Brown & Holden on Pegged Limit Orders

Pegged Orders were first discussed on PrefBlog in a review of Jeffrey MacIntosh’s essay in the Financial Post. A discussion paper published by IIROC, Dark Pools, Dark Orders, and other Developments in Market Structure in Canada requests commentary on potential regulation of this order type; and the order type was also discussed in the November 2009 edition of PrefLetter.

David P. Brown of the University of Wisconsin and Craig W. Holden of Indiana University wrote a paper in 2005 titled Pegged Limit Orders that is of great interest:

Limit orders face mispricing risk – the risk of executing at a stale limit price after an innovation in public valuation, because limit-order traders generally do not continuously monitor market conditions. We analyze the impact of pegged limit orders that automatically adjust the limit price in a hybrid market. We find the direct effect is to increase limit-order profits, reduce dealer profits, and increase market-order losses. However, the indirect effect is to increase the quantity of limit orders submitted. A numerical calibration finds that when dealers supply relatively little liquidity, there is a net benefit to market orders as well.

Well, relatively little liqudity supply from the dealers is a major attribute of the preferred share market, so let’s look at this a little more. They define two types of risk assumed when entering a limit order:

There are two kinds of risk facing limit orders. 1 One is execution risk – the limit order quantity executed is random. A second is mispricing risk – a limit order may execute after an innovation in public valuation (e.g. a public news item) at a mispriced limit price, because limit-order traders generally are off the exchange and do not monitor market conditions continuously. We analyze whether mispricing risk can be reduced by creating pegged limit orders that automatically adjust the limit price, even in the absence of direct intervention by the limit-order trader.

Mispricing risk is especially important during market crashes.

They design a model, play with it, and find:

Initially, we analyze the direct effect of a design change from Regular LOs to Market-PLOs, and then to Quote-PLOs (holding limit-order quantities fixed). We find:

  • • an increase in limit-order trader profits (Quote-PLOs > Market-PLOs > Regular LOs), because updating limit prices avoids states in which limit orders execute at a loss following a public value innovation,
  • • a reduction in dealer profits (Quote-PLOs < Market-PLOs < Regular LOs), because dealers suffer in two ways: (1) dealers cannot profit by picking off mispriced limit orders and (2) updated limit orders are more effective in competing with the dealers for the incoming flow of market orders,
  • • a reduction of market-order trader profits (or equivalently an increase in their losses) (Quote-PLOs < Market-PLOs < Regular LOs), because market orders lose the opportunity to pick off mispriced limit orders.

Which sounds very reasonable. A Market-PLO is linked to a market index, whereas a Quote-PLO is linked to the quote on a particular security.

Next, we analyze the indirect effect of a design change, allowing limit-order traders to choose the optimal quantities to submit. We find an increase in the quantity of limit orders submitted (Quote-PLOs > Market-PLOs > Regular LOs), because designs which avoid mispricing are more profitable. For marketorder traders, we find that the indirect effect is opposite the direct effect and increases market-order trader profits (Quote-PLOs > Market-PLOs > Regular LOs). This is because a greater quantity of limit orders reduces the probability of exhausting the total depth supplied by limit orders and dealers at the inside spread, and trading at prices outside the spread. Finally, we perform a numerical calibration exercise to analyze the combined impact of the direct and indirect effects on market-order trader profits. We find that under conditions when dealers endogenously choose to supply relatively little liquidity, then the indirect effect dominates and market-order traders benefit. Conversely, under conditions when dealers endogenously choose to supply a relatively large amount of liquidity, then the direct effect dominates and market-order traders lose. Empirically testable predictions of the model are that the introduction of pegged limit orders should cause a jump in limit order use, the cost of trading using market orders should decline in stocks where dealers supply relatively little liquidity, and overall volume should increase.

One Response to “Brown & Holden on Pegged Limit Orders”

  1. […] Pegged Orders were last discussed on PrefBlog in the post Brown & Holden on Pegged Limit Orders. […]

Leave a Reply

You must be logged in to post a comment.