*4.1. Experiment 1: Liquidity*

We use e ffective half-spread as our measure of liquidity (e.g., Hendershott and Riordan 2011). As half-spread decreases, liquidity increases. Half-spread is calculated as:

$$\text{Half spread} \, = \, (\text{sign}) \, \frac{\text{(trade price } - \text{ midpoint)}}{\text{midpoint}} \, ; \tag{6}$$

where trade price is the price at which trade occurred, midpoint is the price halfway between the transacting bid and ask price, and sign is determined by how the trade was initiated. If a seller initiated the trade then sign = 1, if a buyer initiated the trade then sign = −1. We compute the half spread at 800 evenly distributed points in time over the course of every single 30-day run (see Table 1). At the end of each run, we compute the average half-spread over the recorded 800 values. Each point on the curve in Figure 1 is thus the average of 50 average half spreads (Table 1). We present the results with 95% confidence intervals. For the first point on the graph, our simulation has 1000 human technical traders and 1000 human fundamental traders, with no algorithmic traders. In each successive point of the graph, the proportion of algorithmic traders increases. The number of technical and fundamental traders is equal at all points.

**Figure 1.** Impact of AT on market liquidity measured by the half-spread.

Results indicate that AT has a dramatic liquidity increasing effect early in its adoption. By the time AT reaches 10%, most of the benefit has already been gained. Further increase in the share of AT contributes very little to liquidity. This result indicates an interesting new hypothesis for the empirical literature: as AT presence increases in developing countries, where it is still only a fraction of the total market, empirical studies could estimate if there is a threshold where most of the benefit of AT already accrues to the country. This would provide practical insight into the timeline of AT impact on market quality in developing countries where AT adoption is still at a nascent stage.

### *4.2. Experiment 2: Statistical Arbitrage*/*Pairs Trading*

Our goal is to determine the impact of statistical arbitrage/pairs trading. Statistical arbitrage is a strategy to profit by trading based on short-term correlations, while assuming that these correlations will persist. We simulate two fundamentally unrelated (low positive correlation) stocks. We introduce fundamental traders and pairs traders and measure the correlation of the prices and the correlation of the fundamental values of the stocks as the proportion of pairs traders increases.

The results in the form of the correlations between the two paired stocks are shown below in Figure 2. All details of the simulation are given in Table 1. The set-up is similar to Experiment 1 except for the types of traders. Figure 2 shows that the correlation of prices is significantly higher than the correlation in fundamental values of the two stocks. This is in line with empirical findings and anecdotal evidence that indicate AT leading to co-movements in market prices of assets (e.g., Zweig 2010), and price spillovers across assets (e.g., Kelejian and Mukerji 2016), which are above and beyond what fundamentals alone can explain.

**Figure 2.** Impact of AT on relation between price and fundamentals.

To take a closer look at what unfolds over the course of a typical run, we present Figure 3, which shows what the market looks like when no Pairs traders are present.

**Figure 3.** Single run of the simulation with no algorithmic traders in the market.

In this run, we control the fundamental values rather than randomly generating them. The first stock's fundamental value is a step function that increases and then decreases. The second stock's fundamental value line is the flat line. We see that when there are no Pairs traders, the prices stay near their corresponding fundamental values. In contrast, in Figure 4 we show the same simulation run now with the market comprising 50% algorithmic Pairs traders that trade on the assumption of positive price correlation. The prices in this case are far from their fundamental values and are highly correlated with one another.

**Figure 4.** Single run of the simulation with 50% algorithmic pairs traders in the market.

This strong impact of AT on prices lends support to findings such as that the initial price impact of an algorithmic trade is larger than that of human orders (Hendershott and Riordan 2011; Hendershott et al. 2011) or that AT contribute significantly to the price discovery process (Brogaard 2010). Our contribution is to show the possibility that the price discovery process might be led astray, due to the strategy combined with the speed of the AT, as we see in Experiment 2.
