Frontrunning the signals: As arbitrage between sophisticates

This paper presents a model in which some sophisticated investors do not wait for receipt of a signal before purchasing an asset. Its critical innovation is an arbitrage equation for frontrunning. Some sophisticates who will receive information in the next period arbitrage against similar sophisticates who will act on that information in that next period when the information is received. The costs of such frontrunning are borne totally by unsophisticated traders—with no gain or loss to sophisticates. Nor does the frontrunning produce any information discovery. Thus, this paper describes a financial-market anomaly: of inefficient financial transactions with gains to no one.

This paper develops a model, whose key feature is a special form of frontrunning, in which sophisticated traders purchase assets in advance of a signal that will be uniformly received by all sophisticates. The price of the asset before receipt of the signal then exactly equalizes the returns to two strategies. One strategy is to buy now; keep the asset if the signal is positive/dump onto unsophisticated traders if the signal is negative. The other strategy is to wait for the signal; then buy the asset if the signal is positive/do not buy if negative. In the model the added transaction costs of buying the asset and selling it if the signal is negative are all absorbed by the unsophisticated traders. Yet, even though the unsophisticated traders are paying for all of the costs of the frontrunning, there are still no gains at all from this trading activity to the sophisticates. (In this paper we use “frontrunning” according to a general vernacular usage: as preemptive action that anticipates similar action by others; this is in the same spirit as—but much more general than—the more specific use of the term in finance as “trading before other traders, based on specific information about the direction in which other traders will trade in the future”).^*While the model in this paper is very special, it raises a question of considerable generality. There is a significant literature regarding the surprising rise in the Gross-Domestic-Product share of the financial sector [Philippon (1)]. Zingales (2) has been similarly concerned with excessive rent seeking in financial markets. Turner (ref. 3, p. 44) has said, further, that “financial activity [goes] beyond those [that] deliver true social value…. Numerous studies have shown that much active asset management adds no value but does add significant cost.” He has also described the huge increase in “intrafinancial” transactions. In casting light on a special case of such transactions, with no gains to those who instigate increased trading, this paper then poses the question, whether there are not many examples of this ilk: in which the returns to the arbitrageurs themselves are negligible, but the costs of this much ado about nothing are borne by unsophisticated others on the sidelines.This paper is based on a three-period barebones model with both sophisticates and unsophisticated traders and also with short-sale constraints. In period 2 the value of the asset is revealed to sophisticated traders; in period 3 its value becomes known to everyone. With transaction costs below a threshold, in period 1 some sophisticated traders will purchase the asset in anticipation of the signal that they will receive in the following period. If the signal in period 2 is positive, they will keep the asset; if it is negative, they will dump it onto the unsophisticated traders. The returns to sophisticates are exactly the same as in the corresponding model, in which trades can only occur in periods 2 and 3, after the revelation of the value of the asset to the sophisticates.The model in this paper thus describes a type of frontrunning absent from previous papers. The literature on frontrunning of which we are aware—notably including Lewis’ Flash Boys (4)—concerns the information advantage of the frontrunners. In those papers frontrunners obtain information in advance of their competitors. That is not what is happening here: These sophisticated frontrunners in period 1 do not have advance information relative to their fellow sophisticates, who will be their competitors in the next period if the signal is positive. Instead, they are making those early purchases (in period 1) to obtain a better price for the asset in anticipation that their sophisticated competitors will bid up that price if the signal is positive. In this case the price in period 1 will just settle at the margin at which the returns to two strategies are exactly equalized; that is, the returns to buy now/dump later in the event of a negative signal are exactly equal to the returns to wait for the signal/buy if positive.The returns to the sophisticates are totally independent of the existence, or nonexistence, of this equilibrium frontrunning. Why so? Because the returns to the sophisticated buyers are anchored: since the number of sophisticates in period 2 who hold the asset will be the same, irrespective of the purchases in period 1. Specifically, the exact same number of sophisticates will hold the asset if the signal is positive; no sophisticates will hold it if the signal is negative (since the period 1 buyers will dump it, and no one else will buy it). Hence the price of the asset in period 2 is anchored. But that means, in turn, that the unsophisticated traders will pay all of the transaction costs involved in the arbitrage.^†Our barebones model also yields some additional results: 1) prices in excess of fundamentals, which are greater with higher probability of a positive signal; 2) increases in losses with increase in the number of sophisticates; and 3) amplification of frontrunning with sequential signals.This paper proceeds as follows. Review of Literature reviews the literature. The Model presents a model of frontrunning. Transaction Costs analyzes the effects of transaction costs and calculates the losses to unsophisticated traders caused by frontrunning. Sequential Signals examines the effects of sequential signals. Conclusion concludes.