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Tuesday 31 January 2012

Limit Orders, on the Crumbling Edge of Behavioral Finance

Crumbling Limits

Although behavioral psychology has helped explain some of the odder effects around investment there remain many sceptics. The reason for this isn’t hard to find, because if you start out assuming that peculiar features of investment markets are caused by rampant misbehavior then you’re quite likely to find evidence to support that assumption.

Some of this is down to irrational behavior, no doubt, but perhaps not in the way that the academics first thought. So, for instance, consider the use of the humble limit order. Used unwisely – which is to say, nearly always – it doesn’t just lose investors money but ruins the researchers’ results into the bargain. Just watch those behavioral biases crumble away.

Winner's Curses

Limit orders are pre-set limits at which stock is automatically bought, as it falls through the limit price, or sold, as it rises. Limits guarantee a maximum or minimum price, but not execution. And they’re very popular:
“Limit order books (LOBs) are used to match buyers and sellers in more than half of the world's financial markets (Ro_su, 2009). Euronext; the Australian Securities Exchange; and the Helsinki, Hong Kong, Swiss, Tokyo, Toronto, and Vancouver Stock Exchanges all now operate as pure limit order markets (Luckock, 2001), and the New York Stock Exchange (NYSE); NASDAQ; and the London Stock Exchange (LSE) (Cont et al., 2010) all operate a bespoke hybrid limit order system”.
Although limit orders provide protection of a sort for investors it also exposes them to the winner’s curse – the problem that by fixing the price they are willing to buy or sell at they can be picked off when their orders become mispriced – which will happen when new information hits the market. Of course, many limit orders will execute rapidly but us private investors are faced with the almighty power of the high frequency traders and, as Peter Hoffman hypothesises:
“Fast traders (FTs) may revise their limit orders upon news arrivals and therefore avoid being ”picked off” (Copeland and Galai (1983)), but only if the next agent is a slow trader (ST). In this stylized environment, a world with only FTs is identical to a world with only STs because speed only matters in relative terms.”
A Bigger Bezzle

The point of this preamble is that limit orders are important, and even relatively short-term “fill or kill” orders are exposed to these risks when individuals are trading against the light-speed limited algorithmic monsters of the high frequency traders (Trading At The Speed of Light). This is just another way in which private investors are taxed by the securities industry and one not even included in the analysis behind the 160 Billion Dollar Bezzle. As the paper above concludes, these practices are never favourable for smaller, slower investors.

Now, if we think through the impact of limit orders on investors it leads us into a curious conundrum. Consider a stock which, out of the blue, announces good news. The market reaction to this will be to push the price of the stock up, to reflect the new information yet, at some point, the rising price is going to start hitting limit orders, where preset sales are going to be triggered. Counterintuitively, investors will start to sell their winning firms.

In reverse, on the downside when a company announces grim tidings the falling price will eventually hit limit orders to buy the stock, and investors will start to buy losers – not quite the original idea behind the winner’s curse, but close enough. Translated, this rather makes it look as though investors are selling their winners and buying their losers, behavior that would normally be considered clear evidence of irrational human bias.

The Limit Order Effect

Juhani Linnainmaa, who we last saw when investigating Are Traders Are Dumber Than A Drooling Dog, has released a fascinating paper based on precisely this hypothesis, Do Limit Orders Alter Inferences about Investor Performance and Behavior? In this he looks at a set of Finnish investors in a market where 76.3% of individual trades are carried out as limit orders, most of which don’t appear to be actively monitored. The results are extraordinary:
“Because of the way limit orders work, investor trading records reflect mechanical effects that distort inferences about investors’ intentions. Even if a limit order book is balanced between buy and sell limit orders, positive news causes more of the sell limit orders to execute, leaving an impression in the trading records that most investors wanted to sell their shares in response to good news … Individuals lose money when their limit orders execute immediately after earnings announcements; that limit order trades lose money after the trade while market order trades do not; that approximately half of the disposition effect disappears if I exclude sales originating from limit orders; and that individuals’ short-term contrarian behavior is mostly due to limit orders.”
Unpicking this a little, the research suggests that the disposition effect (Disposed To Lose Money) – the common behavioral bias where people sell winners and keep losers – can be partially, although not wholly, explained by limit orders, thus reducing the amount of apparent irrationality in the market at a stroke. It also helps explain the curious observation that investors tend to under-react to both good and bad news (see: Regret), because the automatic contrarian effects of limit orders will tend to counterbalance such news. 

Furthermore evidence that private investors have poor stockpicking skills such that their purchases underperform their sales (Overconfidence and Over-Optimism) is also partially explicable by the limit order effect. If news predicts short-term momentum, which it seems to, then limit orders are a contrarian, and losing, bet in the opposite direction. This internet appendix to Linnainmaa's paper confirms this hypothesis.

Intertemporal Risk

As Linnainmaa points out, the limit order effect almost certainly carries over into the US market:
“The fraction of limit orders received by the largest five discount brokers ranges from 35% to 48% in the first quarter of 2006. Limit orders outnumber market orders on average by eight to five.18 Individuals also set their orders to remain in effect for several days. Data from one large U.S. discount broker indicate that 23% of the time, individuals deviate from the same-day expiration (the default choice), letting their orders remain in effect at least until the next day. Individuals let 9% of their orders remain in effect for at least a month.”
Limit orders expose investors to intertemporal risk: the possibility that new information may come to light in the time period between placing the order and it executing. The research also shines a light into the heart of some of the most important effects within behavioral economics, and suggests that the findings are nowhere near as robust as we’ve been led to believe – after all, there’s a difference between people behaving irrationally in response to new information and people simply failing to attend to their limit orders.  

Dumb Money

Of course, pointing out that private investors use limit orders in this way doesn’t explain why they do so – although Linnainmaa looks at this in the internet appendix quoted above. The models suggest a simple explanation:
“Individual investors are uninformed traders who enter the market to profit from other investors’ demand for immediacy”.
Private investors provide liquidity to institutions who may be forced to trade, for reasons outside their control, such as mass redemptions of mutual funds. This is fine when firms aren’t impacted by unexpected news, as it allows dumb trading to capture some of the mean-reverting upside. On the other hand it leaves investors exposed to the vagaries of an uncertain world. No easy lessons here, but if you’re going to use limit orders either set them tight and monitor them like a hawk or set them wide and hope that mean reversion kicks in.

None of this invalidates the research into behavioral bias, but it does show how market structure can imply patterns of behavior, which need to be taken into account when the next set of "irrational" behaviors is discovered.  We are often irrational, but more often we're just lazy. 

N.B. Juhani Linnainmaa's most recent research can be found here.  

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  1. I think there may be a nomenclature issue.

    Limit orders are just the basic building block of a market: the bid/ask are just the best buy/sell limit orders on the market, without limit orders there's no market possible, so 100% of exchanges use them (not "half of the world markets").

    Indeed conceptually it's the only order type needed: market orders can be simulated by limit orders with generous limits, and some responsible brokers do submit virtually all customer orders as limit orders at the exchange level (with computed limits for "market" orders, so as to avoid very short term disruptions).

    The asymmetry between stop limit and plain limit is itself interesting: you get slippage on one side and benefit from it on the other, and the psychology may differ as well I suspect.

    Dumb limits also capture the bid/ask spread, and liquidity rebates if your broker is not too greedy, even in the absence of mean reversal.

  2. That's right, cig. The correct fraction of retail orders that should be limit is 100%. A retail investor should never, ever buy or sell at market. If you want immediate execution, just set your limit a little higher than market if buying, a little lower if selling. (You always get the best price anyway - e.g. if your limit buy is above market, you still buy at market.)

    The risk of a naked market order is that the market gaps and you get execution at a very surprising price. Remember the "flash crash", when people sold $100 stocks for 1 cent? It was because of market orders. There is an analogous upside risk with IPOs; many naive investors have sad tales to tell connected to market buys of IPO stocks.

    On the other hand, open (multi-day) stop orders really are free options for dealers.

  3. I'm not a super sophisticated investor like you guys. I've never used limit orders. However, there's a few shares I wish I had set limit orders on. Would have saved a tonne of money.

  4. followup to phil koop:

    Q: if open stop orders are free options, and thus dumb, then what is smart?

    A: generally, the smart thing is to sell insurance, rather than buy or give it away for free. Instead of a good-till-cancelled buy order at lower than market price, sell naked puts. Instead of a sell order at higher than market, sell covered calls.

  5. The generalizations in the article indicate that the research wasn't done by a market participant.
    A small investor can place a buy order a bit over the low end of a range and not provide a free meal to the market maker handling your order. That is not stupid.

    Tactics for order placement depend on the liquidity of the market. Large cap stocks can accommodate market orders with little price friction. If you are trading small caps, god help you if you place a market order, or any decent size limit order. You face an Execution in the worst sense of the word for the former, and the near certainty of being pennied on the latter.

    It all depends on the situation, and that doesn't appear to be considered in this paper.

  6. A small investor can place a buy order a bit over the low end of a range and not provide a free meal to the market maker handling your order. That is not stupid.

    Yes, but they don't - or at least that's what the empirical evidence quoted in the paper is saying. Furthermore, the failure to manage stale limit orders creates an illusion of behavioral bias. That's all the article says - the fact that a lot of this isn't necessary and can be avoided isn't the point that's being made.