investor trading during the chinese put warrants bubble*

Investor Trading During the Chinese Put Warrants Bubble*

October 2013

Neil PearsonZhishu Yang

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*We thank Yang Zhao for excellent research assistance.

“Bubbles” in Asset Pricing

• There is long-standing theoretical interest in “bubbles,” dating at least to Smith (1776), who attributed them to “overtrading.”

• Interest has intensified following the 1996-2000 boom in the prices of technology stocks

• Recent empirical papers include Brunnermeier and Nagel (2004), Hong, Scheinkman, and Xiong (2006), Greenwood and Nagel (2009), Griffin, Harris, Shu, and Topolaglu (2009), and Xiong and Yu (2011).

• Empirical work is limited by lack of access to detailed data on investors’ trades.* E.g., the empirical analyses in Xiong and Yu (2011) focus on end-of-day closing prices and volume

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*An exception is Kaustia and Knupfer (JFE, 2012), who use Finnish data to study social contagion during a period that included the technology bubble.

Our ContributionWe use detailed brokerage account trading records from a Chinese securities firm to study investor behavior during the Chinese put warrants bubble•The data we have covers almost the entire period of warrant trading, from August 22, 2005 (the date the first warrant was issued) until December 31, 2009Using these data:•We find evidence inconsistent with a leading theory of bubbles, the resale option theory of Scheinkman and Xiong (JPE, 2003)•We find evidence that the order imbalances due to the trades of new investors forecast returns•We present strong evidence that social contagion was an important determinant of the entry of new investors into the warrant market, consistent with arguments of Shiller and various coauthors

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Our ContributionStudying trading behavior during the Chinese put warrants bubble is interesting because Xiong and Yu (AER 2011) make a compelling case that it was a bubble

•Thus, we can be confident that we are seeing the trading behavior during a bubble

Other alleged bubbles are controversial:

•Hall (AER 2001) and Li and Xue (JF 2009) argue that the run-up in the prices of technology stocks during 19962000 can be explained by technology shocks and Bayesian updating of beliefs about future technology shocks.

•Garber (JPE 1989, JEP1990, MIT Press 2000) has offered explanations of the Dutch tulipmania, the Mississippi Bubble, and South Sea Bubble in terms of fundamentals.

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Chinese Warrant Market

Began on August 22, 2005 when the Baosteel call warrant was listed on the Shanghai Stock Exchange

Total of 55 warrants were issued:

• 37 call warrants, 18 put warrants

• 39 listed in Shanghai, 16 in Shenzhen

• Peak issue year was 2006, with 26 warrant issues

• As of the end of our data (Dec. 31, 2009) only one warrant remained trading

Warrants traded like stocks, except that a warrant could be sold on the same day it was purchased

Warrants were not similar to U.S.-listed call and put options

• Calls (puts) did not have matching puts (calls)

• Could not be written or short-sold

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A Few Facts

Database contains 5,692, 241 trades81,811 warrant investors• 80,089 retail investors• 1,722 institutional investorsEach investor, on average, invested in 4.9 different warrants,

executed a total of about 70 transactionsNext slide shows (part of) a transition matrix

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5-minute transition matrix

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Frequency that an Investor Holding Quantity N t of Warrant k at time t Transitions to Holding Quantity N u of Warrant k at Time u

N u = 00 < N u 500

500 < N u 1,000

1,000 < N u 2,000

2,000 < N u 3,000

3,000 < N u 5,000

N t = 0 0.8938 0.9995 0.0001 0.0000 0.0001 0.0000 0.00010 < N t 500 0.0209 0.0029 0.9956 0.0005 0.0003 0.0001 0.0001

500 < N t 1,000 0.0108 0.0050 0.0005 0.9922 0.0015 0.0003 0.00021,000 < N t 2,000 0.0122 0.0057 0.0003 0.0007 0.9910 0.0011 0.00082,000 < N t 3,000 0.0083 0.0062 0.0002 0.0003 0.0009 0.9895 0.00183,000 < N t 5,000 0.0120 0.0063 0.0001 0.0001 0.0005 0.0007 0.98935,000 < N t 10,000 0.0150 0.0065 0.0002 0.0001 0.0001 0.0003 0.001210,000 < N t 20,000 0.0108 0.0066 0.0002 0.0000 0.0000 0.0001 0.000320,000 < N t 30,000 0.0046 0.0072 0.0002 0.0000 0.0000 0.0000 0.000130,000 < N t 50,000 0.0045 0.0077 0.0002 0.0000 0.0000 0.0000 0.0001

N t > 50,000 0.0070 0.0087 0.0002 0.0000 0.0000 0.0000 0.0000

Quantity N t of warrant k held at time t

(beginning of period)

Fraction of observations

with N t in range

1-day transition matrix

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N u = 00 < N u 500

500 < N u 1,000

1,000 < N u 2,000

2,000 < N u 3,000

3,000 < N u 5,000

N t = 0 0.8943 0.9920 0.0011 0.0008 0.0009 0.0007 0.0010

0 < N t 500 0.0209 0.0689 0.9050 0.0094 0.0053 0.0023 0.0021

500 < N t 1,000 0.0107 0.0942 0.0102 0.8599 0.0207 0.0057 0.0035

1,000 < N t 2,000 0.0121 0.1014 0.0060 0.0101 0.8478 0.0155 0.0117

2,000 < N t 3,000 0.0083 0.1051 0.0048 0.0052 0.0131 0.8315 0.0233

3,000 < N t 5,000 0.0119 0.1060 0.0033 0.0023 0.0080 0.0100 0.8321

5,000 < N t 10,000 0.0149 0.1104 0.0032 0.0015 0.0024 0.0053 0.0153

10,000 < N t 20,000 0.0108 0.1133 0.0037 0.0012 0.0010 0.0015 0.0060

20,000 < N t 30,000 0.0046 0.1187 0.0039 0.0011 0.0008 0.0007 0.0022

30,000 < N t 50,000 0.0045 0.1229 0.0036 0.0008 0.0006 0.0005 0.0015

N t > 50,000 0.0070 0.1333 0.0038 0.0009 0.0006 0.0003 0.0008

Quantity N t of warrant k held at time t (close of

previous day)

Fraction of observations

with N t in range

Frequency that an Investor Holding Quantity N t of Warrant k at time t Transitions to Holding Quantity N u of Warrant k at Time u

Transition “cycles”• Theories such as the resale option theory speak to

purchases and sales, each of one unit

• In actual data, an investor might use multiple buys to build up a position, and then liquidate the position using multiple sell orders.

• This raises the issue of how to map the data to the buy and sell transactions that appear in the theory. (A similar issue arises in empirical analyses of the disposition effect.)

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Transition “cycles”Introduce a “transaction cycle:”• Starting from a holding of zero units of warrant k, a “cycle”

begins with purchase of some amount of warrant k.

• Continues through possible multiple purchases and sales, until the investor’s position in warrant k returns to zero. This ends a transaction cycle, which we treat as a single transaction.

• Length of the transaction cycle is the time elapsed from the first purchase that begins the cycle to the last sale that ends it.

• Return to a transaction cycle is the weighted sum of the sale prices, weighted by the quantities sold in the various sells, divided by the weighted sum of the purchase prices, where again the weights are the quantities purchased in the various buys, minus one.

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Table 3. Buys and sells in a transaction cycle

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1 2 3 4 5 > 5535,673 19,689 2,403 620 189 193 558,76772.76% 2.67% 0.33% 0.08% 0.03% 0.03% 75.90%71,782 23,004 4262 1022 324 296 100,6909.75% 3.12% 0.58% 0.14% 0.04% 0.04% 13.67%15,470 9,177 5,932 1,550 469 374 32972.002.10% 1.25% 0.81% 0.21% 0.06% 0.05% 4.48%4908 3770 3024 2279 812 536 15329.00

0.67% 0.51% 0.41% 0.31% 0.11% 0.07% 2.08%1,939 1,643 1,567 1,379 1,049 770 8347.000.26% 0.22% 0.21% 0.19% 0.14% 0.10% 1.12%1,965 1,828 1,939 2,094 2,107 10,220 20,1530.27% 0.25% 0.26% 0.28% 0.29% 1.39% 2.74%

631,737 59,111 19,127 8,944 4,950 12,389 736,258

85.81% 8.02% 2.60% 1.21% 0.67% 1.68% 100%

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> 5

Sum Across All Numbers

of Sales

Sum Over All Numbers

of Buys

Number of buys to build up a position

Number of sales used to liquidate a position

1

2

3

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Table 4. Lengths of transaction cycles

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Transaction Cycle Length Frequency

Cumulative Frequency Frequency

Cumulative Frequency Frequency

Cumulative Frequency

Less than 5min 0.1039 0.1039 0.1041 0.1041 0.0957 0.09575min-10min 0.0856 0.1895 0.0855 0.1895 0.0918 0.187510min-1hour 0.3109 0.5004 0.3103 0.4999 0.3382 0.52581hour-1day 0.2448 0.7452 0.2450 0.7449 0.2320 0.75781day-2day 0.0532 0.7984 0.0533 0.7982 0.0499 0.80772day-5day 0.1096 0.9080 0.1099 0.9081 0.0966 0.90435day-10day 0.0377 0.9457 0.0377 0.9458 0.0373 0.941510day-20day 0.0233 0.9691 0.0233 0.9692 0.0233 0.9649More than 20day 0.0309 1.0000 0.0308 1.0000 0.0351 1.0000Total transaction cycles

All Investors Individual Investors Institutional Investors

736,258 720,454 15,804

Resale Option Theory

• Dividend process D with drift equal tovalue of a “fundamental” variable f that determines the expectation of future dividends; the fundamental variable f itself follows a mean-reverting diffusion process.

• Two groups of investors, A and B, and each investor, regardless of group, observes two signal processes sA and sB.

• The drift of each signal process is equal to f, and the innovations to both signal processes are uncorrelated with the innovations to the fundamental variable f.

• Investors in group A incorrectly believe that the innovation to the signal sA is correlated with the innovation to the fundamental variable f, and investors in group B incorrectly believe that the innovation to the signal sB is correlated with the innovation to the fundamental variable f.

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Resale Option Theory

• The two groups of investors disagree about the interpretation of the signal processes and thus disagree about the value of the asset. This create the resale option.

• Valuation of group A investors include the value of the option to sell to group B at a price group A thinks is incorrect; group B’s valuation of the asset includes the value of the resale option to sell to group A investors at an incorrect price

• Market price of the asset exceeds the fundamental valuation of the group with the higher valuation. The market price of the asset is the valuation, including the value of the resale option, of the more optimistic group of investors.

• Trade occurs when the valuations cross. This crossing of valuations is the essential element of the theory, because it creates the resale option

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Figure 1. Investor Valuations in the Resale Option Theory

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Figure 2. Relation between probability of sale Prob( ≤ t| rt) and return implied by the resale option theory

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Figure 3. Estimates of the conditional sale probability Prob(ti < ≤ tj| rtj) for various time horizons ti and tj.

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Figure 3. Estimates of the conditional sale probability Prob(ti <≤ tj| rtj) for various time horizons ti and tj.

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Figure 3. Estimates of the conditional sale probability Prob(ti < ≤ tj| rtj) for various time horizons ti = 5 minutes and tj

= 10 minutes

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Figure 3. Estimates of the conditional sale probability Prob(ti < ≤ tj| rtj) for various time horizons ti = 5 minutes and tj

= 10 minutes

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Resale option conclusions

• The relations between the sale probabilities and returns estimated from the data are strikingly inconsistent with the predictions of the resale option theory

• For short horizons, they are also inconsistent with the disposition effect

• They are very similar to the relations in Ben-David and Hirshleifer (RFS 2012)

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Role of New InvestorsAn investor who trades warrant k on date t is considered to be a new investor in warrant k on date t if date t is the first date on which the investor trades warrant k.

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Warrant Code

Average Numberof New Investors

Average Closing Price

Number of Trading Days

Correlation Between New Investors and

Closing Price p -value

38001 18.13 1.237 331 0.4330 <0.000138002 44.15 0.433 174 0.4311 <0.000138003 33.86 1.679 447 0.5544 <0.000138004 26.57 2.158 472 0.5734 <0.000138005 34.68 0.810 102 0.5647 <0.0001

580994 30.92 0.995 194 0.5283 <0.0001580995 28.11 0.564 233 0.3382 <0.0001580996 18.44 1.164 235 0.2618 <0.0001580997 60.05 0.516 360 0.8146 <0.0001580998 18.94 1.181 234 0.4645 <0.0001580999 27.97 0.696 235 0.4344 <0.0001Mean 33.23 1.10 266.00 0.5473

New Investor Order Imbalance and Returns• New investor order imbalance in warrant k on date t is the net

of the buy volume of new investors on date t and any sell volume from new investors reducing or closing their positions on the same day, normalized by dividing by the number of warrants outstanding

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Explanatory Variable (1) (2)

Constant -0.0190 -0.0128

-(7.21) -(3.45)

BrokerageNewOrderImbalancek ,t 17.20 22.59

(4.58) (4.87)

BrokerageNewOrderImbalancek ,t -1 -15.08

-(5.20)

R 2 within 0.0283 0.0365

Observations 4,686 4,604

Explanatory Variable (1) (2)

Constant -0.0190 -0.0128

-(7.21) -(3.45)

BrokerageNewOrderImbalancek ,t 17.20 22.59

(4.58) (4.87)

BrokerageNewOrderImbalancek ,t -1 -15.08

-(5.20)

R 2 within 0.0283 0.0365

Observations 4,686 4,604

New Investor Order Imbalance and Returns• New investor order imbalance in warrant k on date t is the net

of the buy volume of new investors on date t and any sell volume from new investors reducing or closing their positions on the same day, normalized by dividing by the number of warrants outstanding

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Of course, the new investor order imbalance is endogenous

First-stage regressions predicting new investor order imbalance

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Additional variables are BrokerageNewInvestorsk,t-j, WarrantReturnk,t-j, BrokerageAverageReturnk,t-j, BrokerageInvestorsk,t-j, BrokerageAverageReturn k,t-j

× BrokerageInvestors k,t-j, and TurnoverRatiok,t-j (j = 1, 2, 3)

Explanatory Variable (1) (2) (3)

BrokerageNewOrderImbalancek ,t -1 0.3184 0.2844 0.2591

(7.32) (7.25) (5.48)

BrokerageNewOrderImbalancek ,t -2 0.1798 0.1360(5.20) (5.64)

BrokerageNewOrderImbalancek ,t -3 0.1400(4.60)

R 2 0.3219 0.3408 0.3614

Observations 4,686 4,604 4,522

Plus additional explanatory variables

Second-stage regressions explaining returns26

Explanatory Variable (1) (2) (3)

Constant 0.0041 0.0028 0.0033

(0.67) (0.49) (0.61)Predicted

BrokerageNewOrderImbalancek ,t17.00 15.01 15.72

(1.91) (1.80) (1.96)

R 2 within 0.0089 0.0071 0.0081

Observations 4,686 4,604 4,522

Social contagion27

• Various writings by Shiller, sometimes with coauthors, have emphasized the role of social contagion in speculative booms and bubbles (Shiller BPEA 1984, AER1990, 2005, 2008; Akerlof and Shiller PU Press 2009; Case and Shiller NEER1988, BPEA 2003).

• Shiller (2005; Chapter 9) emphasizes the role of social contagion and word of mouth communication, and argues that after millions of years of evolution its importance is “hard-wired into our brains.”

• Shiller (2010; p. 41) claims that “…the single most important element to be reckoned in understanding … any … speculative boom is the social contagion of boom thinking.”

How to test whether social contagion was important in explaining entry of new investors?

Kaustia and Knüpfer (JFE 2012) use Finnish data to study whether social contagion affects decision to enter the stock market

Two plausible channels by which peer returns might influence individuals’ entry decisions.

•Potential investors might use peer returns to update beliefs about long-term fundamentals, such as the equity premium.

•Potential investors cannot directly observe peer outcomes and rely on “word of mouth” verbal accounts. One expect that peers will only report positive returns.

Both channels imply that potential investors are influenced by returns of investors with whom they might communicate, i.e. “local” investors

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How to test whether social contagion was important in explaining entry of new investors?

We use panel regressions (with branch-level fixed effects) to explain entry of new investors trading warrant k at branch j on date t.

Our proxy for the returns of “local” investors is the average return of investors trading through the same branch office

•First channel implies key explanatory variables are lags of BranchAverageReturnjkt and BranchAverageReturnjkt × BranchInvestorsjkt

•Second channel implies key explanatory variables are the positive parts, that is lags of max[BranchAverageReturnjkt , 0] and max[BranchAverageReturnjkt , 0] × BranchInvestorsjkt

Also include a number of control variables

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Identification

• Reverse causality? I.e., do we find the correlation between (lagged) returns and entry because entry of new investors is causing the returns?

– No, because we use lagged returns

• Can common time-invariant unobservables be the source of the correlation?

– No, we include branch-level fixed effects

• Is entry being driven by market-wide shocks, that are correlated with branch-level returns?

– Perhaps, but we control for market-wide shocks by including (close-to-close) warrant returns and brokerage-level lagged new investors as controls.

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Identification

• Branch-level time-varying shocks? – Possible channels discussed in Kaustia and Knüpfer (2012) , e.g.

changing prospects of the local economy that work through the stock returns of local companies, are not relevant because the put warrant returns are not plausibly related to the fundamentals of the local economies

– Could results are driven by time-varying shocks that are unique to a branch or small subset of branches, e.g. local media coverage or some other source of local information or “noise.” This channel seems unlikely because the information or noise would have to be something that caused or was correlated with both branch-level returns and entry but not captured by the warrant returns used as controls.

– Despite our skepticism regarding this possible channel, below we carry out additional analyses on a subsample that drops the observations from branches where this possible channel is least unlikely to be relevant.

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Regressions explaining the entry of new investors

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Explanatory variable (1) (2) (3) (4) (5) (6) (7) (8) (9)

BranchNewInvestorsj kt 1 0.5540 0.4328 0.4394 0.5540 0.4328 0.4394 0.5540 0.4328 0.4394

(8.33) (8.86) (6.27) (8.33) (8.86) (6.27) (8.33) (8.86) (6.27)

BranchNewInvestorsj kt 2 0.2419 0.1693 0.2419 0.1693 (0.24) 0.1693

(18.34) (9.52) (18.34) (9.52) 18.3400 (9.52)

BranchNewInvestorsj kt 3 0.1486 0.1486 0.1486

(6.19) (6.19) (6.19)

BrancAverageReturnjkt 1 -0.1178 -1.9066 -2.0103 -3.2008 -2.4170 -2.7380

-(1.70) -(4.36) -(4.06) -(6.07) -(5.32) -(5.50)

BranchAverageReturnjkt 2 0.0360 0.1735 (0.38) 0.0079

(0.90) (0.82) 1.4800 (0.03)

BranchAverageReturnjkt 3 0.0424 -0.1788

(1.09) -(1.05)

Regressions explaining entry of new investors (2)

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Max(BranchAverageReturnjkt 1, 0) 0.0049 0.6715 0.8242 3.1590 1.9965 2.4101

(0.05) (1.46) (1.45) (5.50) (3.75) (4.25)

Max(BranchAverageReturnjkt 2, 0) 0.0215 -0.6860 -0.3256 -0.2989

(0.76) -(3.34) -(1.24) -(1.20)

Max(BranchAverageReturnjkt 3, 0) 0.0637 0.2523

(1.32) (1.41)

BranchInvestorsjkt 1 0.0039 -0.0022 0.0092 0.0016 -0.0082 -0.0005 -0.0001 -0.0070 -0.0007

(0.72) -(0.37) (1.07) (0.35) -(1.46) -(0.06) -(0.01) -(1.24) -(0.08)

BranchInvestorsjkt 2 0.0071 -0.0295 0.0110 -0.0195 0.0100 -0.0179

(1.02) -(4.21) (1.81) -(2.93) (1.61) -(2.72)

BranchInvestorsjkt 3 0.0222 0.0197 0.0193

(3.10) (3.44) (3.02)


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0.0331 0.0400 0.0410 -0.0362 -0.0271 -0.0174

(3.82) (3.78) (3.23) -(8.70) -(7.02) -(3.22)

-0.0021 0.0018 0.0307 0.0267

-(0.75) (1.30) (3.33) (3.59)

0.0031 0.0138

(0.74) (2.55)

0.0704 0.0722 0.0678 0.1081 0.1028 0.0881

(4.53) (4.08) (3.59) (6.57) (6.19) (6.29)

-0.0167 -0.0094 -0.0525 -0.0408

-(3.49) -(2.69) -(4.04) -(3.70)

-0.0049 -0.0215

-(1.14) -(5.01)

Max(BranchAverageReturnjkt 2, 0)

× BranchInvestorsjkt -2



BranchAverageReturnjkt 1 ×

BranchInvestorsjkt -1








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BrokerageNewInvestorskt 1 0.0008 0.0015 0.0035 0.0008 0.0015 0.0034 0.0008 0.0015 0.0034

(0.55) (1.71) (3.44) (0.61) (1.69) (3.48) (0.61) (1.69) (3.48)

BrokerageNewInvestorskt 2 -0.0010 -0.0037 -0.0009 -0.0036 -0.0009 -0.0036

-(2.47) -(8.24) -(2.26) -(8.36) -(2.26) -(8.36)

BrokerageNewInvestorskt 3 0.0006 0.0007 0.0007

(1.36) (1.48) (1.48)

WarrantReturnkt 1 1.4536 2.4996 2.4791 1.2087 1.1022 1.0223 2.2914 2.2421 2.2334

(6.30) (6.55) (6.63) (5.18) (6.00) (5.77) (6.24) (6.36) (6.50)

WarrantReturnkt 2 -1.1269 -0.8511 -0.8575 -0.2984 -1.1158 -0.5406

-(11.00) -(3.92) -(11.73) -(2.47) -(9.59) -(2.73)

WarrantReturnkt 3 -0.0150 0.0503 -0.0630

-(0.16) (0.61) -(0.53)


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TurnoverRatiokt 1 0.0010 0.0004 0.0000 0.0009 0.0003 -0.0001 0.0005 0.0002 -0.0003

(8.64) (3.51) -(0.17) (7.76) (2.27) -(0.66) (4.80) (1.18) -(1.52)

TurnoverRatiokt 2 0.0006 0.0008 0.0005 0.0008 0.0006 0.0008

(4.14) (4.42) (4.48) (4.61) (4.92) (4.73)

TurnoverRatiokt 3 0.0000 0.0000 0.0001

R 2 0.3936 0.5189 0.5273 0.4001 0.5258 0.5325 0.4038 0.5291 0.5355

Observations 180,138 175,100 170,681 180,138 175,100 170,681 180138 175100 170,681

Conclusion

• We find evidence inconsistent with a leading theory of bubbles, the resale option theory of Scheinkman and Xiong (JPE, 2003)

• We find evidence that the order imbalances due to the trades of new investors forecast returns

• We present strong evidence that social contagion was an important determinant of the entry of new investors into the warrant market, consistent with arguments of Shiller and various coauthors

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investor trading during the chinese put warrants bubble*

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