According to the efficient market hypothesis arbitrage against mispricing does not require capital upfront and entails no risk (Shleifer, 2000). In a perfectly competitive market, each arbitrageur might take an infinitesimal small position against the mispricing and pushes prices towards the fundamental value. Capital constraints, therefore, do not exist for such small arbi- trage positions and arbitrageurs would be risk-neutral (Shleifer and Vishny, 1997).
The real world, however, looks different. Capital constraints cause arbitrageurs to act risk- averse, and arbitrage trades are as a matter of fact risky. In a seminal work on limitations of arbitrage, Shleifer and Vishny (1997) formalized a theoretical model on limited arbitrage con- sisting of three time periods and three market participants: irrational noise traders, rational ar- bitrageurs, and rational investors who allocate their funds to arbitrageurs. In this model, arbi- trageurs are specialized in trading only whereas investors do not trade on their own but delegate portfolio management decisions to arbitrageurs. As of now, noise traders are associated with non-informational transactions.6 A misperception of noise traders causes prices to deviate from the fundamental value of an asset. Arbitrageurs, on the other hand, are aware of the true fun- damental value of the asset. The valuation of arbitrageurs and noise traders converge in time period 3, assuming that there is no fundamental risk in the long run. The model asserts that arbitrageurs aim to maximize their profits (which in this model equals the total funds in time period 3) according to the following statement:
𝐸𝑊 = (1 − 𝑞) {𝛼 (𝐷1 ∗ 𝑉 𝑝1 + 𝐹1− 𝐷1) + (1 − 𝛼)𝐹1} + 𝑞 ( 𝑉 𝑝2) ∗ {𝛼 (𝐷1∗ 𝑝2 𝑝1 + 𝐹1− 𝐷1) + (1 − 𝛼)𝐹1} 𝑤𝑖𝑡ℎ 𝛼 ≥ 1 (4)
where EW denotes the arbitrageur’s third period funds, q is the probability that the noise trader’s misperception intensifies in period 2, D1 is the investment value of arbitrageurs in an asset in t = 1, V is the fundamental value of the asset, pt is the price of the asset at time t, Ft is the limited cumulative amount under management for the arbitrageurs, and α describes the sensitivity of assets under management against historical performances. If arbitrageurs lose
money on their positions, investors will not provide more funds and α takes the value of 1. α is greater than 1 if investors withdraw money as a consequence of poor historical performances. An important assumption is, hence, the allocation of funds based on historical performances of arbitrageurs.
The main implication of the model is that performance-based arbitrage, which is the sensitiv- ity of investors to refuse/provide more capital or to even withdraw capital from the fund under management as a result of poor historical performances, causes inefficiencies in particular in extreme situations. This is the case when prices significantly deviate from its fundamentals and arbitrageurs are fully invested. Facing the risk of high short-term losses, arbitrageurs withdraw from the market when arbitrage would be most profitable. Arbitrageurs, thus, face limitations in the moment of their best opportunities.7
The former model on limited arbitrage includes dimensions such as the specialization of arbitrageurs and capital constraints as potential reasons for limited arbitrage. Furthermore, the literature offers several different reasons for limitations on arbitrage which potentially cause market inefficiencies. One explanation refers to the lack of perfect substitutes in the real world. A riskless hedge of assets requires perfect securities, implying a certainty that both, the relative prices of the underlying asset and the hedge, converge. Yet, imperfect markets are character- ized by statistical likelihoods as opposed to certainty (Shleifer, 2000). Arbitrage costs are other prominent obstacles that deter arbitrage opportunities. Direct trading costs, for example, incur for short selling activity associated with arbitrage. To borrow a stock, the short seller must pay a fee to the stock lender or an intermediary. In addition, indirect costs incur if short positions are closed due to the recall of the stock by the lender. Furthermore, stock borrowers must post collaterals if the price of the shorted stock increases and payouts are due if brokers call out the margin-call. Another indirect cost can be attributed to costs related to finding a stock lender in non-centralized shorting markets. Hence, arbitrage is costly and risky in an imperfect financial market (Jones and Lamont, 2002). Other reasons for limited arbitrage are found in the special-
7 Please refer to Shleifer and Vishny, 1997, p. 38 ff, for more details on the theoretical model. The authors describe
in four distinctive propositions the implications of specific extreme situations on the ultimate arbitrageur’s goal to maximize the funds under management in period 3.
ization of arbitrageurs and time constraints. An arbitrageur’s portfolio might lack diversifica- tion as a result of high specialization, which causes the arbitrageur to bear idiosyncratic risks. If prices further deviate from their fundamental value, then specialized arbitrageurs are not able to diversify that risk. Additionally, if prices deviate temporarily and arbitrageurs do not own enough capital to engage in further arbitrage trades, they are forced to close the position and realize losses (De Long et al., 1990; Shleifer and Summers, 1990 and Shleifer and Vishny, 1997). Facing the losses reduces the willingness of the arbitrageur to invest additional amounts (Mitchell et al., 2002). Furthermore, institutional and cultural inhibitions could also potentially deter arbitrage since underlying guidelines might prohibit short selling or partly limit the extent of arbitrage activity (Jones and Lamont, 2002).
The literature documents several implications of limited arbitrage for financial markets. For example, one might assume that high volatility in financial markets attract arbitrageurs because mispricing would frequently exist in such an environment. However, arbitrageurs rather avoid short positions in highly volatile financial markets in particular in the presence of high funda- mental risks. If risk-adjusted excess returns (often called alpha) do not increase proportionally to the volatility, arbitrage becomes less attractive. In addition, higher volatility increases the likelihood of losses, which, given time and capital constraints, deters arbitrage for risk-averse arbitrageurs (Shleifer and Vishny, 1997). Moreover, the literature argues that stocks with high short selling costs often tend to be smaller growth firms with higher market-to-book valuations (Jones and Lamont, 2002). This goes hand in hand with the view on overpriced stocks which tend to be owned by only a few optimistic investors. Arbitrageurs, or more specifically short sellers, avoid buying overvalued stocks (Miller, 1977). Based on their theoretical model, Diamond and Verrecchia (1987) conclude that the absence of trade is a bad signal for financial markets. In their argumentation, abnormal low trading activity may be a result of situations in which informed traders with bad news face short selling constraints and thus cannot trade based on their information. Engelberg et al. (2012), on the other hand, find evidence that short selling activity and advantages from such trades substantially result from an arbitrageur’s ability to analyze publicly available information. However, arbitrageurs rarely anticipate informative news events. The authors do not finally answer the question whether this weak anticipation results from limited arbitrage or other factors.
In summary, systematic and idiosyncratic risk matter both for professional arbitrageurs. Ar- bitrageurs or informed investors are in reality often reflected by only a few highly specialized investors, refuting the view on a perfectly competitive market with homogenous views on asset prices. In imperfect markets, hedging is not costless and risk-free. The classical view on the positive correlation between risk and returns thus changes with limited arbitrage. The antago- nists of arbitrageurs in financial markets are the so-called noise traders. They are mostly re- ferred to the group of uninformed investors. The underlying noise trading theories and concepts are detailed in the next section.