea Company (1720), Mississippi Company (1720) are one of the earliest cases when the bubble was detected: in all of them the actual price started to exceed significantly the intrinsic value of the good, whether it is a commodity good or a stock. There has always been the scientific interest in the essence of bubbles, and these are the examples of ones been intensively studied: The Dot-com bubble in 1995-2000 (e.g. J. Bradford DeLong , Konstantin Magin 2006; Alexander Ljungqvist,?William J. Wilhelm Jr. 2003), 1997 Asian financial crisis bubble ( e.g. Giancarlo Corsetti, Paolo Pesenti, Nouriel Roubini 1999; Simon Johnson , Peter Boone, Alasdair Breach, Eric Friedman 2000), United States housing bubble 2007 (e.g. B. S. Bernanke 2010; R. J. Shiller 2007).

One of the common approaches to explain bubble formation is through behavioral finance. The latter implies that agents do not behave fully rational, rather they use simple rules, called heuristics, to make the decision. However, this method, if based on wrong beliefs, may lead to the systematic errors, as was outlined in Kahneman and Tversky's (1974). Under one of the rules of thumb presented in their work, the representativeness heuristic, the results received on the small sample are transmitted to the whole population. This is called “extrapolation” and, when agents follow this bias, they extrapolate past returns on the future ones. Essentially, this is the mechanism of bubble formation in the extrapolators-driven models.

In this paper the recent financial bubble on the Chinese stock market will be considered. It took place in the second quartile of 2015, reaching the top in middle of June and then collapsed, leading to dramatic fall of 30 % in one month. The motivation for my work is to check whether the agents with extrapolative expectations about returns were present at the Chinese stock market at the moment of bubble formation and, if they were, at what degree they influenced it. There has not been a lot of work done yet with regards of origins of this bubble; moreover, there were no research conducted to check for extrapolation. Apart from overall check for presence of extrapolators, other related questions will be addressed later in the paper. How did the expectations of agents developed with the development of the bubble? Was there any significant difference between agents- extrapolators and other agents? Could the bubble be caused by such irrationality as extrapolative expectations?

Over the last 20 years there has been an increasing amount of research made on the stock markets studying the importance agents' beliefs irrationality. The paper by De Long, Shleifer, Summers and Waldmann (1990) implies that the deviation of actual price from its fundamental value is explained by “unsophisticated” investors opinion. Noisy traders, who are present on the market, bear excessive risk for irrationality in their beliefs and thus create the fluctuations in the prices. Authors suppose that the presence of such risk can resolve many financial anomalies, such as excessive volatilities and mean reversion in prices. The opposite results were received by Lakonishok, Shleifer and Vishny (1994): they did not find any evidence that strategies of rational and irrational investors differ in risk. Authors studied why, using the methodology of the paper, value strategies are able to outperform naпve ones by acting contrarian to the latter. The offered solution is the extrapolation in the beliefs of irrational investors, who buy (sell) the stock, which has performed well (bad) recently as they expect its future growth pattern to resemble the one in past. Cutler, Poterba and Summers (1990) also conducted the research of extrapolation beliefs, under which irrational (“feedback”) investors are not that naпve as in the previous paper. According to their study, past returns behavior is not a decisive factor for estimating future returns, rather the expectations are adaptive and account for new information coming.

The model in my research is closely related to the study by Barberis, Greenwood, Jin and Shleifer (2015). The paper considers the dot-com financial bubble in 1995-2000, while I will study the recent Chinese bubble on the stock market. There are two types of investors presented on the market: extrapolators and fundamentals. For fundamentals investors the “value” signal is the determinant of the demand for stock: that is “ the difference between the price and rational valuation of the final cash flow” according to the paper. The demand by extrapolators is defined by “growth” signal, which is “the weighted average of past price changes”. However, apart from growth signal, which follows directly from definition of strategy with extrapolative beliefs, the authors include the “value” signal in the extrapolators demand. Such adjustment makes extrapolators not as naпve as in the traditional models, which is probably more realistic assumption. The similar set of assumptions for the belief formation was used by Barberis, Greenwood, Jin and Shleifer (2013). The aim of their work was to account significant evidence of extrapolation, found in data, in the existing aggregate stock market models. As the result, the new model was better at explaining the reality than the traditional ones, which did not consider irrational expectations. One of the interesting findings made by authors is that fundamental investors account for the strategy of extrapolators: they realize that the latter's future strategy tightly depends on the past performance of the stocks. As the result, fundamentals do not counteract aggressively to the extrapolators' actions, because they expect these actions to last for some time in future. My work differs from one by Barberis, Greenwood, Jin and Shleifer (2013) for not accounting the abovementioned “smoothing” strategy of fundamental investors. Under the framework of my research, investors with extrapolative expectations put some weight on the “value” signal too; hence fundamental investor cannot be confident which signal (value or growth) will determine extrapolators' demand for stocks.

Barberis, Greenwood, Jin and Shleifer (2015) offered another innovative concept of expectation formation- wavering. As outlined above, the authors supposed that extrapolators' demand for stocks depends both on “value” and “growth” signals, which may give controversial information about future returns. Thus the hesitation between signals, or wavering, occurs, which is the process when “each extrapolator slightly but randomly shifts the relative weight he puts on the two signals” according to the definition in the paper. It is important to note that the degree of wavering is assumed to be constant over time. Also, wavering is considered to be crucial factor to explain large size of trading at which bubble exists: due to random and independent shifts of weights between signals, extrapolators trade with each other and lead to the increase of the transaction volume of the bubblel. Opposite to this work, I have not used the concept of wavering in my research. Instead I have supposed that weights between signals, or, in other words, the relative importance of each signal, are not constant over the time. My research interest is to check whether the relative weights of two signals depend on the development of the bubble. The motivation for this study is supported by the ideas of “An extrapolative model of house price dynamics” by Glaeser and Nathanson (2015). The paper considers the house price formation over the sample with observations from more than 30 years. In the model buyers use past transaction prices as the approximation for current market price of the house, which is the obvious indicator of extrapolative expectations. One of the important findings of the paper is that `bubbles like features of the market disappear when the information is either too good or too bad'; for example, when there is enough direct information on the market, all financial anomalies, such as mean reverting or excess volatility disappears. This finding has motivated me to adjust the initial model in my research and then to check empirically whether new specification is significant. I have supposed that when the bubble evolves, new information about the true value of the stock comes to the market and extrapolators may account it by adjusting weights between signals. Then, when the market only starts to rise, extrapolative “growth” signal will have greater importance in the expectation formation, because there is not enough good information for extrapolators to suspect the existence of the bubble. With the development of the bubble, price continues to rise and depart further from the fundamental value of the stock. After some point, when the difference is significant enough, extrapolators will start to suspect the stock is overvalued, rather than its fundamental value is growing at such speed. Since then, they will increase the relative weight of “value” signal, which is considered as the rational one in this specification of the model. This happens until the bubble will reach its top and price start to decline, which leads to the collapse of the bubble. The described model for signal weights will later be empirically tested on the Chinese bubble at the stock market. By this part of the analysis, my work is related to the `Measuring bubble expectations and investor confidence by Shiller (2000). The aim of the work is to analyze behavior over time of some indicators, which show attitude of investors toward the events happening on the speculative markets. For that, two indicators are taken: `bubble expectation', under which naпve investors hold the positions in stocks in which there is a bubble, and `confidence', when investors underestimate the chance of losses to occur. The author has provided large survey to find out the percentage of population following one of the attitudes and how the received shares develop over time. The result of the research is that although both behavioral indicators have significant deviations through time, they are not large in amplitude. Moreover, none of indicators used in the analysis could detect the financial bubble.

There are some important characteristics of Chinese stock market to take in account. First of all, there are three main types of stock: A- shares which only be hold by locals and licensed international investors under QFII; B- shares can be traded by both foreign and Chinese investors and H-shares, traded at the Hong Kong Exchange. The bubble studied in this paper occurred in the A-shares, when stock returns significantly fell in a short period of time. There have been many different approaches to the origins of such decline. For example, according to the report “August Roadmap: Epic Undeperfomance” (2015) by G. Dennis and H. Park, the reason of such decline were disappointed investors, who expected A-shares to be included into MSCI GEM, but it was announced that there will be no inclusion at that time, but later in future. However, in my research I will study the significant drop in index return caused by the collapse of bubble on the market. My work is similar to Barberis (2011) by highlighting the importance of extrapolation of past returns in the bubble formation.

This paper contributes to the literature by providing first comprehensive scientific research of the recent bubble in China. The event study was conducted and showed that there is a clear evidence of financial bubble. Also, during the most intense development of the bubble, 2 quartile of 2015, new institutional investors entered the market and bought stocks, which were suspected to have the bubble inside of them. As the result, the evidence of majority new investors having extrapolative expectations has been found. Then, this work offers new approach to the relative importance of `value' and `growth' signals for the investor with extrapolative expectations. This is the adjustment of the model offered by Barberis, Greenwood, Jin and Shleifer (2015), but wavering has been replaced by another concept about weights: they were no more assumed to be random through the life of the bubble.

In the next section, the event study of the bubble on the Chinese stock market will be provided. The study is conducted following the guideline outlined by Barberis, Greenwood, Jin and Shleifer (2015), but for another set of data. The analysis could be divided on two parts: first to detect the presence of the bubble, second to check whether this bubble was extrapolator- driven.

In Section 2 new specification of relative weights for investor with extrapolative expectations is empirically tested. Section 5 includes the conclusion, interpretation of results and areas for further research. Section 6 and 7 are references and Appendix correspondingly.



1. Event study

In this section of research the event study of the bubble is conducted following the guideline by Barberis, Greenwood, Jin and Shleifer (2015). The study can be divided into the two parts. In the first one I check whether the bubble actually existed on the market. This is done by verifying that the definition of the bubble, offered in the paper, holds:

“the price of an asset rises dramatically over the course of a few months or even years, reaching levels that appear to far exceed reasonable valuations of the asset's future cash flows. These price increases are accompanied by widespread speculation and high trading volume. The prces eventually ends with a crash, in which prices collapse even more quickly than they rose”

In the second part the bubble is checked to be extrapolator-driven, which is the main research interest of my paper. According to Barberis, Greenwood, Jin and Shleifer (2015), this happens when “ bubble develops, a larger fraction of its investor base will consist of investors with extrapolative-like characteristics”.

1.1 Data

Before switching to the empirical evidence, the choice of the index for the analysis should be justified. As described above, the bubble occurred in the A-shares: type of shares allowed to be traded only by locals and for some foreign investors, if they are listed in QFII. For my research I have picked Shanghai Composite Index (SHCOMP), which is, according to Bloomberg, capitalization-weighted index of all A-shares(measured in CNY) and B-shares (measured in USD)listed on the Shanghai Stock Exchange. The presence of B-shares does not significantly alter the results, because their total proportion in the index has not exceeded the 0,6% of the index from the 01.01.2013 as it could be seen from the Figure 1. For that, time-series weights of A-share and B-share in the SHCOMP were calculated (by 15.06.2016 there are more than 1100 stocks of both types in the index, all information taken from Bloomberg). Please see the Appendix for A-shares and B-shares weights as at 15.06.2016.

Figure 1. The change of total B-shares weight in the SCHOMP over time

The average weight of B-share contributes only to 0,478% of the index, as shown in the Table. Hence, Shanghai Composite Index is an appropriate index to detect bubble in the A-shares, because the index mostly consists of this type of stocks.

For additional information on SHCOMP, please see the Appendix.

Statistics for total B-shares weight in the SCHOMP

B- shares (USD)
min	24.07.15	0,336392
avg		0,478197747
max	07.02.14	0,60375

1.2 The check of the existence of the bubble

The definition of the bubble used by Barberis and Coauthors (2015) could be broken up into two statements and then checked separately:

(1) There has been a significant increase in the prices within relatively short period and then- the significant decrease in prices

(2) The bubble should happen at high trading volume

While the first part of the definition is pretty obvious and intuitive, the second one, although being generally accepted, needs more careful explanation. Barberis and Coauthors (2015) approached the increased volume by the wavering concept (the latter, although it has been explained in the literature overview section, is not used in this paper). Still, one of the main predictions of the original paper is that there is the positive relation between the volume trading and returns of the stock over the same period. As the prediction of (2) is easier to be estimated than the (2) statement itself, while leading to the same results, I will estimate the prediction instead.

Let's check the statement (1):

There has been a significant increase in the prices within relatively short period and then- the significant decrease in prices.

For that, the cumulative returns for potentially overvalued A-shares (an appropriate proxy is Shanghai Composite Index (SHCOMP)) should be compared with the cumulative returns of the broader market (an appropriate proxy is Vanguard FTSE Emerging Markets (FTSE EM); the distribution of countries with largest weights in FTSE EM could be found in Appendix).

The suspected bubble in A-shares started to develop in the second quartile 2015 and collapsed in the middle of July; the considered period for difference in returns will be from 01.03.2015- 26.08.2015.

From the figure 2 it could be seen that starting from the beginning of the March SHCOMP index has significantly increased and outperformed the index for the broader market. SCHOMP reached its peak at July 12^th with the cumulative return greater 1,53, while FTSE EM at that period declined slightly and accounted for 0,99. After this peak the SCHOMP index had a dramatic fall, almost reaching the level of the broad market index. Obviously, there is anevidence that statement (1) holds.

Statistics for SCHOMP index

	date	value	change %
Beginning of the period	02.03.2015	3336,285
Local max	12.06.2015	5166,35	55%
Local min	26.08.2015	2927,288	-43%

Figure 2. Cumulative returns for SCHOMP and FTSE EM

Now let's check the statement (2):

Now we should to estimate the dependence between trading volume and the cumulative returns of Shanghai Composite Index. As we have already data for the index returns, the proxy for trading volume should be found. Turnover, that is the total amount traded in the index's currency, can be a good proxy; the values are received from the Bloomberg TURNOVER section.



Figure 3. The correlation between turnover and return of SCHOMP

Only by looking on Figure 3 one can see that before the middle of July there has been a strong positive dependence between index return and turnover, which is justified by correlation coefficient equal to 0.7988. After June 12^th returns experienced dramatic drop- at that time the collapse of potential bubble happens; however, the turnover value has even increased further. This could be explained by the fact, that after the collapse investors started to sell their A-shares at large quantities, making the correlation coefficient between returns and turnover on the whole period equal to -0,445. Obviously, there is significant evidence that statement (2) holds.

Using the data considered above, both statements hold and the conditions in the definition of the bubbles are satisfied. It means that there is significant empirical evidence to assume that there was a financial bubbles in A- shares in 2015.

1.3 The check for bubble driven by investors with extrapolative expectations

Following the Barberis, Greenwood, Jin and Shleifer (2015), the study whether the bubble is extrapolators-driven could be divided into two parts, similar to the 3.2 analysis:

(a) when bubble develops, new investors enter the market

(b) The majority of new investors are extrapolators in the expectation formation

Let's analyze the (a) statement:

Step 1. To be able to detect whether there was some unusual, excessive entrance of new investors on the market, the sample of stocks, which will be analyzed, first need to be determined. This simplification has to be done, because due to the limitation in the time and resources it is impossible to study each stock in the SHCOMP - there are more than 1030 of them. Hence, the appropriate criteria should be introduced to choose the sample with 30 shares:

· The stock is included in the Shanghai Composite Index at the 01.03.2015- the approximate date of the beginning of the bubble

· Stocks are sorted in the decreasing order by their relative weights in the index. Stocks with largest weights are at greater interest to study, as they may have more serious impact on the market

· The drop in value from 02.03.2015 to 26.08.2015 should be greater than 30%. This assumption is done, because the primary aim of my research is to study and to detect extrapolative behavior. The larger decrease in the value - the more chances of the presence of extrapolative expectations.

As the result, the sample of 30 shares was formed. You could see the list in the Appendix.

Step 2. For each of the 30 stocks in the sample the following weekly data was received for more than a two-year period - from 13.04.14 to 01.05.16:

- The total amount of institutional investors at the certain date (the end of the week).

It is important to note that in my research there are only institutional investors. This has been done because there will not be necessary information for further research for other types of investors. For example, there is no information about portfolio holdings of individual investors, as this is not the public information. However, the knowledge about agents' portfolio structure is essential for the analysis of statement (b), where the final decision will be made: whether the agent is an extrapolator or not.

- The amount of new investors bought the stock during the week

Then, at the end of each week the ratio of new investors to the total amount of investors was calculated. Then average of these ratios among all 30 shares was calculated, and as the result we receive weekly ratios of new investors to the total amount of investors for our sample. The same procedure was provided to Vanguard FTSE Emerging Markets ETF (FTSE EM) index and to MSCI China. As the result, we could compare the coefficient of entrance of new investors of our sample from SHCOMP with the same coefficients for broader China market and Emerging markets.

All data was received from Bloomberg. In the Appendix you may find Step 2 procedure for calculation of coefficient of new investors on the example of China Merchants Securities Co Ltd stock.

Figure 5. New investors coefficient for the sample from SHCOMP, MSCI China and FTSE EM

On the Figure 5 above the coefficient of new investors is higher than the one for emerging markets over the whole considered period. Moreover there is a clear evidence of new investors enter the market by buying stock from our sample in the May 2016, then the coefficient stays at the high level for next three months and then it drops to one of the lowest values, when investors start to leave in the August 2016. There is anobvious evidence in support of statement (a).

Now let's analyze the (b) statement:

The aim of the last part of the event study is check whether the investors, which enter for the first time the market with the bubble inside, are extrapolators. We start with considering our sample with 30 stocks. Using Bloomberg, we detect which institutional investors bought stock from our sample for the first time in the 2^nd quartile 2015 (the period of bubble development). Each stock was bought on average 12-15 times and then was put into the buyer's portfolio. The next step would be to range all stocks in that portfolios and then to range portfolios themselves. However, as there are more than 300 portfolios to estimate, such comprehensive analysis is not possible under limited time and resources. That is why here we should rather choose few portfolios but to provide more sophisticated analysis.

Again, several criteria were established:

· only institutional investors: we do not consider the individual investors as there portfolios are not in the public access, hence no further analysis would be possible

· investors should buy the stock for the first time / at least for the first time in the portfolio in 2 quartile 2015

· Consider investors only with active management policy: those with passive management, such as ETF, will simply follow the market. Hence, if the market is rising due to the bubble inside, they will also rise in value; by that their behavior will looks like extrapolative one. That is why it is better not to include them if we want to detect true extrapolators.

· The position in the 2 quartile 2015 should be greater than 100,000 stocks. Otherwise, the smaller buy/ sell trades will not significantly influence the market.

· The investor is better to invest in at least 3 stocks from the sample. This will increase our chances to detect extrapolators.

· Investor should invest not only in the Chinese stock market. Under our methodology if the investor invests only in China, there could be the same case as with passive management: investor will follow the market, while not being an extrapolator. This is due to the fact that Chinese economy has declined overall, but not in some certain spheres.

As the result, following investors are left:

Chosen institutional investors

Row Labels	Active management	Amount of stocks invested from the sample	total amount of position hold> 100,000 shares	Geographical diversification (China < 50%)
ALLIANZ DRESDNER ASSET MGMT	Yes	1	Yes	Yes
EAST CAPITAL ASSET MGMT	Yes	7	Yes	Yes
FUH-HWA INVESTMENT TRUST CO LTD	Yes	3	Yes	Yes
KB ASSET MANAGEMENT	Yes	4	Yes	Yes
KDB ASSET MANAGEMENT CO LTD	Yes	9	Yes	Yes
MATTHEWS INTERNATIONAL CAPITAL	Yes	3	Yes	Yes

As the final step of the event study, the ranging procedure will be applied.

For the chosen institutional investors we start to consider the portfolio, in which it holds the position of one of our 30 stock from the sample (this information id taken from Bloomberg). However, if all the stocks in the portfolio are from Chinese stock market, the portfolio is not diversified. As outlined above, in the last criterion of choosing institutional investor to study, we do not consider this situation as a representative one; hence, in this case, another one portfolio of the company will be considered - the one not from Chinese market. This would help us to detect truly extrapolative behavior.

Then, at each period considered, all stock from all the portfolios will be classified together and ranged according to their returns. Then, each portfolio will achieve its our ranking as the weighted ranks of all stock in that portfolio. The same analysis will happen at 7 different periods and the results are presented in the Table. Then, via looking at the changes of portfolio returns over the time, they were divided on 2 groups: extrapolators and non-extrapolators by the following logic:

Portfolio, which performs well during the development of the bubble (that is 2 quartile 2015) and then returns decrease, is considered to have extrapolative expectations. (not marked in table)

Portfolio, which in general has opposite return behavior or no pattern could be seen in its behavior is considered as non- extrapolator. (marked red in the table)

The evidence in support of relevance of our analysis is that the results received are on general intuitive: for example, both JP Morgan portfolios, one of the largest investment bank in the world, turned to be non extrapolators.

Rankings or portfolios over time

Fund	30.09. 14	31.12. 14	31.03. 15	30.06. 15	30.09. 15	31.12. 15	31.03. 16
EAST CAPITAL LUX - CHINA ENVIRONMENTAL	5,79	7,41	8,95	4,95	4,34	4,76	5,08
EAST CAPITAL LUX - EMERGING ASIA FUND	5,09	6,71	5,72	7,34	7,12	6,08	5,22
FUH HWA GLOBAL THEMATIC FUND	8,00	0,00	5,45	3,99	4,68	6,61	6,41
JPMORGAN CHINA PIONEER A-SHARE FUND	4,65	7,54	8,33	8,30	7,24	6,64	5,20
JPMORGAN EMERGING MARKETS EQUITY FUND	5,87	5,59	5,28	4,76	5,45	4,64	5,50
KB CHINA A SHARE GROWTH SECS MASTER (EQUITY)	5,29	8,83	9,32	9,05	8,74	5,00	3,97
KB VALUE FOCUS SECS MASTER INV TR EQUITY	5,81	4,90	5,02	5,99	5,98	5,04	5,95
KDB CHINA SPECIAL A SHARE SECURITIES MASTER-EQUI	6,00	9,06	7,32	5,72	6,77	4,22	4,59
KDB KOREA BEST SECS MASTER INV TR (EQUITY)	5,76	4,55	4,54	4,61	5,35	4,54	6,34
MATTHEWS ASIA DIVIDEND FUND	5,57	5,16	5,53	5,40	6,43	6,69	7,16
VANGUARD FTSE EMERGING MARKETS ETF	6,00	5,62	5,46	5,65	5,81	4,41	5,23
Investment Company	30.09. 14	31.12. 14	31.03. 15	30.06. 15	30.09. 15	31.12. 15	31.03. 16
POTENTIAL EXTRAPOLERS	5,62	6,91	6,81	6,28	6,38	4,94	5,19
NON EXTRAPOLERS	6,02	6,10	6,15	5,61	5,95	6,14	6,07
VANGUARD	6,00	5,62	5,46	5,65	5,81	4,41	5,23

In the Figure 6 the average values of both extrapolators and non-extrapolators were taken and presented on the graph. Also, the market portfolio was included. Based on the graph below we could see, that the equally weighted portfolio with extrapolative expectations would significantly outperform equally weighted portfolio with non-extrapolative expectations by 1 rank. However, starting from 4^th quartile of 2015 the latter portfolio would significantly outperform the former one. This result is consistent with the existence of financial bubble.

To conclude, the results of our event study are a) there was a bubble in 2^nd quartile 2015 and b) There is the evidence of investors with extrapolative expectation in that bubble. investor extrapolator market



Figure 6. Returns of portfolios of extrapolators, non-extrapolators and market.



2. Adjusted weights of value and growth signals

2.1 New model of expectation formation

After the event study was conducted and evidence both of financial bubble and significant amount of investors with extrapolative expectations, in this part of work we will concentrate more on how the expectations are formed.

As was assumed above, there are two types of investors on the market - one with extrapolative expectations and other with fundamentals.

Following the model by Barberis, Greenwood, Jin and Shleifer (2015), fundamental investors form their beliefs about future based on the “value signal”, which is the difference between actual price and fundamental value of all future cash flows. By traditional models, extrapolative investors based their beliefs on the “ growth” signal, that is the weighted average of all past returns; however Barberis and his coauthors (2015) assumed that “value” signal also matters for extrapolators. Similar to their work, I will keep both signals in the extrapolative expectation formation model. Still, I will departure from their assumption that weights between signals are assigned randomly. I suppose, that weights of two signals change over time. The idea is as follows: assume there is the bubble on the market, stocks get overvalued and their values increase with time. In the beginning, investor with extrapolative expectations do not suspect there is a bubble, he assumes that the stock prices are growing due to increase in their fundamental values. At this stage, the greater weight is given to the growth signal. When bubble develops, the actual value deviate further from the fundamental one. As we assume that value signal matters for extrapolators, they start to suspect that large deviation from the fundamental value can be the evidence of the bubble. As the result, they increase the weight of value signal and start to make expectation similar to the fundamental investors.

In the next subsection I will test empirically the model, described above. The aim of the analysis is to check whether the weights between signals are set randomly, and if they are not, to see is there any pattern to be noticed.

2.2 Empirical analysis

As we consider the same bubble on the Chinese stock market as before, I will use the same variables as in the event study in the Section 3. As the dependent variable I will use the return (let's denote them by R) from the equally weighted portfolio, constructed from the 30 stocks in the abovementioned sample (in the Section 3 the formation of this sample is discussed in details). As the event study has detected the evidence of extrapolative returns based on that sample of 30 stocks, then returns R could be used as the return estimated by extrapolators. The determinant variables are value signal and growth signal. However, as these signals are not observable, the proxies should be used instead. For the growth signal, the market return will be taken as proxy; while for the value signal - the average of target returns estimated by analytics, who analyzed the companies of 30 stocks in the sample (the data was taken from Bloomberg).

The regression with same variables will be run in different periods during the development of the bubble. The original specification is

Returnt = a +b₁ Market Return_t + b2 Target Return_t

We will describe the regression in details for one period, the others will be conducted similarly and their EViews outcomes could be found in Appendix.

The first period to analyze is 3d quartile of 2014- from 01/10/14- 31/12/14. As daily returns, used in my model, are time series, the first of all stationarity test should be done.

As p-value is greater than 5% significance level, the Null Hypothesis under the UnitRoot test is not declined, which means data is nonstationary. However, after doing differencing, the time series becomes stationary ( p-value is less than 5% s.l..). Other time-series data also become stationary after first difference.

When other specification is tried, all the problems disappear: both coefficients get significant at 5% s.l., there is no heteroscedasticity in the model. The right specification is PARCH (1,2) in volatility

Also, all information criteria decreased in comparison to OLS.

Other regressions were made, and all coefficients are as that:

Weight Market Return	Weight Target
121,80%	25,00%
139,00%	36,00%
133,00%	-40,00%
140,00%	-103,00%
120,00%	-17,00%
120,00%	-28,00%
109,80%	29,00%
93,00%	4,00%
62,88%	37,12%
54,05%	45,95%
51,85%	48,15%

Similar to the work by Pedhazur (1997), I take Beta coefficients as the relative weights of signals.

Then, if the graph is made based on such weights, we can notice that in the period of bubble development investor put more weight on the growth signal. However, after some point, they started to increase the weight put on value signal.

The conclusion is that the weights are not random among the signals, and the connection with the bubble can be observed.



Figure 7



Conclusion

In my thesis paper, I have explained the extrapolation bubbles on the example of bubble in Chinese economy, which happened recently with the A-shares

I have conducted the event study with the help of which I investigated that there was a financial bubble in the Chinese market and not just sharp decline in the prices. The results I have received tells us about the presence investors which had the extrapolative expectations

Extrapolators are forming there expectations by two signals: value and growth signals.

The main difference of my work compared to those that have been undertaken in the past few years and, particularly Barberis N., Greenwood R., Jin L., and Shleifer A. (2013), is that the extrapolators assigns more weight on the value signal. This evidence was a results of my empirical analysis.

However, further investigations should take into account larger samples (more than 30). It would be also interesting to conduct the analysis from the point of view of individual investors, but not from the point of view of institutional ones.



List of references

1. Barberis N., Greenwood R., Jin L., and Shleifer A. (2013), “x-capm an extrapolative capital asset pricing model”

2. Barberis N., Greenwood R., Jin L. and Shleifer A. (2015) “Extrapolation and Bubbles”, National bureau of economic research

3. Bernanke B. S. (2010); Shiller R. J. (2007)

4. Breach, Eric Friedman (2000)

5. Cutler D., Poterba J. and Summers L. (1990) “Speculative Dynamics and the Role of Feedback Traders”, American Economic Association

6. De Long J., Shleifer A., Summers L. and Waldmann R. (1990) “Noise Trader Risk in Financial Markets”, The University of Chicago Press

7. Dennis G., Park H., «August Roadmap: Epic Inderperfomance», 2015

8. Giancarlo Corsetti, Paolo Pesenti, Nouriel Roubini (1999); Simon Johnson , Peter Boone, Alasdair

9. Glaeser E. and Nathanson C. (2015) “An extrapolative model of house price dynamics”, National bureau of economic research

10. J. Bradford DeLong, Magin K. (2006) “A short note on the size of the dot-com bubble” , National bureau of economic research ; Alexander Ljungqvist,?William J. Wilhelm Jr. (2003) “IPO Pricing in the Dot-com Bubble”, The Journal of Finance

11. Kahneman and Tversky's (1974)

12. Lakonishok J., Shleifer A. and Vishny W. (1994) “Contrarian Investment, Extrapolation, and Risk”, The Journal of Finance

13. Shiller (2000) `Measuring bubble expectations and investor confidence', The Journal of Psychology and Financial Markets

14. UBS Report, «Macro-Strategy Key Issue. China's correction: Implications and Opportunities», July 2015

15. Pedhazur (1997)

Appendix

The weights of A-shares and B-shares at 15.06.2016

Currency	Weight	Share class
CNY	99,551896	A shares
USD	0,448104	B shares

Additional information for SHCOMP index

SCHOMP index shows different stages of the bubble

Statistics for SHCOMP during the bubble period

	data	value	Change %
beginning	02.03.15	3336,285
top	12.06.15	5166,35	55%
first decline	08.07.15	3507,192	-32%
second decline	26.08.15	2927,288	-17%
			-43%

Top 10 emerging countries with largest weights in the FTSE EM

Country	Weight
China	22,10
Taiwan	15,26
India	11,91
South Africa	7,69
Brazil	7,46
Hong Kong	5,25
Mexico	4,97
Malaysia	4,55
Russia	4,26
Thailand	2,85

The sample of 30 shares to analyze the entrance of new investors

Ticker	Name	Weight	MAX Dropdown
601299 CH Equity	China CNR Corp Ltd	0,506726	-50%
601633 CH Equity	Great Wall Motor Co Ltd	0,384181	-62%
600999 CH Equity	China Merchants Securities Co Ltd	0,632883	-64%
600837 CH Equity	Haitong Securities Co Ltd	0,693375	-63%
600887 CH Equity	YILI	0,335707	-42%
600018 CH Equity	Shanghai International Port Group Co Ltd	0,599179	-57%
601318 CH Equity	Ping An Insurance Group Co of China Ltd	1,481302	-46%
600030 CH Equity	CITIC Securities Co Ltd	1,149817	-65%
601688 CH Equity	Huatai Securities Co Ltd	0,507882	-63%
600893 CH Equity	Avic Aviation Engine Corp PLC	0,251074	-64%
601788 CH Equity	Everbright Securities Co Ltd	0,336067	-62%
601377 CH Equity	Industrial Securities Co Ltd	0,296024	-61%
601989 CH Equity	China Shipbuilding Industry Co Ltd	0,64226	-70%
600276 CH Equity	Jiangsu Hengrui Medicine Co Ltd	0,235539	-30%
601901 CH Equity	Founder Securities Co Ltd	0,431273	-64%
600690 CH Equity	Qingdao Haier Co Ltd	0,244784	-54%
601390 CH Equity	China Railway Group Ltd	0,573123	-68%
601328 CH Equity	Bank of Communications Co Ltd	0,933714	-46%
601006 CH Equity	Daqin Railway Co Ltd	0,614246	-55%
600048 CH Equity	Poly Real Estate Group Co Ltd	0,428785	-54%
601601 CH Equity	China Pacific Insurance Group Co Ltd	0,840975	-48%
600208 CH Equity	Xinhu Zhongbao Co Ltd	0,240117	-66%
601818 CH Equity	China Everbright Bank Co Ltd	0,643291	-48%
600050 CH Equity	China United Network Communications Ltd	0,463596	-63%
600585 CH Equity	Anhui Conch Cement Co Ltd	0,322841	-55%
600886 CH Equity	SDIC Power Holdings Co Ltd	0,282234	-61%
600111 CH Equity	CNRE	0,244965	-57%
600010 CH Equity	Inner Mongolia BaoTou Steel Union Co Ltd	0,326257	-63%
601336 CH Equity	New China Life Insurance Co Ltd	0,418333	-57%
601111 CH Equity	Air China Ltd	0,260743	-60%

Below you can see the example of Step 2 procedure, provided to the stock of China Merchants Securities Co Ltd (600999 CH Equity) in order to calculate total amount of investors, new investors who recently bought the stock and the ration of new to the total investor at the end of each weel over some period.

600999 CH Equity

NUM_NEW_INST_BUYERS	units		EQY_INST_HOLD	units		Ratio
13.04.14	15		13.04.14	68		0,220588235
20.04.14	15		20.04.14	68		0,220588235
27.04.14	16		27.04.14	70		0,228571429
04.05.14	26		04.05.14	78		0,333333333
11.05.14	25		11.05.14	78		0,320512821
18.05.14	25		18.05.14	78		0,320512821
25.05.14	25		25.05.14	77		0,324675325
01.06.14	26		01.06.14	76		0,342105263
08.06.14	26		08.06.14	76		0,342105263
15.06.14	26		15.06.14	75		0,346666667

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