Data processing: financial – business practice – management – or co – Automated electrical financial or business practice or... – Finance
Reexamination Certificate
1999-09-15
2002-12-10
Millin, Vincent (Department: 3624)
Data processing: financial, business practice, management, or co
Automated electrical financial or business practice or...
Finance
C705S03600T, C705S035000, C705S037000
Reexamination Certificate
active
06493682
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the field of securities trading and, in particular, to a method of determining when to place an order, subject to uncertain execution, in exchange for better execution prices, an example of which is limit order trading in the U.S. equity market.
2. Summary of the Related Art
An investor choosing to place a purchase limit order may not receive execution if the price rises, but will receive execution if the price falls sufficiently. The investor misses some of the gains and suffers more of the losses. However, in noisy or mean-reverting markets, limit orders may provide superior returns by reducing the costs of execution. Thus, limit order trading involves the risk of non-execution but also offers the promise of superior returns. Similarly, an investor placing an order on electronic crossing networks (ECN) such as POSIT® faces a similar tradeoff. The investor may receive superior trade performance but risks that the trade will not be executed.
Much of the current literature on order placement focuses on the decision of traders to place limit orders and the implications of this decision for the market's bid-ask spread. Clearly, understanding the structure of markets and the motivations of the market maker is essential, and there have been a number of important papers on this subject. However, another important segment of the financial community is the “buy side” of the market; investors attempting to trade optimally for their own account. (When we refer to investors, we contemplate traders acting as agents for investors, investors trading on their own behalf, and traders transacting proprietary inventory.) Very little has been written or produced which links the portfolio planning stage of investment with the trading process. We believe this methodology provides new insights into using limit orders optimally given portfolio characteristics and therefore has broad implications for investors.
While there is a sizeable background literature on limit orders, in contrast, the literature on trading with ECN's is almost nonexistent. In a recent working paper, Simaana, Weaver, and Whitcomb (1998) discuss ECN's and show that they reduce the average spread on NASDAQ traded stocks. No literature exists on when investors should choose ECN orders vs. market or limit orders. We are unaware of any commercially available products that perform this analysis.
The literature on optimal order strategies includes Cohen, Maier, Schwartz, and Whitcomb (1981), who show that a non-trivial bid-ask spread will exist in securities markets, that limit orders become more attractive if the bid-ask spread increases, and also that the probability of limit orders executing does not approach one as the limit order price approaches the market price.
A number of papers also address the limit order book in an equilibrium context. These include Glosten (1994), who examines the market produced by an electronic limit order book and shows that it provides a minimum spread and does not invite competition from a dealer market. Chakravarty and Holden (1995) also theoretically examine whether traders wish to submit market or limit orders in an equilibrium setting.
Harris and Hasbrouck (1997) detail the type of orders and participants on the NYSE, and Keim and Madhavan (1997) provide a summary of the evidence on trading costs and their economic significance. Copeland and Galai (1983) show how a dealer's decision to set quotes is similar to writing a put and call option to an informed trader, and how an option analysis can produce realistic bid-ask spreads. While our analysis focuses on a possibly risk averse investor placing a limit order rather than a risk neutral dealer setting quotes, the basic costs and benefits of our analysis are similar to Copeland and Galai (1983). Because placing a limit order is analogous to writing an option to the market (or dealer), the fundamental expectations equations we present are consistent with Copeland and Galai (1983).
The prior art does contain several papers that discuss methods for finding optimal placement strategies, and several papers that discuss related issues. The papers that discuss optimal placement strategies include Handa and Schwartz (1996), Angel (1994), Harris (1998), and Foucault (1999). None of these papers models risk-averse investors, a feature that allows us to generate more realistic implications as well as tying the order placement decision with overall portfolio risk. These papers also include a number of restrictive assumptions that decrease the realistic applicability of their work, and they do not fully provide a method for estimating and using the joint distribution of returns and order fill rates.
Handa and Schwartz (1996) examine the returns from placing a limit order depending on the arrival of liquidity or informed counterparty traders. Handa and Schwartz (1996) also empirically examine the returns for executed and non-executed limit orders. However, whereas Handa and Schwartz (1996) as well as Copeland and Galai (1983) and others classify traders as informed or uninformed, and the expected costs and gains are evaluated for a single-security transaction by a risk neutral trader, the method of the present invention represents the investor's information in terms of expected return and variance of expected return, rather than with the dichotomous informed/uninformed framework. This permits more flexibility in quantifying “information,” and it enables the investor to examine the relation between expected returns, execution probabilities, and returns to various strategies.
Handa and Schwartz (1996) also do not fully model security returns and fill probabilities as correlated random variables, thus their conclusions are markedly different from those given by the present invention. For instance, they find that in the “forced” case, where investors plan on purchasing the security by the close of the trading window, a limit order strategy is always inferior to a market order strategy. This result is in direct contrast to the results of the present method.
Angel (1994) models the limit order decision under the assumption that orders arrive as a Poisson process, an assumption which is both unrealistic and unnecessary to the more general method of our invention. Our model is thus less restrictive than the Angel model in that it does not depend on a particular order generating process. Harris (1998) considers a dynamic model but again under strict discrete assumptions as to investor's information and as to the pricing process. While Harris (1998) and Angel (1994) solve for optimal strategies, the limitations of their assumptions (as well as the fact that they do not consider risk-aversion), makes their models more interpretable as examples of solutions under certain cases.
Foucault (1999) uses a game theoretic model to examine the number of limit and market orders given in a limit order market. His results are partly driven by assuming a trading period of unknown length and also that in equilibrium traders are indifferent between placing limit or market orders. One of Foucault's findings is that limit orders are less likely to be executed if volatility is high. The findings of our empirical work are in contrast to this result of his model. Our method shows that as volatility increases, execution probabilities increase, and frequency of limit order placement decreases because the desirability of limit orders decreases.
In related work, Lo, MacKinlay, and Zhang (1997) present a survival probability model of limit order execution time using industry limit order data. While survival times are an important part of the limit order decision, this approach does not show how investors can optimize limit order placement.
Bertsimas and Lo (1997) present an interesting theoretical analysis of dynamic execution cost control. Their paper demonstrates an approach to optimally segment a large block order into smaller blocks, thereby minimizing trading costs. Howev
Horrigan Holly T.
Wald John K.
Kyle Charles R.
McDonnell & Boehnen Hulbert & Berghoff
Millin Vincent
Pendelton Trading Systems, Inc.
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