The “limits of arbitrage” agenda

Dimitri Vayanos, Denis Gromb, 10 April 2010

a

A

Each financial crisis reminds us that governments are vital to the functioning of financial markets – with the current crisis being a particularly painful reminder (see for example Boone and Johnson 2010, Dewatripont et al. 2009).

Standard models, however, are ill-suited to analysing public policy. These models were developed to study the properties of asset prices; they typically ignore financial institutions and the financial constraints to which they are subject. Institutions, jointly labelled “arbitrageurs” in the theory, are instead assumed to have unfettered access to all the capital they need.1

Frustratingly optimistic theory

For economists with a public policy interest, what one might call the “unconstrained arbitrage” hypothesis delivers a frustratingly optimistic message. Financial markets are in a socially efficient equilibrium; consequently, public intervention is at best redistributive and at worst inefficient. This result, a special case of the so-called fundamental welfare theorems, captures the idea that in a free market economy, prices adjust so that profit-maximising agents end up making socially efficient choices.

Recent developments in financial economics may offer a more useful framework for policy analysis. To understand how these developments came about, we must take a step back and understand what unconstrained arbitrage really means for asset prices, the empirical challenges this hypothesis has met with, and the new theories emerging to deal with those challenges.

No free lunch on Wall Street

The main implication of the “unconstrained arbitrage” hypothesis is that there should be no arbitrage opportunities in equilibrium or, in plain English, no free lunch on Wall Street. This cornerstone of both the modern theory of asset pricing and its industry applications has itself two important corollaries.

  • First, assets with similar payoffs should trade at similar prices (law of one price).
  • Second, asset prices should change only in response to news about fundamentals, and news being by definition unpredictable, asset returns should also be unpredictable (efficient market hypothesis).

The main impetus to reconsider standard models was provided by what financial economists have affectionately dubbed “market anomalies”.

  • For a start, some pairs of assets with very similar payoffs consistently trade at substantially different prices, in apparent violation of the law of one price. Newly issued “on-the-run” government bonds can trade at significantly higher prices than older “off-the-run” government bonds with nearly identical payoffs.
  • Other anomalies concern the predictability of asset returns such as the “momentum effect”, whereby an asset's recent price performance tends to persist in the short run.

In both cases, the standard theory predicts that arbitrageurs would spot these proverbial free lunches, trade on them, and eliminate them in the process. For instance, arbitrageurs would buy the off-the-run bond and short the on-the-run bond to exploit their relative mispricing, but doing so they would narrow the price gap so that by the time mere mortals wake up, the free lunch has come and gone and all but crumbs are left.

These empirical discoveries have prompted a very active debate among financial economists (as well as very active trading by hedge funds).

  • Some try to reconcile the anomalies with more sophisticated versions of the standard theory that still retain the assumption of unconstrained arbitrage.
  • Others reject the more fundamental assumption that traders are rational and instead explain the anomalies based on behavioural biases.
  • Yet another group lies somewhere in between, believing that arbitrageurs are crucial for the workings of financial markets but thinking of them as having to do their job with one hand tied behind their backs.

The limits of arbitrage

In a recent paper (Gromb and Vayanos 2010) we review the achievements and promises of this third way, the “limits of arbitrage” literature. This research seeks to understand why perfect arbitrage does not always happen in practice, i.e. why anomalies arise and persist. Its focus is on the process of arbitrage, with an emphasis on financial institutions, the real-world incarnations of textbook arbitrageurs, and on the constraints they face.

The premise is that arbitrageurs face constraints in that they cannot always raise the capital they need even when they face good investment opportunities. As it turns out, this simple premise has far-reaching implications for finance, and financial economists are only beginning to understand their full range and scale.

Suppose for instance that some investors suddenly want to sell a large amount of a given asset. These investors may be individuals, day-traders, mutual funds, banks, it does not matter for our example, and neither does the reason why they so suddenly want to sell. In any event, this “supply shock” has the potential to cause a drop in the asset’s price, which would offer an attractive investment opportunity for arbitrageurs.

Without constraints, arbitrageurs as group would simply absorb that supply shock, i.e. buy the asset the investors want to sell. If they required additional capital to buy the asset, arbitrageurs would be able to find it. As a result, even a large shock would have only a limited price impact. But once we consider that arbitrageurs face financial constraints, the picture is totally different. Indeed, if arbitrageurs cannot raise additional capital easily, they may not be able to absorb the shock fully and selling pressure can have a substantial and lasting price impact. Overall, when arbitrageurs as a group are flush with money, financial markets’ behaviour should resemble that of the standard theory. But if and when their capital is low, strange things can happen.

This simple enough insight is proving very fruitful. Let’s consider two of the tastier pieces of fruit. Both come from an important remark. If arbitrageurs’ capital affects asset prices, the reverse is also true.

First, the new approach has helped explain how small shocks can have big effects, as tends to be the case in financial crises. Consider again our supply shock example. We have seen that arbitrageurs facing financial constraints may not be able to absorb this shock, allowing it to have a substantial price impact. Things may be even worse. Suppose that before the shock, the arbitrageurs hold substantial amounts of that asset. A shock might cause the asset’s price to drop, implying a capital loss for the arbitrageurs. Not only may arbitrageurs not be able to absorb the shock fully, they may even be forced to liquidate assets themselves, pushing prices further down. In that case, arbitrageurs’ effect on asset prices is neither stabilising nor neutral, it is destabilising.

Second, the limits of arbitrage can rationalise episodes of contagion across asset markets. Here’s how it works. Following a supply shock in one market, the capital of arbitrageurs may be depleted. But since arbitrageurs draw from the same pool of capital to absorb shocks in different markets, a drop in their capital may force them to liquidate positions in other markets, affecting asset prices in those markets. Overall, a shock in one market affects other markets.

Inefficient markets

Research on the limits of arbitrage might very well reshape our understanding of financial markets. The next and arguably most important question however is whether it can provide a useful framework for public policy. Despite its relevance, the welfare analysis of asset markets with limited arbitrage is still in its infancy. But we believe it has great potential.

This research emphasises the role of financial institutions in the functioning of asset markets. Accordingly, these institutions’ financial health affects the functioning of markets. As we have seen, the reverse is also true. Their financial health is itself affected by asset prices through the capital gains and losses arbitrageurs realise. Now the question is whether arbitrageurs take financial positions putting their capital at risk in a way that is desirable for them and society as a whole. In an earlier paper laying out a model of financially constrained arbitrage (Gromb and Vayanos, 2002), we explain why the answer is “No.” In technical jargon, the welfare theorems do not hold.

Chain externalities

Follow the logic. Supply shocks have the potential to cause movements in asset prices, which constitute profit opportunities for arbitrageurs. Each arbitrageur however needs capital to be able to grab those tasty snacks. That’s fine; he might simply set capital aside in good times to be used when the opportunity arises and cash is king. In fact, a number of prominent investors follow such a strategy of keeping dry powder ready for when the goings get tough. Of course, setting capital aside means foregoing some risky but profitable opportunities available to arbitrageurs. Yet each arbitrageur can compare the benefit of investing in those opportunities to the cost of being short of capital in case of a big shock, and then decide for himself on the right amount based on this cost-benefit analysis. So far, still no inefficiency. However, there is something each arbitrageur does not fully take into account when deciding how much dry powder to keep and how much capital to put at risk. Indeed the cost of being short of capital in case of a shock is less than the implied social cost. When an arbitrageur is short of capital, not only is he unable to exploit the price movement caused by the shock, but as we have seen, his inability to do so amplifies the price effect of the shock. In turn lower prices cause other arbitrageurs to incur bigger capital losses, forcing them to liquidate assets, further depressing prices. This chain reaction has the effect of depriving arbitrageurs of capital right at the time when it would be most socially useful.

Policy

While in the standard model the invisible hand and its competitive prices elves gently guide towards taking socially optimal decisions, here they don’t. Instead, they drive arbitrageurs to put too much of their capital at risk. Since the price system cannot do its job of guiding agents, it can be good if someone else, a regulator perhaps, can provide that guidance. Regulation incentivising or even forcing arbitrageurs to take less risk could make everyone better off, arbitrageurs included.

How might this be best achieved? Risk-based capital requirements? Taxes and subsidies? A lender of last resort policy? Asset purchase programs? This is pretty much where this research agenda is at. The answers to these fascinating questions are still pending and hotly debated by academics and practitioners (see, for example, Sarkar and Shrader 2010). Hopefully, they’ll be ready by the time the next crisis hits.

References

Boone, Peter and Simon Johnson (2010), “The doomsday cycle”, VoxEU.org, 22 February.

Dewatripont, Mathias, Xavier Freixas, and Richard Portes (2009), “Macroeconomic Stability and Financial Regulation: Key Issues for the G20”, VoxEU.org, 2 March.

Gromb, Denis, and Dimitri Vayanos (2002), “Equilibrium and Welfare in Markets with Constrained Arbitrageurs”, Journal of Financial Economics.

Gromb, Denis, and Dimitri Vayanos (2010), “The Limits of Arbitrage: The State of the Theory”, Annual Review of Financial Economics, forthcoming.

Sarkar, Asani, and Jeffrey Shrader (2010), “Financial Amplification Mechanisms and the Federal Reserve’s Supply of Liquidity during the Crisis,” Federal Reserve Bank of New York Staff Reports, no. 431 


1 Textbook arbitrageurs represent professional arbitrageurs such as hedge funds and proprietary trading desks, but also and more generally financial intermediaries such as dealers, banks or mutual funds.
 

Topics: Financial markets, International finance
Tags: law of one price, limits of arbitrage, risk

Professor of Finance, INSEAD and CEPR Research Fellow

Dimitri Vayanos

Professor of Finance and Director, Paul Woolley Centre for the Study of Capital Market Dysfunctionality, LSE