Market Making and Mean Reversion
Chakraborty and Kearns test the profitability of a market making algorithm as a security’s price changes over time using time series models, and find that market making strategies are generally profitable for mean-reverting time series models. For purposes of this paper, a market making algorithm is defined as a strategy which electronically buys and sells a product simultaneously in order to profit from the difference between the product’s bid and ask price. A distinction between market making algorithms and pure statistical arbitrage algorithms is made.
A market making algorithm is designed to reduce directional risk by acquiring a relatively equal number of long and short positions. Therefore, a non-directional market with high volatility is ideal for this type of algorithm. Alternatively, a statistical arbitrage algorithm seeks to exploit directional markets by acquiring an imbalance of long and short positions in order to make a profit.
A market making algorithm is most profitable with any random walk that reverts to its opening price. The authors use the Ornstein- Uhlenbeck (OU) process to show a market making algorithm is profitable when run for a sufficiently long period of time, with profit growing linearly with time. The OU process assumes the volatility of a price curve is constant, while another model used, the Schwartz model, assumes volatility is a linear function of price. These models are illustrated in the paper.
One limitation to this study is that it considers no market impact of executed orders placed by the algorithm on future prices. However, the data does show that even when mean reversion is weak, market making strategies can be profitable over an ample period of time.