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      Delayed arbitrage

      Another way that arbitrageurs can deal with noise trader risk is via delayed arbitrage. This is discussed in an article by Abreu and Brunermeier (2002). They build a model for arbitrage that considers uncertainty about the market timing decisions of other rational arbitrageurs, and thus the timing of the price correction. They call this problem synchronisation risk. The model shows that rational arbitrageurs do not act immediately on knowledge of security over-valuation, but instead wait for other rational arbitrageurs to learn about the over-valuation. Acting immediately might lead to losses, if enough other rational arbitrageurs do not know of the over-valuation and fail to act at the same time.

      The lesson from this model for traders is clear: arbitrage is more than just identifying mis-priced assets. A good short-seller should combine knowledge of mis-pricings with a catalyst. In this case, the catalyst is knowledge that other traders are about to short the security too. This concept of delayed arbitrage can help explain why apparently obvious market bubbles can continue to grow. Short-sellers, the very people who might be expected to prick the bubble and bring over-valued securities back into line, can be absent when they are needed most. And they would be absent for good reason – they want to avoid being overwhelmed by a tidal wave of optimistic noise traders.

      Tidal waves and market bubbles

      Such tidal waves of noise trading emerge much as fads and fashions do. Where market participants obtain information and opinions from the same source, or share opinions with one another on websites or other media, noise traders can begin to believe in a common story, to imitate one another’s trading and to herd in their behaviour. As momentum builds, a fashion can develop into a bubble.

      One of the most famous purported market bubbles from recent years involved the rapid ascent in technology, media and telecom (TMT) stocks from around 1998 through to March 2000 and their subsequent sharp decline (March 2000 – March 2003). Brunnermeier and Nagel investigated the activities of hedge funds around the time of this ascent and collapse in TMT stock prices. Their article was published in 2004, by which time the NASDAQ index had fallen over 75% from its peak of March 2000 and just about everyone grounded in realism agreed that the TMT stock phenomenon of the late 1990s had been a bubble.

      One might expect that hedge funds were trying to short-sell egregiously over-valued TMT stocks in 1999 and early 2000, but the authors found that hedge funds were in aggregate over-weighted in technology stocks in 1999 and early 2000.

       Why might this have been?

      These hedge fund positions cannot be explained by barriers to short-selling: if short-selling was too difficult or too costly, a fund would simply hold a zero position in the security, or at the very least some under-weighted position relative to the benchmark weight of the security. Funds would certainly not have held over-weighted positions if they believed that the shares were about to fall in price. This notion is reinforced by a separate study by Geczy et al. (2002) that found that short exposure to dotcom stocks was neither costly nor difficult during this period.

      In light of this evidence, Brunnermeier and Nagel concluded that hedge funds were ‘riding the technology bubble’, rather than short-selling apparently over-valued stocks. In a market with many optimistic noise traders, it might not pay to immediately short-sell over-valued stocks. Informed traders almost certainly knew that TMT stocks were over-valued, but feared the army of optimistic ‘new paradigm’ noise traders enough to stay well away from shorting TMT stocks…for years on end!

      Don’t be a hero!

      The advice for traders tempted to short-sell assets that appear to be in a bubble is to avoid any isolated, heroic action. Sit it out until the tide turns, or (for the thrill-seeking) join in and ride the bubble, while keeping a very close eye on the exit door!

      A number of high-profile investors and traders ignored this advice and paid the price with their jobs or funds. Amongst the best known victims of synchronisation risk and TMT noise trader madness were Julian Robertson at Tiger Asset Management, who closed his investment company in March 2000 after incurring losses; and, amongst long-only portfolio managers, value investor Tony Dye, chief investment officer at Phillips & Drew asset management in London, whose employment ended only three days before the peak of the market.

      Reverse broking

      Traders can find shortcuts to the problem of synchronisation risk. In practice, arbitrageurs can enter immediately into seemingly attractive positions and then proceed to advise their known contacts, such as brokers and peers, of the attractiveness of that position. This is sometimes known as ‘reverse broking’. In their observational study of a hedge fund, Hardie and MacKenzie (2007) observed the following situation:

      The trader asked his assistant to construct a spreadsheet of recent prices of the two bonds, which supported the view that it was indeed an anomaly and thus a trading opportunity. Having first made the necessary purchases and short sales to take advantage of it, the trader then phoned a contact in an investment bank to direct his attention to the anomaly – ‘There is at least half a point in that trade, and there is zero market risk’ – and sent him the spreadsheet.

      The purpose of this activity is to encourage dissemination of the idea and to alert other arbitrageurs to the opportunity. This has two effects: first, it lowers the risk of greater divergence of the position from fair value, so limiting margin calls and the risk of performance-based arbitrage. Secondly, it might bring the trades of other actors forward in time, thus reducing synchronisation risk. This suggests a social dimension to arbitrage, well beyond simply identifying mis-priced securities. Where such reverse broking is based on the interpretation of factual information (as opposed to false rumours) it is an entirely legitimate activity.

      More complicated worlds

      So far, we have considered a very simple world, populated only by informed arbitrageurs and uninformed noise traders. And yet this simple world has already led to a better understanding of arbitrage and risk, and has allowed for the development of bubbles.

       What happens if we add in other market actors?

      One example of a more complicated model is provided by De Long et al. (1990) who create a model with two assets: cash and stock. There are three types of traders: positive feedback traders, fundamental-versus-price-comparator investors and utility-maximising informed rational speculators.

       Positive feedback traders simply buy stock after its price has risen, and sell after its price falls. They are associated with price momentum trading or trend following, stop-loss orders (selling a risky asset after a price drop below some pre-defined level), dynamic hedging (selling a risky asset after a price fall, and vice versa), and the liquidation of positions by investors unable to meet margin calls.

       Fundamental-versus-price comparator investors are simply disciplined ‘value’ investors. They acquire stock when it trades below its assumed fundamental value and sell stock when it rises above its assumed fundamental value.

       Informed rational speculators, on learning some news about a security, not only trade in response to the news, but also trade additionally in anticipation of the positive feedback traders’ response to the rational speculator’s trading. Stock price movements in response to news thus become exaggerated.

      The model reveals patterns of stock prices that are consistent with the empirical evidence of positive serial correlation of returns over periods of weeks or months (i.e. price momentum), followed by mean reversion over several years. Such patterns could also be obtained without anticipatory trading by rational speculators, so long as positive feedback traders operate in the market. The authors argue that in the presence of positive feedback traders, it might be rational for investors to “jump on the bandwagon and not buck the trend” when prices are trending. This is exactly the sort of behaviour that Brunnermeier and Nagel found amongst hedge

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