I. INTRODUCCIÓN
1.2. Trabajos previos
Testing the Marginal Trader Hypothesis.
I use a statistical measure of herding proposed by Lakonishok et al. (1992). The authors argue that herding behaviour can only be detected within subsets of traders. Hence, this particular measure of herding behaviour is extremely suitable for my experiments because is based on trades conducted by a subset of market participants such as ‘Best Agents’ and ‘All Agents’ over a period of time. I measure herding behaviour as the average tendency of a group of traders (‘Best Agents’ and ‘All Agents’) to buy (sell) Dow Jones, IBM and GE at the same time. This herding behaviour measure accesses the correlation in trading patterns for a particular group of traders and their tendency to buy and sell the same set of financial instruments. Hence, herding behaviour leads to correlated trading.
The measure of herding behaviour for a given financial instrument i, in a given trading day t, H i t
, , is defined as
H i t ,
B i t ,
/B i t,
S i t,
p t
AF i t ,
(30)
Let B i t
, S i t
, be the number of traders in this subset who buy [sell] a financialinstrument i in trading day tand H i t
, be the measure of herding in financial instrument ifor trading day t. In other wordsB i t
, is the number of traders who increase their holdings in Dow Jones, IBM and GE in the trading day (net buyers), S i t
, is the number of traders who decrease their holdings (net sellers), p t
is the expected proportion of cash traders possess in that trading day.The adjustment factor AF i t
, is related to the fact that under the null hypothesis of no herding, i.e. when the probability of any trader being a net buyer of any financial instrument isp t
, the absolute value of B i t
,
B i t, S i t
,
p t
is greater than zero.114
,AF i t is, therefore, the expected value of B i t
, /
B i t
, S i t,
p t
under the null hypothesis of no herding. Since B i t
, follows a binomial distribution with probabilityof
p t success,AF i t
, can be estimated given p t
and the number of agents trading in that financial instrument in that day. For any financial instrument,AF i t
, declines as thenumber of agents trading in that financial instrument rises (Lakonishok et al., 1992 and Bikhchandani and Sharma, 2001).
The herding measures in my experiments are computed for each financial instrument – trading day and then averaged across different subgroups such as ‘Best Agents’ and ‘All Agents’. Values ofH i t
, significantly different from zero are interpreted as evidence of herding behaviour.Tables 8.0, 9.0 and 10.0 represent my main results on herding behaviour. The third and fourth column of the tables reports the mean and median herding measures for the whole sample. The mean herding measure (the key measure) of Dow Jones at 1% ‘Best Agents’ is 0.048 and it implies that if p t
, the average fraction of changes that are increases, was 0.5, then 54.8% of the traders of ‘Best Agents’ subgroup were changing their average holdings of Dow Jones in one direction and 45.2% in the opposite direction. The presence of herding is also confirmed by the relatively large median herding measure of 0.011. However, herding behaviour is less prominent when the market is populated by more artificial traders. For instance, the remainder of the market represented by ‘All Agents’ group indicate that only 53.7% of the traders change their average holdings of the index in one direction and 46.3% in the opposite direction. Table 8.0 illustrate the same statistical trend at 5%, 10% and 20% levels.IBM herding statistics (Table 9.0) demonstrate the presence of substantially less herding behaviour. For example, the mean herding measure of IBM at 20% ‘Best Agents’ shows that 50.9% of the traders change their average holdings of the security in one direction and 49.1% in the opposite direction. ‘All Agents’ at 20% level of the same security indicate insignificant herding behaviour of 50.4% of the traders change their holdings of IBM in one direction and 49.6% in the opposite direction.
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The median herding measure is even smaller, only 0.001, which suggest that there is very insignificant herding behaviour. GE herding statistics on Table 10.0 also indicate the presence of less herding comparing to Dow Jones.
1% N Mean Median Best Agents 17441 0.048* 0.011* All Agents 17441 0.037* 0.008* 5% Best Agents 17441 0.042* 0.010** All Agents 17441 0.030* 0.006* 10% Best Agents 17441 0.039* 0.008* All Agents 17441 0.024* 0.005** 20% Best Agents 17441 0.021* 0.006* All Agents 17441 0.013* 0.002*
Table 8.0 Dow Jones herding statistic based on 17,441 trading days for ‘Best Agents’ and ‘All Agents’.
*Results are statistically significant at the 1% level. **Results are statistically significant at the 5% level.
The mean and median herding statistics are presented for ‘Best Agents’ and ‘All Agents’. The herding statistic for a given day is defined as H i t , B i t , /B i t, S i t , p t AF i t , where B i t , is the number of traders who increase their Dow
Jones holdings in the day (net buyers), S i t , is the number of traders who decrease their Dow Jones holdings (net sellers),
p t is the expected proportion of traders buying in that day, and AF i t , is the adjustment factor explained in the text. The herding measures are computed for Dow Jones in each day and then averaged across ‘Best Agents’ and ‘All Agents’.
116 1% N Mean Median Best Agents 17441 0.031* 0.004* All Agents 17441 0.025* 0.002** 5% Best Agents 17441 0.029** 0.003* All Agents 17441 0.017* 0.001* 10% Best Agents 17441 0.018* 0.002* All Agents 17441 0.010* 0.001* 20% Best Agents 17441 0.009* 0.001* All Agents 17441 0.004* 0.001*
Table 9.0 IBM herding statistic based on 17,441 trading days for ‘Best Agents’ and ‘All Agents’.
*Results are statistically significant at the 1% level. **Results are statistically significant at the 5% level.
The mean and median herding statistics are presented for ‘Best Agents’ and ‘All Agents’. The herding statistic for a given day is defined as H i t , B i t , /B i t, S i t , p t AF i t , where B i t , is the number of traders who increase their IBM
holdings in the day (net buyers), S i t , is the number of traders who decrease their IBM holdings (net sellers), p t is the expected proportion of traders buying in that day, and AF i t , is the adjustment factor explained in the text. The herding measures are computed for IBM in each day and then averaged across ‘Best Agents’ and ‘All Agents’.
1% N Mean Median Best Agents 17441 0.035* 0.005* All Agents 17441 0.021* 0.002* 5% Best Agents 17441 0.027* 0.005* All Agents 17441 0.018** 0.002* 10% Best Agents 17441 0.020* 0.003* All Agents 17441 0.011* 0.001* 20% Best Agents 17441 0.013* 0.002** All Agents 17441 0.005* 0.001*
Table 10.0 GE herding statistic based on 17,441 trading days for ‘Best Agents’ and ‘All Agents’.
*Results are statistically significant at the 1% level. **Results are statistically significant at the 5% level.
The mean and median herding statistics are presented for ‘Best Agents’ and ‘All Agents’. The herding statistic for a given day is defined as H i t , B i t , /B i t, S i t , p t AF i t , where B i t , is the number of traders who increase their GE
holdings in the day (net buyers), S i t , is the number of traders who decrease their GE holdings (net sellers), p t is the expected proportion of traders buying in that day, and AF i t , is the adjustment factor explained in the text. The herding
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My observations suggest that the price formation caused by the collective behaviour (competition and co-evolution) of the entire market is more cohesive than that of any small subset of agents. This is due to the greater genetic diversity that is represented in the total population leading to more diverse (heterogeneous) trading rules and behaviour. Moreover, greater genetic diversity means greater flexibility in the virtual market clearing price
mechanism. At a broad level my results do not support the Marginal Trader Hypothesis (MTH) which explains market efficiency as a consequence of the actions of a small pool of traders such as ‘Best Agents’ who are capable of setting prices and acting without bias. In fact, it seems that the virtual market populated by ‘All Agents’ reacts to price changes in a timely manner.
All my experiments indicate that there is no tendency towards price crashes or bubbles. Hence, herd behaviour causes no long-run mispricing of assets because the market is consistent with the steady flow of information. It is a well-known fact that bubbles and herding behaviour are difficult to be appropriately identified and their magnitude cannot be determined until after the fact. This limits the ability of policymakers to respond to them in efficient manner. Both phenomena have an indirect effect on the economy, because investors and firms alter their behaviour in response to the price changes. For instance, when a particular corporation’s asset price rises, the corporation may respond by increasing its physical capital investment spending higher than it otherwise would have. This suggests that herding behaviour and bubbles may cause a misallocation of resources leading to economic inefficiencies. The inflation and growth is likely to rise above a sustainable level, forcing central government intervention such as raising interest rates. On the other hand, high interest rates increase a firm’s borrowing costs, leading to reduced profitability. The convergence of action of traders in my experiment provides valuable information to the policymakers about whether they should be concerned about the presence of bubbles and herding and their destabilising effects. I found evidence of herd behaviour over daily time intervals to be much stronger, revealing the short-term nature of the phenomenon. My experimental results are in line with the theories of Avery and Zemsky (1998) and DeLong et al. (1990) that herding causes asset prices to deviate from fundamentals. Decamps and Lovo (2002) argue that herding behaviour prevents agents from learning the market fundamentals.
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However, there is no evidence of a price-destabilising process in place, as the market discounts the informativeness of trades during herding (Avery and Zemsky, 1999). Generated Dow Jones prices do in general follow fundamentals in the long run, but they periodically depart from them, which is more evident in the case of the ‘Best Agents’ price series.
My results confirm the claim of Decamps and Lovo (2002) that asset prices ultimately converge to fundamentals in the long run:
Pr(lim ) 1 t
tE V H V
(31) Where V represent the true value of the security at time t, E is the expected value of the asset at time t,H describes the history of agents actions up until time t t.
Tables 8.0, 9.0 and 10.0 empirically show that the presence of herding in individual stocks is broadly consistent with the findings of Lakonishok, Shleifer and Vishny (1992) and
Bikhchandani and Sharma (2001), which claim that the possibility of observing intentional herding behaviour at the level of individual stocks is relatively low.
My artificial stock market observations indicate that herding is more likely to occur at the level of investment in a group of stocks, such as Dow Jones than at the level of individual stocks. Lakonishok et al. (1992) suggest that this is due to swings in demand for a group of stocks which have a large effect on stock prices than swings in demand for individual stocks. Moreover, the authors argue that companies might also be more apt to herd in industry groups as opposed to individual stocks. Bikhchandani and Sharma (2001) argue that is unlikely that investors observe each other’s holdings of individual stock soon enough to change their own portfolios. This is the reason why according to the authors one is more likely to find herding in a group of stocks. The other reason for the presence of more herding in a group of stocks is that different companies within the group migh try to infer information about the quality of investments from each others’ trades and herd as a result (Shiller and Pound, 1989; Banerjee, 1992; Bikhchandani et al., 1992). However this does not exclude the possibility of more extensive herding behaviour in particular categories of stocks, such as stocks of a specific size or performance record (Lakonishok et al., (1992).
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There has been an argument that herding should be more persistent within particular industry groups of stocks, such as technology ones, due to their uncertain cash flows. From this point of view, one might expect to record significantly more herding in IBM stocks than General Electric stocks. Experimental tests with IBM assets indicate that there is weak presence of herding behaviour observed in price series generated by both ‘Best Agents’ and ‘All Agents’ at all different group sizes.
Artificial traders simulate a dynamic and competitive market based on the survival-of-the- fittest principle. This type of stock market is characterised by large order flow and small price fluctuations. My findings correspond to the well-known empirical fact that large fluctuations in prices are highly likely to emerge in less active markets with small order flow (Cont and Bouchaud, 2000).
Cont and Bouchaud (2000) quantified this process using the statistic:
32
1
1
/ 2
1
c x orderk
n
c
A c
c
(32)where kmeasures the kurtosis, norderis the order flow; A c
is a normalisation constant with a value close to 1. The equation above explains that kurtosis
k of the price change is inversely proportional to the order flow norder.In other words a market with small order flow (illiquid market) is more likely to experience large price fluctuations with higher frequency than a market where there are substantially more orders processed per unit time as is the case in my artificial stock market.
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5.3.2 Volatility analysis of price series generated by ‘Best Agents’ and ‘All Agents’. Is the