Conclusiones

In the simulation experiments, we compare different scenarios which are configured as follows. In each scenario the base configuration is extended by one additional group of aggressive traders which has not been part of the base configuration. A group is specified by a particular aggressive strategy and a particular latency. Figure 5 shows the results of the simulation experiments. The plots corresponding to the base configuration are denoted as

‘base’. The key of the abbreviations, and the scheme of the Box-Whisker plots, is the same as in figure 4. To capture the effects of market efficiency and trading, eight indicators are used.

Most of these indicator are already known from the quantitative validation of the model presented in Section 5.1. Two indicators are new: adaption time and distortion. Adaption time denotes the time between two moments in which the dynamics of prices and the fundamental value cross each other or are equal. This interval can be read as a measurement of the tendency of prices to adapt to changes of value. Distortion refers to the mean absolute difference between price and value.

As a first insight, we observe that intraday volatility rises, if trend followers are induced (top row, left panel). Furthermore, the distortion in the market is enhanced (third row, right). This applies for both, the LF-trading and the HF-trading group. The insight that trend-followers deteriorate market efficiency is already well-known (see Beja and Goldman, 1980, and followers). Trend followers exacerbate price movements by trading on them. In this way, they tend to drive prices away from value. In our model, the greater volatility of prices feeds back to the volatility expectations of traders. As traders observe greater volatility, they expect greater price movements in the future. If returns are expected to be greater, losses due to the bid-ask become less weighty. As a result, traders expect more transactions to be profitable.

This disembogues into a rise of the trading volume (bottom, left). As trend followers are aggressive traders, the liquidity of the market decreases and the bid-ask spread growths (bottom row, right). Furthermore, we observe trend-following to produce a decrease of the tail-index of the return distribution (second row, left and right). In other words, the share of extreme returns rises. This is due to the fact that trend-followers induce positive feedback in the dynamics of prices. As a result, the power-law shape of the return distribution becomes more pronounced.

Mean traders behave contrarily to trend followers as they bet on price movements to revert. This behaviour tends to dampen price movements. This leads to a lower result for intraday volatility (top row, left). As traders expect lower volatility in the future, fewer transactions are expected to be profitable and trading volume declines (bottom, left). The lower absorption of liquidity, finally leads to a reduction of the bid-ask spread (bottom, right).

We can conclude that trend followers tend to destabilize the dynamics of prices. In contrast, mean traders stabilize the dynamics; however they tend to detain prices from adjusting to value (third row, left).

Figure 5: Market efficiency – same number. Indicators of market efficiency for the base configuration and six scenarios in which the base configuration is extended by 10 traders of a particular group. For key of abbreviations see figure 4.

In contrast to the results for mean-reversion traders and trend-followers, the results for noise traders and event-traders are less significant. The effects of high frequency noise traders on adaption time and market distortion constitute exceptions. Since noise traders do not account for the fundamental value, they tend to increase both indicators (third row, left and right).

A very important observation can be made with respect to the dimension of the effects established. Apart from the tail index, the effects are more pronounced if the respective strategy is used by low frequency than by high frequency traders. This finding becomes more astonishing by considering the degree to which the different groups participate in trading.

Figure 6 illustrates the share of the total trading volume for each group. The plots show that HF-trend followers and HF-noise traders have a significantly greater share of trading than the respective LF-groups. We can conclude that HF-trend followers have a relatively little effect of price dynamics although their participation in trading is relatively great.

Figure 6: Trading shares. The share of each trader group of the value of the total trading volume in the market. For key of abbreviations see figure 4.

To control for differences in trading shares, we conduct a second series of experiments. This time, we induce as many traders of the different groups as needed to get approximately equal shares in trading (here: about 5%). The results are displayed by figure 7. This time, the difference in the size of the effect of HF-groups and respective LF-groups is even more pronounced. Whereas the LF-groups produce significant changes of several indicators, the influence of the respective HF-traders is very slight.

Figure 7: Market efficiency – same volume. The same as in figure 5 but this time the number of traders of the additional groups is as high as needed to produce approximately the same the trading volume from each of these groups. For key of abbreviations see figure 4.

Figure 8: Market efficiency – same volume, same inventory control. The same as in figure 7 but this time the inventory coefficient of HF-traders is set equal to the one of LF-traders (𝒗𝑯𝑭𝑻= 𝒗𝑳𝑭𝑻,⅂𝒎𝒎). For key of abbreviations see figure 4.

The difference between the influence of HF- and LF-groups can only be due to those parameters which discriminate between these groups. These properties are (i) the latency of traders (𝜂𝑔) and the degree of inventory control (𝑣𝑔). The following experiment will turn out that the crucial parameter is inventory control, while the role of speed is relatively humble.

This finding can be gained by annihilating the difference in inventory control between HF- and LF-traders. This is achieved by setting 𝑣_𝐻𝐹𝑇 equal to 𝑣_{𝐿𝐹𝑇,⅂𝑚𝑚}. In other words, we construct a hypothetic scenario in which HF-traders do not adhere to a stricter inventory control than other traders. Figure 8 displays the results.

This time, most effects of the HF-groups seem to be equal or slightly greater than the effects of the respectively LF-groups. In sum, we cannot detect significant differences between the effects of LF- and HF-groups anymore. This observation indicates that the strong inventory control of HF-traders reduces their effects for the dynamics of prices. We believe the explanation for this finding to be quite simple. To achieve low holding times, any long or short positions that has been build up, needs to be liquidated short time later. This implies that HF-trading need to reverse any transaction quickly. For example, if they have bought in one moment, they are going to sell some seconds or minutes later. The reversion of transactions tends to level out the impetus induced by the original transaction. In this way, due to their rigorous inventory control, aggressive HF-traders tend to annihilate their impacts on the price dynamics quickly and autonomously. As a result, their effect for the dynamics of prices is relatively low.