AreaExamTR2638 - Relationship between Trading Volume and...

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Relationship between Trading Volume and Security Prices and Returns Walter Sun Area Exam Report MIT Laboratory for Information and Decision Systems Technical Report P-2638 Exam Date: Thursday, February 6th, 2003 Exam Time: 4:15PM - 6:15PM Exam Room: 35-338 (Osborne Room) Abstract The relationship between trading volume and securities prices is a complex one which, when understood properly, can lead to many insights in portfolio theory. Over the past forty years, much work has been done trying to understand this relationship. In this document, we will attempt to introduce and discuss some of these papers. First, we introduce basic topics of finance theory, such as the Capital Asset Pricing Model and two-fund separation. With this knowledge, we proceed to discuss how volume and price move together, how unusual volume can be a predictive measure of future price changes, and also how volume can allow us to infer a hedging portfolio. In each case, we present theoretical models which support empirical results. Finally, we analyze some sample price and volume data around the most recent quarter of earnings announcements.
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CONTENTS i Contents List of Tables iii 1 Introduction and Motivation 1 1.1 Gazing into the Crystal Ball - Predicting Price Movements . . . . . . . . . . . . . . 1 1.1.1 Martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Trading Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.3 Interpretation of Information . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Initial Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Volume’s Effect on Variability of Returns . . . . . . . . . . . . . . . . . . . . 3 1.2.2 Volume’s Predictive Nature for Price Changes . . . . . . . . . . . . . . . . . . 4 1.3 Document Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Overview of Portfolio Theory 6 2.1 Capital Asset Pricing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Why Everyone Holds the Market Portfolio . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Beta of a Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3 Two-fund separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Arbitrage Pricing Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Using APT to Justify Diversification . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Multi-factor Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Efficient Frontier and Markowitz’s Portfolio Selection Model . . . . . . . . . . . . . . 8 2.4 Short Selling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Lemons Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 The Volume-Price Relationship 11 3.1 Volume is Positively Correlated with Absolute Price Changes . . . . . . . . . . . . . 11 3.2 Probabilistic Model for Trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2.1 Consensus on Interpretation of Information . . . . . . . . . . . . . . . . . . . 11 3.2.2 General Case of Information Interpretation . . . . . . . . . . . . . . . . . . . 14 3.3 Volume is Heavy in Bull Markets, Light in Bear Markets . . . . . . . . . . . . . . . . 16 4 Serial Correlation of Returns with Abnormal Volume 18 4.1 Price Movements on Private Information . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Mean Reversion from Non-Informational Trading . . . . . . . . . . . . . . . . . . . . 19 4.2.1 Reasons for Non-Informational Trading . . . . . . . . . . . . . . . . . . . . . 19 4.2.2 Risk-Averse Investors as Market Makers . . . . . . . . . . . . . . . . . . . . . 19 4.2.3 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.2.4 Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5 Inferring the Hedging Portfolio from Prices and Volume 24 5.1 Definitions and the Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.2 Two-factor Turnover Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.3 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.3.1 Estimating the Hedging Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.3.2 Forecasting Market Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.3.3 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
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ii CONTENTS 6 An Analysis of Current Data 30 6.1 Testing the Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.2 Dataset Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 7 Conclusions 34 A Statistics Review and Overview 35 A.1 Transforms of Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A.1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A.1.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A.1.3 Moment-Generating Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 35 A.2 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 A.2.1 Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 A.2.2 p-Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 A.2.3 Law of Large Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 A.3
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