Prices of Stocks in Efficient Market - Research Paper Example

Table of Contents Efficient Market Hypothesis: 2 1 The weak form of EMH 2 2 Semi-strong form of EMH 2 3 Strong form of EMH 3 2. Statistical Testing of EMH: 3 3. Data: 3 4. Methodology 4 5. Descriptive Test: 5 6. Autocorrelation Test: 5 7. Appendix 6 8. References 12 Efficient Market Hypothesis: Prices of stocks in an efficient market reflect all available information. Participants in such market would not be able to earn abnormal profits. The intrinsic value of a stock is equal to the future discounted value of cash flows to investors. Company's intrinsic value which is based on its future performance is dependent on currently available information. Company's share price changes only with the emergence of new information that is expected to change a company's profitability. Profitability in an efficient market only exists in response to new information. In 1970, Fama proposed the efficient market hypothesis (EMH). He classified it into three levels based on the definition of available information: weak, semi-strong and strong forms. He further suggested three models for testing market efficiency: the Fair Game model, the Submartingale model, and the Random Walk model. The weak form of EMH attracted all the attention of empirical research in both developed and emerging markets results. This is because if evidence fails to support the weak-from of EMH, stricter forms of EMH would consequently fail (Wong and Kwong, 1984). The weak form of EMH The weak form of EMH considers a market to be efficient if information contained in past prices is already reflected in current market prices. Information from historical prices would not enable market traders to make superior returns as this information is already accounted for in current prices. Semi-strong form of EMH The semi-strong form of EMH considers a market to be efficient only if current market prices reflect all publicly available information, such as information on interest rates, dividends announcements, quarter and annual earnings, etc. Thus market traders would not make superior returns from analysis of market information because market prices will immediately adjust to new news. Strong form of EMH If all market information is immediately reflected in market prices, even private information (inside information) and market participants could not benefit from such knowledge, the market is referred to as strong form of EMH. This assumes that the cost of inside information is zero. This assumption does not exist in reality and thus the strong form of EMH is not likely to hold. Statistical Testing of EMH: The efficient market hypothesis was tested by a number o f statistical test such as autocorrelation, runs test and variance ratio tests. Data: The data used to test for weak form EMH was collected from Yahoo Finance (2008). Historical daily prices for British Petroleum from the British Stock Market were collected 1st of January 2003 to 3rd of November, 2008. This data contains opening price, daily high, daily low, closing price, daily traded volume, and an adjusted close price. Data representing the market is represented by the FTSE 100 British index. FTSE 100 is an index of the largest 100 firms in the UK based on market capitalization. Historical daily prices for FTSE 100 were collected from 1st of January 2003 to 3rd of November, 2008 from yahoo (2008). Daily return is computed by using the following equation: Return (rt) = closing price at any day (pt) - closing price at day before (pt-1) A natural logarithmic transformation is performed on all data of BP and FTSE 100. Daily returns are computed by using the following equation: Return (rt) = closing price at any day (pt) - closing price at day before (pt-1) To generate a time series of continuously compounded returns, daily returns are computed as follows: rt = log (pt) - log (pt-1) = log (pt/pt-1) Where return at some day: rt Closing Price at day (t): pt Closing price at day (t-1): pt-1 Methodology The weak form of EMH states that successive price changes of a stock are independently distributed which is referred to as the random walk. Thus historical prices of stocks could not be used to predict its future changes. First, descriptive statistics are conducted on the above mentioned data. Next, to detect the random walk of stock prices in our data, parametric autocorrelation test is used to examine whether consecutive stocks returns are independent each other. Descriptive Test: Statistical descriptive tests are conducted on data obtained for BP as to better understand the collected data as shown in appendix 1. It was found that the mean of open price is $539 with a standard deviation of $2. The mean for highest daily price for the BP stock is $544 with a standard deviation of $2. The mean for lowest daily price for BP is $534 with a standard deviation of $2. The mean for closing price for BP is $538 with a standard deviation of $2. The mean of log (pt / pt-1) is 0.00005 with a standard deviation of 0.00017. Autocorrelation Test: Autocorrelation is the correlation of the values of a variable with values of the same variable at lagged periods. The Durbin Watson test statistic is used to test for autocorrelation. The null hypothesis (Ho) states that probability equals zero while the alternative hypothesis (H1) states that probability is not equal to zero. Appendix 1: Descriptive Statistics for British Petroleum Open High Low Mean 539.09294 Mean 544.07000 Mean 533.83099 Standard Error 2.04213 Standard Error 2.04211 Standard Error 2.03276 Median 547.00000 Median 551.00000 Median 542.50000 Mode 560.00000 Mode 563.00000 Mode 568.00000 Standard Deviation 79.59077 Standard Deviation 79.59005 Standard Deviation 79.22540 Sample Variance 6334.69120 Sample Variance 6334.57618 Sample Variance 6276.66351 Kurtosis -0.70992 Kurtosis -0.94346 Kurtosis -0.91947 Skewness -0.16534 Skewness -0.21150 Skewness -0.22701 Range 537.95000 Range 357.50000 Range 361.75000 Minimum 358.00000 Minimum 365.50000 Minimum 348.75000 Maximum 895.95000 Maximum 723.00000 Maximum 710.50000 Sum 818882.17000 Sum 826442.33000 Sum 810889.28000 Count 1519.00000 Count 1519.00000 Count 1519.00000 Confidence Level(95.0%) 4.00570 Confidence Level(95.0%) 4.00566 Confidence Level(95.0%) 3.98731 Close Volume Mean 538.67338 Mean 59376647.99210 Standard Error 2.03322 Standard Error 919156.64397 Median 547.00000 Median 50250700.00000 Mode 532.00000 Mode 0.00000 Standard Deviation 79.24335 Standard Deviation 35823533.24323 Sample Variance 6279.50872 Sample Variance 1283325534028790.00000 Kurtosis -0.93088 Kurtosis 5.42940 Skewness -0.21974 Skewness 1.52899 Range 355.50000 Range 359712200.00000 Minimum 356.50000 Minimum 0.00000 Maximum 712.00000 Maximum 359712200.00000 Sum 818244.86000 Sum 90193128300.00000 Count 1519.00000 Count 1519.00000 Confidence Level(95.0%) 3.98821 Confidence Level(95.0%) 1802951.42256 Adj Close log (pt - pt-1) Mean 513.48303 Mean 0.00005 Standard Error 2.48045 Standard Error 0.00017 Median 535.00000 Median 0.00000 Mode 535.00000 Mode 0.00000 Standard Deviation 96.67373 Standard Deviation 0.00660 Sample Variance 9345.81087 Sample Variance 0.00004 Kurtosis -0.97362 Kurtosis 6.58398 Skewness -0.50149 Skewness 0.31193 Range 397.29000 Range 0.08276 Minimum 293.70000 Minimum -0.03680 Maximum 690.99000 Maximum 0.04596 Sum 779980.73000 Sum 0.07565 Count 1519.00000 Count 1519.00000 Confidence Level(95.0%) 4.86546 Confidence Level(95.0%) 0.00033 Appendix 2: Descriptive Statistics for FTSE 100 Open High Mean 5262.759 Mean 5297.162 Standard Error 22.41802 Standard Error 22.48616 Median 5350 Median 5377.1 Mode 6087.3 Mode 6233.1 Standard Deviation 861.2723 Standard Deviation 863.8901 Sample Variance 741790 Sample Variance 746306 Kurtosis -1.21522 Kurtosis -1.24322 Skewness -0.13156 Skewness -0.12128 Range 3445.4 Range 3287.7 Minimum 3287 Minimum 3466.4 Maximum 6732.4 Maximum 6754.1 Sum 7767832 Sum 7818612 Count 1476 Count 1476 Confidence Level(95.0%) 43.9746 Confidence Level(95.0%) 44.10826 Low Close Mean 5228.363 Mean 5262.948 Standard Error 22.31533 Standard Error 22.40693 Median 5318.8 Median 5350 Mode 6567.1 Mode 6087.3 Standard Deviation 857.3268 Standard Deviation 860.846 Sample Variance 735009.2 Sample Variance 741055.8 Kurtosis -1.1846 Kurtosis -1.21421 Skewness -0.14415 Skewness -0.13108 Range 3420.2 Range 3445.4 Minimum 3277.5 Minimum 3287 Maximum 6697.7 Maximum 6732.4 Sum 7717064 Sum 7768112 Count 1476 Count 1476 Confidence Level(95.0%) 43.77315 Confidence Level(95.0%) 43.95283 log (pt - pt-1) Mean 3.02E-05 Standard Error 0.000135 Median 0.000202 Mode 0 Standard Deviation 0.005195 Sample Variance 2.7E-05 Kurtosis 11.21297 Skewness -0.30754 Range 0.077016 Minimum -0.04024 Maximum 0.036781 Sum 0.044615 Count 1476 Confidence Level(95.0%) 0.000265 References Abrosimova, N., Dissanaike, G. & Linowski, D. (2002). Testing Weak-Form Efficiency of the Russian Stock Market, University of Cambridge. Onour, I. (2004). Testing Weak-Form Efficiency of Saudi Stock Exchange Market. Ministry of Economy and Planning, Riadh, Saudi Arabia. Yahoo, finance (2008). Data obtained on November 02, 2008 from http://uk.finance.yahoo.com/q/hps=BP.L&b=1&a=00&c=2000&e=4&d=10&f=2008&g=d Wong, K. A. & Kwong, K.S. (1984). The Behaviour of Hong Kong Stock Prices, Applied Economics 16, pp. 905-917. Read More