DOCSLIB.ORG

Standard Template for PM and Short Reportsat JIBS

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Standard Template for PM and Short Reportsat JIBS The Validity of Technical Analysis for the Swedish Stock Exchange Evidence from random walk tests and back testing analysis Master Thesis in Economics Author: Dan Gustafsson Tutor: Per-Olof Bjuggren, Louise Nordström Jönköping May 2012 Abstract In this paper I examine the validity of technical analysis for the Swedish stock index OMXS30 between 2001-12-28 and 2011-12-30. Results indicate that OMXS30 followed a non-random walk and that technical trading rules had predictive power over future price movements. Results also suggest that technical trading rules could be used to outperform a buy-and-hold strategy. i Table of Contents Abstract ........................................................................................... i 1 Introduction ............................................................................... 1 1.1 Background and Problem Discussion ..................................................... 1 1.2 Previous Research ................................................................................. 2 1.2 Method ................................................................................................... 3 2 Theoretical framework .............................................................. 3 2.1 The Random Walk Theory ...................................................................... 3 2.2 The Efficient Market Hypothesis ............................................................. 4 2.3 Behavioural Finance ............................................................................... 5 2.4 The Dow Theory ..................................................................................... 6 2.5 Technical analysis .................................................................................. 7 3 Research method ...................................................................... 8 3.1 Random Walk Tests ............................................................................... 8 3.1.2 The Box-Pierce Q-test ........................................................................ 8 3.1.3 Lo & MacKinlay’s Variance Ratio Test ............................................... 9 3.2 Trading Rules ....................................................................................... 10 3.2.1 Standard Moving Average ................................................................ 11 3.2.2 Exponential Moving Average ............................................................ 11 3.2.3 The Relative Strength Index ............................................................. 12 3.2.4 RSIstoch ........................................................................................... 12 3.3 Data Selection ...................................................................................... 13 4 Empirical Results .................................................................... 13 4.1 Empirical Results for the Random Walk Tests ..................................... 13 4.2 Empirical Results from Technical Trading Rules .................................. 16 4.3 Empirical Results for Different Investment Strategies ........................... 19 5 Summary and Conclusion ...................................................... 22 References ................................................................................... 23 Appendix ...................................................................................... 26 ii 1 Introduction In the course of years, literally thousands of research papers have tried to appraise the state of the stock market. In fact, during the past ten decades, few other topics have been so ex- haustively studied. The rewards to those who are able to anticipate the market are enor- mous - no wonder the field has attracted so many financial economist and practitioners. The intensive research has all tried to answer the investor’s problem of how to behave in the stock market. As a result, two rather different disciplines have arisen. The first disci- pline is commonly referred to as fundamental analysis and the second discipline as tech- nical analysis. Fundamental analysis tries to find the “correct” value of a security and, as the name implies, looks at economic fundamentals to do so. Technical analysis on the other hand, appraises securities with the use of historical price information. In this paper I will examine the validity of technical analysis for the Swedish stock index OMXS30 and see if a strategy based on technical trading rules could have outperform a buy-and-hold strategy. As such, this paper will be an interesting contribution to the general discussion of market efficiency, behavioral finance and technical analysis. 1.1 Background and Problem Discussion At a first glance, the use of technical analysis is quite appealing. The primary reason is the anticipation to time and beat the market (buy low and sell high) and spend an inordinate amount of time and research doing so. An investor would no longer need to depend on profit-loss-statements, auditor’s reports and dividend records. Instead, all an investor need is historical price data and a trading rule which generates buy and sell signals. However, finding a trading rule that generates profitable buy and sell signals is easier said than done. As such, to avoid being whipsawed by seemingly erratic market price movements, an inves- tor should first and foremost try to understand the fundamental condition of the stock market before applying technical analysis. For example, if stock markets follow a random walk, market timing would be impossible using technical analysis. As such, a long term in- vestment strategy based on the assumption that stock markets generate good rewards in the long run (from now on called the buy-and-hold strategy), would be superior to any strategy based on technical trading rules. If price movements are predictable, on the other hand, technical analysis should be the obvious choice for any investor when appraising securities. Previous studies have lent some support to the idea that technical analysis could be used to outperform a buy-and-hold strategy for the Swedish stock exchange (SSE). For example, both Frennberg and Hansson (1992) and Säfvenblad (2000) rejected the random walk hy- pothesis (the first obstacle for technical analysis) for the SSE, finding high levels of auto- correlation. Säfvenblad (2000) suggested that the underlying reason for the SSE’s non- random walk behavior was negative feedback trading1 (where investors sell after price in- 1 Feedback trading is a form of trading strategy including: profit taking, herding and dynamic asset allocation (Säfvenblad, 2000) 1 creases). An additional study supporting the use of technical analysis for the SSE is Metghalchi, Chang and Marcucci (2005). Findings suggested that simple moving average techniques have had predictive power over future price movements and could outperform a buy-and-hold strategy for the Swedish stock index OMXS30 between 1986 and 2004. However, except for Metghalchi et al (2005), the validity of technical analysis for the SSE has been notably unexamined until now. Furthermore, as Metghalchi et al findings were based on stock market data between 1986 and 2004, I believe it is high time for a revisit. As such, I will in this paper examine the validity of technical analysis for the Swedish stock in- dex OMXS30 and see if a strategy based on technical trading rules could have outperform a buy-and-hold strategy. To do this I will test the following hypotheses: (1) OMXS30 fol- lowed a non-random walk, (2) technical trading rules did have predictive power over future price movements and (3) strategies based on technical trading could outperform a buy-and- hold strategy. 1.2 Previous Research Criticism of technical analysis often derives from academic research supporting the “weak form” efficient market hypothesis as defined by Fama (1970). Specifically, the validity of technical analysis is often dismissed due to the belief that stock markets follow a random walk. Examples of studies supporting the random walk hypothesis are: Fama (1965)2, Fama & Blume (1966)3 and Jensen & Benington (1970)4. However, numerous of research papers have challenged the random walk hypothesis. In addition to Frennberg & Hansson (1992) and Säfvenblad (2000), empirical evidence supporting non-random walk behavior for stock markets are: Lo and MacKinlay (1988)5, Berglund & Liljeblom (1988)6, Chan (1993)7 and Lima & Tabak (2006)8. 2 Fama (1965) examined stock price movements of the Dow Jones Index between 1956 and 1962. Findings suggested that price changes were uncorrelated over time and therefore consistent with the random walk hypothesis. 3 Fama & Blume (1966) applied Alexander’s filter technique on closing prices of individual securities of the Dow Jones Index between 1956 and 1962. Fama & Blume concluded that the random walk theory was ad- equate for the average investor due to low serial dependence. 4 Jensen & Benington (1970) reexamined Levy’s trading rules for the NYSE between 1931 and 1965. Findings suggested that Levy’s trading rules were outperformed by a buy-and-hold strategy and that price move- ments had followed a random walk. 5 Lo & MacKinlay (1988) tested the random walk hypothesis by comparing variance estimators for the CRSP return index between 1962 and 1985.Findings strongly rejected the random walk hypothesis. 6 Berglund and Liljeblom (1988) examined the Helsinki stock exchange between 1977 and 1982. Findings suggested first order autocorrelation in index returns due to trading procedures. 7 Chan (1993) examined
Load more

Recommended publications
  • Testing the Random Walk Hypothesis for Helsinki Stock Exchange
    Testing the Random Walk Hypothesis for Helsinki Stock Exchange Niklas Miller School of Science Bachelor’s thesis Espoo, 16.4.2018 Supervisor and advisor Prof. Harri Ehtamo Copyright ⃝c 2018 Niklas Miller Aalto University, P.O. BOX 11000, 00076 AALTO www.aalto.fi Abstract of the bachelor’s thesis Author Niklas Miller Title Testing the Random Walk Hypothesis for Helsinki Stock Exchange Degree programme Engineering Physics and Mathematics Major Mathematics and Systems Analysis Code of major SCI3029 Supervisor and advisor Prof. Harri Ehtamo Date 16.4.2018 Number of pages 25+2 Language English Abstract This Bachelor’s thesis examines the random walk hypothesis for weekly returns of two indices, OMXHPI and OMXH25, and eight stocks in Helsinki Stock Exchange. The returns run from January 2000 to February 2018. In order to test the null hypothesis of a random walk, the study employs three variance ratio tests: the Lo– MacKinlay test with the assumption of heteroscedastic returns, the Chow–Denning test and the Whang–Kim test. The variance ratio estimates produced by the Lo–MacKinlay test are analyzed for various lag values. The results indicate that both indices and all stocks, except for UPM–Kymmene, follow a random walk at the 5 percent level of significance. Furthermore, the variance ratios are found tobe less than unity for shorter lags, which implies that stock returns may be negatively autocorrelated for short return horizons. Some stocks and both indices show a high variance ratio estimate for larger lag values, contradicting a mean reverting model of stock prices. The results demonstrate, in contrast to previous studies, that Helsinki Stock Exchange may be an efficient market and thus, that predicting future returns based on historical price information is difficult if not impossible.
    [Show full text]
  • The Efficient Market Hypothesis
    THE EFFICIENT MARKET HYPOTHESIS A Thesis Presented to the Faculty of California State Polytechnic University, Pomona In Partial Fulfillment Of the Requirements for the Degree Master of Science In Economics By Nora Alhamdan 2014 SIGNATURE PAGE THESIS: The Efficient Market Hypothesis AUTHOR: Nora Alhamdan DATE SUBMITTED: Spring 2014 Economics Department Dr. Carsten Lange _________________________________________ Thesis Committee Chair Economics Dr. Bruce Brown _________________________________________ Economics Dr. Craig Kerr _________________________________________ Economics ii ABSTRACT The paper attempts testing the random walk hypothesis, which the strong form of the Efficient Market Hypothesis. The theory suggests that stocks prices at any time “fully reflect” all available information (Fama, 1970). So, the price of a stock is a random walk (Enders, 2012). iii TABLE OF CONTENTS Signature Page .............................................................................................................. ii Abstract ......................................................................................................................... iii List of Tables ................................................................................................................ vi List of Figures ............................................................................................................... vii Introduction .................................................................................................................. 1 History .........................................................................................................................
    [Show full text]
  • Technical Analysis and Random Walks
    ~ Technical Analysis and Random Walks There are two kinds of security analysis . Fundamental analysis seeks to forecast each stock 's return by studying the prospects for the company 's business . Technical analysis attempts to forecast the return by searching for patterns in past stock prices . Although a glance at any chart of past stock prices will often suggest such patterns , these could be no more than an optical illusion . Consider , for example , the following series of graphs . Figure 1.1 depicts the level of the Dow Jones Average during 1981. It appears to be characterized by typical short -term patterns . Yet when it is reconstructed in figure 1.2 as a chart of the weekly changes in the index , the symmetry disappears and is replaced by an apparently mean - ingless jumble . The next two diagrams reverse the process . Figure 1.3 is a hypothetical series of random price changes . There neither is nor appears to be any pattern in figure 1.3. Yet when it is reconstructed in figure 1.4 as a chart of the levels of the counterfeit prices , the resulting graph acquires many of the characteristics of actual charts of the market , even to the " head and shoulders " pattern that is beloved by technical analysts .] The moral of the story is this : Do not assume without questioning because there are regularities in price levels that The Reaction of Common Stock Prices to New Information 4 Figure 1.1 The weekly levels of the Dow JonesAverage in 1981 appear to be characterized by regular patterns. Figure 1.2 The changesin the Dow Jonesdo not appear to follow any pattern.
    [Show full text]
  • Openair@RGU the Open Access Institutional Repository at Robert Gordon University
    OpenAIR@RGU The Open Access Institutional Repository at Robert Gordon University http://openair.rgu.ac.uk Citation Details Citation for the version of the work held in ‘OpenAIR@RGU’: SANUSI, M. S., 2015. Market efficiency, volatility behaviour and asset pricing analysis of the oil & gas companies quoted on the London Stock Exchange. Available from OpenAIR@RGU. [online]. Available from: http://openair.rgu.ac.uk Copyright Items in ‘OpenAIR@RGU’, Robert Gordon University Open Access Institutional Repository, are protected by copyright and intellectual property law. If you believe that any material held in ‘OpenAIR@RGU’ infringes copyright, please contact [email protected] with details. The item will be removed from the repository while the claim is investigated. MARKET EFFICIENCY, VOLATILITY BEHAVIOUR AND ASSET PRICING ANALYSIS OF THE OIL & GAS COMPANIES QUOTED ON THE LONDON STOCK EXCHANGE Muhammad Surajo Sanusi A thesis submitted in partial fulfilment of the requirements of the Robert Gordon University for the degree of Doctor of Philosophy June 2015 i Abstract This research assessed market efficiency, volatility behaviour, asset pricing, and oil price risk exposure of the oil and gas companies quoted on the London Stock Exchange with the aim of providing fresh evidence on the pricing dynamics in this sector. In market efficiency analysis, efficient market hypothesis (EMH) and random walk hypothesis were tested using a mix of statistical tools such as Autocorrelation Function, Ljung-Box Q-Statistics, Runs Test, Variance Ratio Test, and BDS test for independence. To confirm the results from these parametric and non-parametric tools, technical trading and filter rules, and moving average based rules were also employed to assess the possibility of making abnormal profit from the stocks under study.
    [Show full text]
  • Stock Market Prices and the Random Walk Hypothesis: Further Evidence from Nigeria
    Journal of Economics and International Finance Vol. 2(3), pp. 049-057, March 2010 Available online at http://www.academicjournals.org/JEIF ISSN 2006-9812© 2010 Academic Journals Full Length Research Paper Stock market prices and the random walk hypothesis: Further evidence from Nigeria Godwin Chigozie Okpara Department of Finance and Banking, Abia State University Utur - Nigeria. E-mail: [email protected]. Accepted 29 January, 2010 The weak form hypothesis has been pointed out as dealing with whether or not security prices fully reflect historical price or return information. To carry out this investigation with the Nigerian stock market data, we employed the run test and the correlogram/partial autocorrelation function as alternate forms of the research instrument. The results of the three alternate tests revealed that the Nigerian stock market is efficient in the weak form and therefore follows a random walk process. Thus, the opportunity of making excess returns in the market is ruled out. Keywords: Market efficiency, weak form hypothesis, stock market returns, equity, run test, autocorrelation test. INTRODUCTION A stock market is a public market for the trading of stringent for small and medium scale enterprises. A close company stock and derivatives at an agreed price. The comparative observation in the trading activities of the stocks are listed and traded on stock exchanges. The Nigerian stock exchange reveals that the share of Nigerian stock exchange (NSE) is the center - point of the government stock from 1963 to 1990 had been Nigerian Capital Market, while the Securities and overwhelmingly exceeding the industrial equities. But as Exchange Commission (SEC) serves as the apex from 1991 to date the reverse became the case to the regulatory body.
    [Show full text]
  • Test of Random Walk Hypothesis: a Study in Context of Indian Stock Market *Dr Sonali Yadav
    Test of Random Walk Hypothesis: A Study in Context of Indian Stock Market *Dr Sonali Yadav ABSTRACT Presence or absence of random walk has always caught show that Indian stock market is not 'weak form efficient'; thus, attention of academicians, stockbrokers, individuals, the prices do not follow a random walk and there exists a pattern institutional investors, financial institutions, and regulators in in them. If these patterns can be exploited at the right time and the area behavioral finance. If the markets are 'weak form right manner, investors can earn abnormal returns from the efficient', technical analysis fails to make any comments on market. This result also supports the relevance of technical future price behavior. With this view, the current paper analysis as a trading strategy. At the same time, the market contributes to the existing literature by investigating the weak- regulators should re-think as to why the markets are not form market efficiency in Indian Stock market, one of the fastest efficient despite numerous measures taken since 1991. emerging markets of the world. Daily data of Bombay Stock Exchange (BSE) 200 index-based companies over the period of 1 Keywords : Augmented Dickey Fuller Test, Phillip Parron Test, January 1991 to 31 December 2016 is tested employing Runs Test, Random Walk, Runs Test, Variance Ratio Test, Weak Form Augmented Dickey–Fuller Test (ADF) Test, Phillips Perron Test Efficiency (PP) Test, Normality Test and Variance Ratio Test. All five tests * Assistant Professor, IBS, Gurgaon, India TEST OF RANDOM WALK HYPOTHESIS: A STUDY IN CONTEXT OF INDIAN STOCK MARKET NTRODUCTION been observed that as the market matures over time due to strengthening of regulatory environment and improvement in I Stock markets are efficient! Are they? Can there trading conditions, the stock market tends to move towards be abnormal gains by capitalizing on efficiency, Emerson et al.
    [Show full text]
  • Testing for Random Walk Hypothesis with Or Without Measurement Error
    Testing for random walk hypothesis with or without measurement error Tin-Yu Jonathan Hui A thesis submitted in partial fulfilment of the requirement for the degree of Master of Science of Imperial College London and Diploma of Imperial College London September 2012 1 ABSTRACT In biological study it is common to take observations over time and thus there is strong need in developing tools to analyse time series data. Variations of dynamics over time are often modelled for estimation and forecasting. The random walk process in particular is one of the most commonly used models and serves as the null hypothesis in many theories. As a result, this paper adopts the Q-statistic and Variance-Ratio (VR) Test to test the random walk hypothesis and assesses their testing power against AR(1) model. It is shown that both the Q-statistic and VR Test are valid tests in testing against AR(1) and VR has a higher testing power. Testing power decreases when ϕ approaches unity as the AR(1) process becomes less distinguishable from random walks. In population genetics allele frequencies fluctuate along generations, known as genetic drift. If there exist external forces such as selection, the drift will then have a trend and drive the allele to extinction or fixation. This motivates the second test for a trend in random walk. Both Likelihood Ratio Test and modified Variance-Ratio can test for trends within random walk models. It is shown that the power of the two tests increases with the trend-to-standard deviation ratio. In general the Likelihood Ratio Test provides a better power in testing for a trend.
    [Show full text]
  • Testing the Random Walk Hypothesis of Stock Indexes Through Variance- Ratio
    Periodicals of Engineering and Natural Sciences ISSN 2303-4521 Vol.7, No.1, January 2019, pp. 12~19 Available online at: http://pen.ius.edu.ba Testing the random walk hypothesis of stock indexes through variance- ratio Sadi Fadda, PhD Article Info ABSTRACT The Random Walk is considered to be a tool trying to explain the characteristic of movement of prices in the financial markets. It can also be Received Dec 3, 2018 seen in the form of a trial to demonstrate the non-predictability of future changes in the financial markets through reliance on the characteristics identified based on past price changes. In this paper used is the variance-ratio test initiated by Lo and MacKinlay to test the Random Walk Hypothesis for a Keyword: more recent data of eleven Stock Indexes, seen as main indexes of the current Random Walk Hypothesis market. Variance Ratio Stock Indexes 1. INTRODUCTION As any investor would wish to be able to predict the movement direction of some asset price, the Random Walk Hypothesis argues it not to be a realistic option. Just as the name itself suggests, the assumption of the Random Walk Hypothesis (RWH) is that the prices experience change (walk) in an unpredictable direction and measure. The expected return should remain the same, and the covariance between any two separate returns should always be 0. The initiator of the RWH was [1]. Informationally Efficient Market defines a market where all the relevant information that impacts the price of a financial instrument is available to everyone at no additional cost. The efficient market hypothesis (EMH) states that all the share prices are a reflection of its relevant information, whereby the stocks trade at the price they are worth.
    [Show full text]
  • The Economics of Financial Markets
    The Economics of Financial Markets Roy E. Bailey Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge ,UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridg e.org /9780521848275 © R. E. Bailey 2005 This book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2005 - ---- eBook (EBL) - --- eBook (EBL) - ---- hardback - --- hardback - ---- paperback - --- paperback Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. The Theory of Economics does not furnish a body of settled conclusions imme- diately applicable to policy. It is a method rather than a doctrine, an apparatus of the mind, a technique of thinking, which helps its possessor to draw correct conclusions. It is not difficult in the sense in which mathematical and scientific techniques are difficult; but the fact that its modes of expression are much less precise than these, renders decidedly difficult the task of conveying it correctly to the minds of learners. J. M. Keynes When you set out for distant Ithaca,
    [Show full text]
  • On Random Walk Hypothesis by Aijia Zhang ABSTRACT. the Random
    On Random Walk Hypothesis By Aijia Zhang ABSTRACT. The random walk hypothesis popularized by Burton Malkiel’s book, A Random Walk Down Wall Street, has been the object of discussions to many scholars and finance professionals. The hypothesis states that short-term stock price movements are statistically random and thus not predictable. The theory is consistent with the efficient-market hypothesis and has real implications for investors and security analysts as it implies the limitations of technical and fundamental analysis to earn a profit in the stock market. This paper will first describe two important approaches to predicting stock price changes and some basic assumptions behind the random walk theory. Then it will focus on examining the independence and the distribution of stock price changes. So far, empirical data shows strong support for the random walk hypothesis. The random walk hypothesis has elicited many debates and discussions among scholars and finance professionals. This concept was first proposed by the French broker Jules Regnault who published the first book about the modern theory of stock price changes. Formal research can be traced back to the French mathematician Louis Bachelier in 1900. It was not until the 1970s that the term was popularized by the book, Random Walk Down the Wall Street, by Burton Malkiel, who was an economics professor at Princeton University. In Malkiel’s book, he described an experiment in which he asked his student to construct a stock chart of a hypothetical stock initially selling at $50. Each successive price change was determined by a coin flip. Consequentially, the hypothetical stock chart resembled a normal stock chart and even displayed repetitive patterns.1 The random walk hypothesis states that stock price changes are random and are thus cannot be predicted based on past information.
    [Show full text]
  • Efficient Market Hypothesis
    Efficient Market Hypothesis 1EfficientMarketHypothesis The Efficient Market Hypothesis (EMH) applies Rational Expectations to the pricing of assets: When investors use all available information in forming expectations of future rates of return, the equilibrium price of the asset equals the optimal forecast of funda- mental values based on the available information (i.e., the present value of expected future returns on the asset). In an efficient financial market, all information currently available is reflected in the asset price. An implication of EMH is that asset price follows a random walk (or more generally, a martingale). 1.1 Random Walk and Martingale If changes in stock prices caused by arrival of new information is random, then the level of stock prices follows a random walk: pt+1 pt = εt+1. − To make full use of past stock price data, we can consider a more general form of EMH, that is, stock prices follow a martingale: E (pt+1 pt Ωt)=0, − | where Ωt = pt,pt 1,pt 2,... Martingales are random variables whose future variations { − − } are completely unpredictable given the current information set. In other words, the directions of the future movements in martingales are impossible to forecast. Thus, the best forecast of tomorrow’s stock price is today’s price: E (pt+1 Ωt)=pt. | 1 1.2 Implications 1. Any change in market price from one period ahead will be completely accounted for by new information on market fundamentals which arrives between time t and t +1.Ifthe predicted price (E (pt+1 Ωt)) based on publicly available information is different from | the current price (pt), there exists an arbitrage opportunity.
    [Show full text]
  • Variance Ratio Tests of the Random Walk Hypothesis for European
    The European Journal of Finance 9, 290-300 (June 2003) Variance ratio tests of the random walk hypothesis for European emerging stock markets GRAHAM SMITH* and HYUN-JUNG RYOO Department of Economics, School of Oriental & African Studies, University of London, Thornhaugh Street, Russell Square, London WC1H0XG, UK '[email protected] The hypothesis that stock market price indices follow a random walk is tested for five European emerging markets, Greece, Hungary, Poland, Portugal and Turkey, using the multiple variance ratio test. In four of the markets, the random walk hypothesis is rejected because of autocorrelation in returns. For the Istanbul market, which had markedly higher turnover than the other markets in the 1990s, the stock price index follows a random walk. This contrasts with the results of earlier research, carried out for periods of lower turnover, which rejected the random walk hypothesis. Keywords: emerging markets, random walk hypothesis, stock prices, variance ratio tests 1. INTRODUCTION Equity markets play a central role in the pricing and allocation of capital and the pricing of risk and their efficiency can be assessed by examining the behaviour of equity prices. In markets that are weak-form efficient, equity prices completely reflect all of the information contained in the past history of prices and do not convey information about future changes in prices. If they did convey such infor- mation there would be profit-making opportunities for Investors and so markets would be imperfect. A widely used test of weak-form efficiency is to see whether equity prices follow a random walk - a test that can be used with individual equities or with stock price indices.
    [Show full text]