High-frequency data analysis

Table of Content

Table of Illustrations and Equations

1 Introduction

2 Basic Facts
2.1 Financial Market
2.2 Market Microstructure
2.3 High-Frequency Data

3 Bid-Ask Spread
3.1 Definition
3.2 Approaches and Research
3.3 Roll-Model (1984)

4 Empirical Analysis of the Roll-Model
4.1 Data Analysis
4.2 Empirical Part
4.3 Conclusions

5 Final Remarks

Appendix

Bibliography

Table of Illustrations and Equations

Illustration 1: Path of observed Market Prices

Illustration 2: Probability Distribution & Combined Joint Distribution

Illustration 3: Positive Roll estimators

Illustration 4: Spreads of A

Illustration 5: Spreads of B

Illustration 6: Dickey Fuller Test

Illustration 7: Standard Deviations of Price Differences (Stock A, B)

Illustration 8: Volatility of Price Differences

Formula 1: Variance for Discrete Values

Formula 2: Covariance for Discrete Values

Formula 3: Autocorrelation

Formula 4: Empirical Autocovariance

Figure 1:

1 Introduction

Today the financial market becomes more complex and includes more competition. Reasons are trends like globalization, liberalization and lower-cost trading mechanism. The market microstructure research has the aim of an efficient market. It is focused on the structure of the financial market. The investigation becomes possible through the availability of high-frequency data. Those data exist especially in the United States and like that most of the research focuses this market. To explain the phenomena, which have been found adequate, models that fit the characteristics of high-frequency data have to be developed.

The research is important to understand actions on the market as well as develop new efficient mechanism. One part of the market microstructure field is the bid-ask spread. It will be focus of this paper. In the first two parts it will be discussed theoretically. In the last part one model will be empirically analyzed and tested on its usefulness and validity.

The second part of this paper explains the basic elements surrounding the research of bid-ask spread. Those are the financial market, market microstructure as well as high-frequency data. In the following part the bid-ask spread itself, approaches, researches and models focussing the spread will be discussed. The model of Roll (1984) will be explained in detail. The last part will be the empirical analysis of the model of Roll. It is analyzed with data from the NASDAQ.

2 Basic Facts

In this chapter the basics of this paper will be discussed. The bid-ask spread is part of the market microstructure discussion. Market microstructure research aims at the financial market and is possible through the availability of high-frequency data. Those data are important for the statistical analysis of financial market phenomenon.

2.1 Financial Market

The financial market is a market where buyers and sellers contract to exchange financial instruments and services. There are different possibilities to characterize this market. The market can have a national or international dimension. Another alternative is the distinction between short- and long-term instruments that aims at the date when the financial transaction is completed. Former claims are mostly traded on money markets, latter ones on capital markets. The instruments used on the market can be primary or secondary ones. On the primary market the instruments are emitted and on the secondary one existing ones are traded.^[1] Those are the main characteristics. Each financial market is specified by its trading mechanism.

The main determinants of a trading mechanism are the market participants, the place and the rules. The market participants are buyers and sellers, who can contact each other directly as well as intermediaries, through which they can interact. One type of intermediary is the market maker. He is a specialist and quotes prices to buy or sell the asset. The place focuses on how the instruments are traded, on a central physical location or electronically. The rules determine how the process works. They contain what can be traded, who can trade, when and how orders can be submitted, who may see or handle the orders, how orders are processed and how prices are set. Each mechanism has its own set of rules like that it is not useful to describe each trading mechanism.^[2]

One goal of a market is price discovery. The main alternatives therefore are the order-driven and quote-driven form. Former means that complete orders with price and volume are named. Latter contains a market maker. Today hybrid forms establish.^[3] In general price discovery with intermediaries and without them is possible.

Many determinants influence the actions of the market, which have to be studied on the one hand, and are complicate to investigate on the other hand. The kind of traded goods, how the market participants are supplied with information, their perception about the future as well as institutional characteristics influence the price formation and how to do business.^[4] Other factors affecting the buying and selling behavior of traders and market makers are risk aversion, private information and wealth constraints.^[5]

2.2 Market Microstructure

Market microstructure analyzes how specific trading mechanisms affect the price formation process. In other words it considers the structure or institutional characteristics of capital markets. The financial market can be formed in several ways and many determinants influence its actions like explained in 2.1. It is important to look how and by what returns are influenced as well as which market form is efficient and how it becomes efficient. The application of market microstructure is found in regulation of markets and in finding new trading mechanisms.^[6]

Market microstructure aims at the secondary market, where existing instruments are traded. The neoclassic capital market models assume that all market participants have homogeneous expectations about the future. Prices for buyers and sellers are equal and thus they are price takers.^[7] Implicit the trading mechanism plays no role there.^[8] Furthermore it assumes perfect markets, free market entry and no transaction costs. The market microstructure on the other hand assumes an imperfect capital market, asymmetric information allocation and that the provision of information is not for free.^[9]

The need to understand the relationship between competition, market structure and market quality is greater than ever. Reasons are current trends like globalization, liberalization of capital markets, democratization of information technology, development of new lower-cost trading mechanism and the expansion of derivatives markets in developed and emerging economies.^[10] Like that it is intensively researched now. Stocks compete for customers by means of service quality and pricing quality because there are increasing possibilities for investors, through the rise of new electronic communication networks.^[11]

The object of research is for example how different systems of price discovery influence trading activities and price formation^[12] or the efficiency of different trading systems (open out-cry system, computer trading system).^[13] The measurement of execution costs and market liquidity, the comparison of alternative market making mechanism, the impact of competition and the potential for collusion among market makers are other aspects.^[14] The increased availability of detailed and sometimes real-time data on prices, orders and other market information makes a detailed empirical investigation possible.^[15]

In economic and finance market microstructure is actively researched. Many markets and many models are within the research. Empirical measures are required to test some of these models and to determine the importance of market microstructure effects for other research areas. Those aspects are for example non-synchronous trading, bid-ask spread, techniques of modeling transaction data^[16] and duration models. Focus of this paper is the bid ask spread. It has to be considered that high-frequency data are used. Methods of analyzing them data have to be found and studies of its special characteristics have to be made.^[17]

2.3 High-Frequency Data

High-frequency data are observations taken at fine time intervals. In finance that means daily or more often. In security markets that are transaction-by-transaction or trade-by-trade data. High-frequency data are important in studying issues with regard to trading processes and market microstructure. The reasons for that development are advances in data acquisition and processing techniques.^[18] In Germany electronic quotation systems provide data since 1988 but relevant data for the bid-ask spread are not available for German floor trading. The spreads on the electronic quotation and trading system may not be representative because most of the trading is still concentrated on the floors.^[19] On American markets the data availability is better. In the early 1990 intra-day data on every trade from the NASDAQ and NYSE became available.^[20]

High-frequency data have some unique characteristics that do not appear in lower frequencies. Different aspects have to be considered by financial economists and statisticians when analyzing those data.^[21] Empirical characteristics of transaction data are unequally spaced time intervals, transaction activity exhibiting periodic pattern and multiple transactions within a single second.^[22] Transaction prices are always quoted in discrete units or ticks, for example $0.125 for equities. They do not really fit existing frameworks. Reasons are for example irregular sampled intervals and thus unlikely identically distributions. Transaction data can be obtained but they have a great size. Like that they are hard to manipulate but it is also difficult to analyze them.^[23]

In the process of modeling economic phenomena some features of the data will be lost. It is important to determine which features to focus on. The process of trading can have important impact on the statistical properties of financial asset prices. Reasons are institutional structures and that securities are not traded at evenly spaced intervals and sometimes they are not traded at all throughout the day. In markets with market makers a spread between the buying and selling prices exist. This can have an impact on the autocorrelation of price changes. For some purposes such aspects of the market’s microstructure can be ignored, particularly when longer investment horizons are involved. That means it is unlikely that the negative autocorrelation in the five-year returns is caused by prices bouncing back and forth between bid-ask prices.^[24] In a lot of workings the influence of the market structure on an important part of the transaction cost empirical researched, which is the bid-ask spread and its components.

3 Bid-Ask Spread

There are a lot of researches and models, which investigate different aspects of the market to cover efficient structures. One aspect of research is the bid-ask spread. After defining and explaining the spread, approaches and research are addressed. The model of Roll (1984) will be explained and discussed in detail because it will be statistically analyzed in part 4.

3.1 Definition

Investors look among other things for liquidity. It is maintained by market makers in many organized exchanges^[25]. Liquidity is the ability to buy or sell securities quickly, anonymously and with relative little price impact. Market makers are one type of intermediary who quotes prices and sells or buys whenever the public wishes. That is the advantage for the market participants. Therefore the market maker can sell at a higher ask price and buy at a lower bid price. This is his primary compensation for providing liquidity.^[26] The bid-ask spread is like that the costs when a security is bought and at the same moment sold. For the investor the aspect of liquidity that means the bid-ask spread is important because it is considered to be a good proxy for the cost of immediacy.^[27]

The bid-ask spread complicates the calculation of returns. One security has more than one price. The bid price, the ask price and the transaction price which need neither to be the bid, nor the ask and does not necessarily lie between them. Through prices bouncing back and forth between bid and ask prices, spurious volatility and autocorrelation in returns is created although the value of the security is unchanged. This aspect is used in the model of Roll (1984), that accounts the impact of the bid-ask spread on time-series properties of asset returns.^[28] Although the bid-ask spread is small it has important consequences. The negative lag-1 autocorrelation is referred to as the bid-ask bounce.^[29]

When taking quoted spread as the spread between the quoted bid and ask prices

Quoted spread = bid price – ask price (1)

the spread is useful for measuring the maximum price that an investor would expect to pay for a transaction. The problem, discussed above, is that trades are frequently executed within the quotes. The effective spread as a measure of transaction costs allows for trades within or outside the quotes.^[30]

(2)^[31]

When the price of the trade, the bid quote and ask quote are available, it is easy to calculate the effective spread. If they are not available an estimator will maybe be helpful. One estimator of the effective spread is that from Roll. It seems unnecessary to estimate bid-ask spreads because those quotes are observable but quoted spreads (1) may differ from effective ones (2). A reason can be that market makers do not update their quotes or wish to rebalance their inventory or provide discounts to customers that are trading for reasons other than private information so that the transaction occurs at prices within the spread.^[32]

[...]

^[1] See Heffernan (2002), pp. 1957 et seq.

^[2] See O’Hara (1995), pp. 7 et seqq.

^[3] See Cramer (1999), p. 229.

^[4] See Möller/Hüfner (2001), p. 1277.

^[5] See O’Hara (1995), p. 12.

^[6] See O’Hara (1995), p. 1.

^[7] See Cramer (1999) p. 1291.

^[8] See O’Hara (1995), p. 3.

^[9] See Neus/Hirth (2001), p. 1306.

^[10] See Mayhew (2002), p. 931.

^[11] See Freihube/Krahen/Theissen (2002), p. 255.

^[12] See Möller (2001), p. 1279.

^[13] See Tsay (2002), p. 175.

^[14] See Campbell/Lo/MacKinley (1997), p. 83.

^[15] See O’Hara (1995), p. 2.

^[16] See Campbell/Lo/MacKinlay (1997), p. 83 et seq.

^[17] See Tsay (2002), p. 176.

^[18] Ebenda, p. 175.

^[19] See Schmidt/Iversen/Treske (1999), pp. 80, 89.

^[20] See Pahls (2001).

^[21] See Tsay (2002), p. 175.

^[22] See Tsay (2002), p. 181.

^[23] See Campbell/Lo/MacKinlay (1997), p. 107.

^[24] Ebenda, p. 83.

^[25] On the NYSE market makers are important (Tsay, p. 179); Nasdaq and Germany has market makers as well as public investors transacting directly with each other (Schmidt/Iversen/Treske, p. 90)

^[26] See Campbell/Lo/MacKinlay (1997), pp. 99 etseq.

^[27] See Schmidt/Iversen/Treske (1999), p. 80.

^[28] See Campbell/Lo/MacKinlay (1997), pp. 100 et seq.

^[29] See Tsay (2002), pp. 179 et seq.

^[30] See Schultz (2000), pp. 921 et seqq.

^[31] See Schultz (2000), p. 925; Mayhew (2002), p. 937.

^[32] See Campbell/Lo/MacKinlay (1997), pp. 101 et seq.