**1. Introduction**

Algorithmic trading (AT) in US stock markets has grown at a blistering pace, starting from the mid-1990s when it accounted for only 3 percent of the market, to recent times when it has reached almost 85% of dollar trade volumes (Zhang 2010). What we learn from markets like the US where AT has progressed very far, can be practically useful in charting the path ahead for developing countries, where AT is still at a nascent stage (Sherry 2017).

The aim of this paper is to bridge the gap between researchers' empirical results and the real-world attempts (e.g., by regulators) to understand how each algorithmic trading strategy works. We do this by using simulations to systematically demonstrate how the behavior of various algorithms result in the observed impact on market quality (liquidity, price spreads, trade-related price discovery, and correlation of asset prices).

Specifically, our simulated markets give us the flexibility to start from the AT strategies of our choosing and simulate the resulting market outcomes. In this way, our work attempts to evaluate if AT strategies can indeed lead to the market outcomes that empirical studies have deduced from market data. Our line of research can also aid market regulators by providing a platform capable of isolating and testing the market impact of specific AT strategies.

Empirical analysis of algorithmic trading have estimated its impact on various aspects of market quality (see for example, Brogaard 2010; Brogaard et al. 2014; Chaboud et al. 2014; Hasbrouck and Saar 2013; Hendershott et al. 2011; Hendershott and Riordan 2011; Kelejian and Mukerji 2016; Menkveld 2013; Riordan and Storkenmaier 2011; Zhang 2010). However, many of the findings are contradictory. These contradictions in the empirical literature may be the result of differences in methodologies, time periods, and samples of assets analyzed. Even in the same work, there are often differences in the degree to which the impact of algorithmic trading is felt in among different types of assets, and transactions. In addition, for each empirical finding there are different explanations that could produce the observed impact of algorithmic trading.

In its actual work in the practical world, algorithmic trading has made rapid progress in technology, and this has led to an arms-race among participants for acquiring the fastest and most efficient algorithms and machines (Hasbrouck and Saar 2013). As a side e ffect, increased competition has eroded profits. Regulators have also clamped down on algorithmic trading, following accusations of market manipulation (McCrank 2015). Market manipulation, once thought of as a predominantly developing market issue (Sohel Azad et al. 2014), has now featured quite prominently in developed countries via AT. One of the outcomes of this scenario is that AT is resorting to high risk strategies in hopes of making profits (Philips 2013).

These factors indicate that it would be useful to go a step beyond measuring AT's impact and attempt to unravel how this impact is actually created by the operation of di fferent strategies in AT. Toward this ultimate goal, in this work, we create a computer simulation of the asset market. Our computer simulation gives us the capability to characterize the impact of AT on market quality and test its sensitivity to changing situations such as the volume of algorithmic versus human trading. Since proprietary trading algorithms are not public information, we make simplifying assumptions about the traders that allow us to approximate their behavior. Naturally, the algorithms that actually operate in the marketplace have developed nuances that this exercise does not capture. However, we expect that our results still provide a useful estimation of overarching and longer-term market outcomes.

We model two trader types: fundamental analysts and technical analysts. Both types of traders can be either human or algorithmic. We simulate the behavior of traders to test the liquidity and price discovery in the market as the percentage of algorithmic traders' increases. As a measure of liquidity, we use e ffective half-spread (e.g., Hendershott and Riordan 2011). Our results indicate that liquidity improves as the proportion of algorithmic traders increase, although most of the liquidity increase is achieved at very low levels of AT. We also investigate statistical arbitrage, which is a commonly used AT strategy, where algorithmic traders use short-term price correlations to predict price movements, and trade to profit from them. Our simulations measure the extent to which this may lead to price movements unrelated to fundamentals. Our findings indicate a significant movement away from fundamentals, with the rise of AT.

Thus, our findings match the real world where AT has changed the landscape of market transactions and has had profound implications for market participants (e.g., Kelejian and Mukerji 2016), and for those charged with market oversight (e.g., U.S. Commodities Futures Trading Commission and U.S. Securities and Exchange Commission 2010). The reason for the changes being experienced is the important di fferences that set human and algorithmic traders apart, even though their strategies might seem similar. First, AT can make decisions based on much more information and much faster than human traders (Hasbrouck and Saar 2013). Second, human traders use their judgement in addition to trading strategies. AT, on the other hand, makes decisions mechanically. This mechanical decision making may sometimes lead to absurd and undesirable outcomes (Zweig 2010). Recognizing this shortcoming in AT, firms designed safeguards where, under defined conditions, there is a trigger that makes the AT stop for human input (U.S. Commodities Futures Trading Commission and U.S. Securities and Exchange Commission 2010). However, the system is far from perfect and has led to occasional turmoil in the markets. For example, investigation into the "flash crash" of 2010 revealed that a set of algorithmic trades had led to a cascading of prices and extreme volatility. This triggered a practical shut down of markets as ATs paused for human input (U.S. Commodities Futures Trading Commission and U.S. Securities and Exchange Commission 2010).

By providing a clear focus on how AT strategies lead to market outcomes, our findings deepen our understanding of the real-world workings of the asset market, as the participation of AT increases. They serve to clarify existing empirical results in the literature, as well as to sugges<sup>t</sup> future avenues

of empirical research. Specifically, our findings in both experiments provide some support for the existing empirical results in the literature. In each case, they also provide practical nuances in the results, which can be used to form new hypotheses for future empirical work.

The rest of the paper is laid out as follows. Section 2 presents the literature review. Section 3 lays out our simulated market model, while Section 4 presents the experiments based on varying the degree of AT participation and evaluating the impact of AT strategies. Section 5 concludes the paper.
