Roy Roth and Dr. Scott Condie, Economics Department
Hidden limit orders have been increasingly important in asset markets over the past several years. These orders are hidden in the sense that they are not displayed or announced in any way until another order is sent to the market that trades with the hidden order. Traditionally, the two major order types in asset markets are market orders and limit orders. A market order contains instructions to buy or sell a given number of shares of a specific asset immediately at the best possible price, while a limit order signals a trader’s willingness to buy (sell) a certain number of shares of a specific asset at a price no higher (lower) than a given price. Market orders are generally executed immediately, while a limit orders remain active until traded against (generally with a market order) or cancelled. For this reason, limit orders accumulate for an asset and form what is known as the limit order book. For instance the limit order book for theoretical asset XYZ could have orders to sell 100 shares at $10.01 and $10.02 and buy 100 shares at $9.99 and $9.98. If a market order to buy 200 shares hit this market, 100 shares would be bought at $10.01 per share and an additional 100 shares would be bought at $10.02 per share. However, if a hidden limit order to sell 100 shares of asset XYZ were on the book at a price of $10.00 per share, the transaction would be very different. In that case the first 100 shares would be bought a $10.00 and the second 100 at $10.01. Despite the fact that the hidden limit order does not change the way the market looks before the market order is submitted, it clearly has a large effect on the outcome. In this project we are interested in analyzing when traders would use a hidden order versus a visible order, and how other traders respond when it is revealed that hidden order is executed. An important consideration in this analysis is the set of rules markets use to determine order priority. Because we use NASDAQ data, we use their rules in our model, specifically that limit orders are given priority first based on price, then on hidden status (visible orders at the same price are prioritized over hidden orders), and finally by the time the order was placed.
We use an extension of the Glosten-Milrom (1985) model of market makers that allows for hidden orders. In this model there is one asset and 3 types of agents: noise traders who trade for exogenous reasons, speculators attempting to make money by predicting whether the asset’s price will move up or down, and market makers who try to make money by providing liquidity to both speculators and noise traders. In this model, there are 3 states of the world, in one state no information event occurs, in the second an event occurs indicating that the price of the asset should be lower, and finally an information event could occur signaling the price of the asset should be higher. Speculators know what state of the world has occurred and trade accordingly. Noise traders trade for exogenous reasons regardless of what has happened, and market makers adjust their limit orders in a Bayesian fashion based on the market orders they observe. For instance, if a lot of buy orders come in, that increases the likelihood that a positive information event has occurred, and market makers adjust their prices upward.
Furthermore, in our model market makers are heterogeneous, informed market makers know if an information event has occurred (though they do not the direction) while uninformed market makers do not know if an information event has occurred. If no event has occurred, there is little uncertainty about the price of the asset, so the spread (the difference between the lowest offer and the highest bid) should be narrow, however, if an event occurs it could be good or bad, thus there is a great deal of uncertainty about the price and thus spreads should be wide.
In our model there exists an equilibrium where the informed market makers place hidden orders inside the spread when no information event has occurred, and place visible limit orders outside the spread when an information event has occurred. This equilibrium generates two testable predictions. The first is that when a hidden order is executed inside the visible spread, in the subsequent milliseconds the visible spread should tighten. The second is that when limit orders begin to accumulate outside of the visible spread it should widen in the coming milliseconds.
Using data from NASDAQ, one of the largest asset markets in the United States, we are able to reproduce the limit order book for all assets traded on NASDAQ. Additionally, we are able to observe the execution of hidden orders. With this data we can directly test the two predictions of our model. Specifically, we run the following two regressions for each asset each day:
Γt+Δ = φ0 + φ1OSt + ηt.
Where Γ represents the spread, h represents the execution of a hidden order (with the control group being the executions of visible limit orders) and OS representing a visible order placed outside the current spread (with the control being orders placed at or inside the spread). Our model predicts that β1 should be negative while φ1 should be positive. Our tests largely support these hypotheses. Most tests of the first hypothesis give statistically significant (5% level) results in the right direction for 30-40% of assets (around 50% yield insignificant results). Support for the second hypothesis is even more pronounced with statistically significant (5% level) results for about 60% of assets across several specifications.
Though far from a complete treatment of the use of hidden orders, these results are nevertheless informative, and indicate that differentially informed market makers may be using hidden orders to attempt to profit from an information advantage. We are also working on an alternative model where speculators choose to use hidden limit orders rather than market orders to take a position. Further work could focus on the effect that hidden orders have on market efficiency and how they should be treated from a regulatory point of view.
Glosten, L. R., & Milgrom, P. R. (1985). Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of financial economics, 14(1), 71-100.