Behavioural Finance does not negate the arbitrage mechanism per se and its price correcting ability. However, it argues that not every deviation from fundamental value created by actions of irrational traders will be an attractive investment opportunity for rational arbitrageurs (Szyszka, ). Even when an asset is highly mispriced, many arbitrage strategies which are designed to correct and eliminate the fundamental mispricing, are ultimately risky and costly for the arbitrageur. Therefore many strategies are perceived to be unattractive which results in the mispricing remaining unchallenged for a comparatively long period of time.
The theory of arbitrage can be traced back to Friedman (1953), he stated that rational traders will quickly undo any mispricing caused by irrational traders. An example to illustrate this argument is cited in Baberis and Thaler (2002)
"Suppose that the fundamental value of a share of Ford is $20. Imagine that a group of irrational traders becomes excessively pessimistic about Ford's future prospects and through its selling, pushes the price to $15. Defenders of the EMH argue that rational traders, sensing an attractive opportunity, will buy the security at its bargain price and at the same time, hedge their bet by shorting a 'substitute' security, such as General Motors, that has similar cash flows to Ford in future states of the world. The buying pressure on Ford's shares will then bring their price back to fundamental value."
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Friedman's argument is based on two underlying assumptions. Firstly, as soon as an asset deviates from its fundamental value, an attractive investment opportunity will arise from this mispricing. Secondly, rational traders will immediately react to the situation by purchasing the asset, thereby correcting the mispricing. Behavioural Finance doesn't dispute the fact that an attractive investment opportunity will be exploited, it argues that arbitrage strategies that are developed to correct the mispricing can be both risky and costly, resulting in the mispricing remaining unchallenged.
When an arbitrageur observes a mispriced asset on the market, they need to find a similar asset which is priced correctly on another market, to enable them to correct this mispricing. Thus, taking an opposite arbitrage position. If the trader is unable to take up this position they face fundamental risk. That is, the risk that new information comes to the market and changes the fundamental value of the asset in the wrong direction.
Referring back to the example of Ford and General Motors cited Baberis and Thaler (2002), if the trader buys Ford's stock at $15, but then there is bad news in the market which causes the stock to fall below the initial purchase value, this will result in losses for the trader. Even if the arbitrageur has a short substitute security such as General Motors, the problem is, substitute securities are rarely perfect and often highly imperfect, making it almost impossible for the trader to remove all the fundamental risk. Therefore, by shorting Generla Motors, it protects the arbitrageur against adverse news about the car industry as a whole, however, it still leaves them exposed to bad new that is specific to Ford.
Even when arbitrageurs are able to hedge the fundamental risk that they face and take a long position in the asset where it is cheaper and a short position in the same asset on another market where it is more expensive, the trader is still exposed to Noise Trader Risk.
Noise trader risk can be defined as, the risk that irrationality on the market may become stronger and may drive mispricing to an even grater extent (Shleifer & Vishny (1997). As the mispricing increases, the gap between long and short positions increases which in turn goes against the belief of rational arbitrageurs. If this trend continues, an arbitrageur whose investment horizon is usually relatively short and who often borrows money to fund their trades, may be forced to close their positions before the mispricing is corrected, ultimately resulting in them suffering significant losses. Shleifer (2000), has argued that noise trader risk, the risk from traders who are attempting to buy into rising markets and sell into declining markets, limits the extent to which one should expect arbitrage to bring prices quickly back to rational values, even in the presence of an apparent bubble. Even the most rational arbitrageurs will regret selling a share short which may collect a greater price in the future, even if that price is unreasonably high.
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Noise traders can be defined as those whose investment decisions rely more on psychological factors than on sound investment management principles (Friedman, 1953). According to the EMH, an irrational investors' trading cannot be effective in the long run as efficient rational arbitrageurs will counteract their trades eliminating them from the market. Furthermore, noise traders buy and sell shares in an uncorrelated random manner and in turn their trades cancel each other out, leaving asset prices unaffected.
However, the evidence of persistent anomalies in the stock market dictates that noise traders can most definitely affect equilibrium prices even in the long run. According to De Long et al (1990), this is because rational arbitrage in reality is not only limited but can also create by itself price inefficiency under certain circumstances. The understanding behind the ability of noise traders to alter the fundamental value of a stock lies in the limitations faced by rational arbitrageurs. The two main limitations are short investment horizons and risk aversion.
Rational arbitrageurs cannot entirely eliminate the effects of noise traders on the market if the size and the ability of the former group to trade are very limited (Camerer, 1989). Consequently, a single arbitrageur who notices a mispricing in the market faces not only the noise trader risk, but also the risk of synchronization of actions of other rational traders (Abreu & Brunnermeier (2002). Typically a single arbitrageur does not have the momentum to correct the mispricing on their own. The individual needs other arbitrageurs who will follow his strategy. However, the individual does not know if and how quickly other rational traders will react to the same arbitrage opportunity and take up a similar positions. Also, the risk aversion of arbitrageurs by itself limits their ability to cancel noise traders, even if arbitrageurs have infinite buy-and-hold horizons (Shiller, 1984). As stated by Black (1986), if noise traders undervalue or overvalue stocks for a long period of time, the short horizon under which arbitrageurs' performance is evaluated limits their ability to force asset prices back to their fundamental values. As a result, due to the limitations of arbitrage noise traders are able to force asset prices away form their equilibrium value for extended periods of time.
Rational arbitrageurs also have to realise that noise trader strategies may become even more extreme and unpredictable, resulting in increased risk for the arbitrageur. This additional risk can be referred to as 'noise investor risk'. Noise investor risk is systematic and non-diversifiable which in turn creates additional volatility on the stock markets. Rational arbitrageurs would not bear this risk unless compensated with higher expected returns (De Long et al., 1990). This once again limits the successfulness of rational arbitrageurs.
Arbitrage can become a costly activity for a number of reasons. Firstly, transaction costs which include bid-ask spreads, commissions and price impact can limit the arbitrageur in exploiting an obvious mispricing. Secondly, the fees charged for borrowing stocks to take a short position can often be off-putting. As cited by Baberis and Thaler (2002), D'Avolie (2002) finds -
"That for most stocks, they range between ten and fifteen basis points but they can be much larger; in some cases, arbitrageurs may not be able to find shares to borrow at any price."
A further barrier they may face is legal constraints. For example, in many large pension funds short-selling is prohibited altogether. Finally, the vast amount of research and learning required to exploit a mispricing in a further deterrent. Shiller (1984) found that even if noise trader demand causes a persistent mispricing it ay not be detectable for arbitrageurs without large amounts of time and resources.
Limits of arbitrage have been confirmed empirically by cases of evident mispricing that remain unchallenged in the market for long periods of time.
An example of this is the case of 'twin shares'. In 1907, Royal Dutch and Shell merged their interests on a 60:40 basis while both remaining separate entities. The stocks of Royal Dutch traded mostly on the US and Dutch Stock Exchange and were to claim 60 percent of the total cash flow, while shares in Shell which traded in the UK were to claim 40 percent of the total cash flow of the two firms. Theoretically, the market value of Royal Dutch equity should always be 1.5 times greater than the market value of Shell. Empirical evidence shows that Royal Dutch was sometimes 35 percent underpriced relative to Shell and at times they were 15 percent overpriced. It took until 2001 for the shares to finally sell at their correct values. This is a key example where two shares that are perfect substitutes to each other would allow the opportunity of easy arbitrage profits. The main risk in this situation is noise trader risk, there is the fear that the share will become even more undervalued in the near future.
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A further example of the limits of arbitrage comes form 'carve-outs'. This involves transactions when a publicly listed mother company sells a majority stake in its daughter company in the Initial Public Offer (IPO). Baberis and Thaler (2002) give an empirical example of this. In March 2000, 3Com sold 5 percent of its wholly owned subsidiary Palm inc. in an IPO, retaining the remaining 95 percent. After the initial offer, a shareholder in 3Com indirectly owned 1.5 shares of Palm Inc. At close of business on the first day after the offering, Palm Inc. shares were valued at $95, putting a theoretical value of 3Com at $142 per share. What actually happened was 3Com's trading price was $81 per share, implying a market valuation of 3Com's business out side of Palm Inc. at around minus $60 per share. In this extreme case the market value of stocks offered by the IPO was higher than the valuation of the whole mother company holding a majority stake in the daughter company. This mispricing occurred for several weeks. Baberis and Thaler (2002) analyse this case and argue that implementation costs prevented arbitrageurs profiting from this mispricing.
Yet another example comes from the inclusion of a new stock on the S&P 500. Schleifer (1986) discovered that when a stock is added to the index, on average, the price jumps by 3.5 percent and much of this increase remains. A prime example of this is when Yahoo was added to the index, its share price rocketed 24 percent in a single day. Arbitrage is limited in this case due to the fundamental risk and noise trader risk faced by traders. They may find it is very difficult to find a substitute stock and also there is the risk that the price will continue to rise in the short run. In the case of yahoo, its share price was $115 before its addition in the index and it had risen to $214 a month later.
In all of these above examples, rational arbitrageurs face risks, costs and problems with their fundamental strategies which makes arbitrage unappealing for the trader..