The Properties and Predictability of the US Stock and the UK Stock - Essay Example

The purpose of this paper is to identify the properties and predictability of the US stock and the UK stock. The time series properties of the two indices were characterized and further coefficient of correlation between them was identified. The Other January effect was observed for the two indices and its presence in the two stocks were identified. The long horizon regression analysis is done on the stock data expanding over 31 years (Jan 1973 – Dec 2004). It was found out that the US stock provided better returns but was more volatile than its UK counterpart. The rates of return on the two indices were correlated. Both the indices generally followed the Other January effect. Introduction New York Stock Exchange (the US Stock) was officiated on March 18, 1817. London stock exchange (the UK Stock) was founded in 1801. The two stocks combined have the highest Market cap (17.0 trillion) and largest volume (3.1 trillion) in the world [1]. Any movement in these markets pushes stock indices all over the world. Drawing parallels from the common and integrated political and economic interests the host countries of these stock indices, it can be hypnotized that these market are correlated. This paper tries to identify, if any, correlation present between the two indices. As mentioned before the NYSE and the LSE sit on huge pile of money and are influential. Hence it is important to figure out their predictability. This paper assesses the predictability of these stock indices. The paper has been segregated into three segments: First section characterizes time series properties of the stocks namely its rate of return and its volatility. Second section identifies the January effect. Section three provides an estimation of predictability using long-horizon regressions. For the purpose, monthly data of the stock indices starting from January, 1973 till December, 2004 is analyzed. 1. Time Series Analysis The rate of return is defined as the money earned on an investment (in stocks). Volatility is the measure of fluctuation in the asset (stock) prices. Mean and variance of rate of return and volatility is used to characterize a stock [2]. Curve of distribution of data is measured by Skewness and Kurtosis of the graph. A normal distribution curve is bell shaped symmetric around the mean. A positively skewed distribution is skewed to right. Skewness is measured as 3rd movement of mean. A Kurtosis is a measure of flatness of the top of the graph. Larger value of degree of kurtosis would mean sharper peak [11]. The rate of return of the indices was analyzed against time. The volatility of the market was also measured. The rate of return was measured as the difference of natural log of the monthly index value. Volatility was measured as the standard deviation of rate of return of the market in a year. Each Index was characterized by its mean of rate of return and its variance of rate of return and volatility. [3] Rate of return Volatility Mean (ln values) Variance Skewness Kurtosis Mean (ln values) Variance Skewness Kurtosis UK 0.010753 0.0034 -0.18 7.31 0.053 0.000682 0.94 1.65 US 0.008991 0.0022 -0.95 6.35 0.043 0.000313 0.72 0.90 The result showed that rate of return on was higher in UK index than in US index by around 20%. Also, the UK market was around 23% more volatile than the US market. Variance of rate of return and volatility showed that UK market was more spread than US stocks. High degree of kurtosis for rate of return of the UK and the US stocks suggested sharp peak of the distribution graph. From degree of kurtosis it could be inferred that volatility was not restricted to certain range of stock return values but was spread over a long value range of returns. It is to be noted that in 31 years starting from Jan 1973, US market grew from 98.66 to 3087.82 (31X) in Dec 2004, while the UK markets grew from 319.53 to 19639.99 (61X) in the same period. Distribution of rate of return data was left tailed for both US and UK stocks while distribution of volatility data was right tailed for both the stocks. The correlation between the two markets was also analyzed. Coefficient of Correlation Rate of return 0.63 Volatility 0.66 There was a correlation observed between the rates of return of the two indices. There was a correlation observed between the volatility of the markets. These numbers showed that the markets influence each other. 2. The Other January Effect The Other January effect is described as a phenomenon where returns of January indicate the performance of the stock for rest of the year [4]. This phenomenon has been under observance since 1973. It must not be confused with the January effect. January effect is described as a phenomenon where small and low priced stocks perform exceptionally well in January though they have a past record as a non performers. At first look the Other January Effect can be attributed to the investor’s sentiments which trickle down the rest of the year. But the pattern followed by the market is affected from the macroeconomic and business cycle can also be a possible reason for the trend. It has been observed that the return in January is a predictor of rate of return for rest of the year for all kinds of listed firms: SMEs, firms with high value stocks and growth stocks. Also, analysis showed that the month January is special in the scenario. Other months do not act as predictors with such high efficiency [5]. Also, there has been no specific pattern to suggest that the other January effect is a short horizon phenomenon. The other January Effect can be a powerful tool to predict the market and other portfolios [6]. Incorporating it into asset pricing benchmarks may help evaluate portfolio managers’ performance. In this paper, rate of return was analyzed for the month of January and for the rest 11 months cumulatively starting from 1973 up till 2004 for the UK and the US indices. The graphs show the movement of rate of return for January and rest 11 months through time. In the US stock returns data, of 18 times when the returns in January were high, 10 times the cumulative stock markets returns for the rest 11months were high. Of 13 times when the returns in January were low, 7 times the cumulative stock markets returns for the rest 11months were high. In the UK stock returns data, of 17 times when the returns in January were high, 13 times the cumulative stock markets returns for the rest 11months were high. Of 14 times when the returns in January were low, 10 times the cumulative stock markets returns for the rest 11months were high. The result of the analysis is shown in the graphs. A general rule can be deduced that if the rate of return of indices in January is high, the rate of return for the year can be expected to be high. The reverse is not true. When the rate of return of January is low it does not indicates that the rate of return will be low. 3. Long Horizon Regression Predicting markets is one of the routines followed to earn good money. For quite some time (till mid - 1980s) market was supposed to be unpredictable. Later it was found that the markets are predictable, even if they are efficient [7]. Aim of this section is to identify any correlation between dividends and rate of returns and hence justify the hypothesis: whether markets are predictable. It is conventional wisdom that markets are predictable at longer horizons and that dividend is a deciding factor to estimate rate of return of the markets [8]. The model to estimate rate of return is called the discounted-cash-flow or present-value model. As markets move in exponential curves, the linear models are less efficient (as they impose restriction) in explaining the properties of the market than non linear models [9]. The log linear model captures the market behavior and does not impose any restrictions on the expected returns. Its explanation is provided by the phenomenon that each day having slight predictability of returns when added to the horizon increases it’s over all predictability. Autocorrelation examines if the given data forms a pattern. It evaluates the randomness of the data. The data were regressed to identify log linearized equation. Long horizon regression was done for 3 months, 6 months, 12 months and 24 months. The equation obtained from the regression was used to generate calculated returns. UK Index Horizon 3 6 12 24 Slope 0.34575 0.294662 0.22843 0.205415 Constant -1.30883 -1.08246 -0.78626 -0.67066 US Index 3 6 12 24 Slope 0.246216 0.24237 0.234478 0.229954 Constant -0.50062 -0.48724 -0.45885 -0.43293 These calculated values were then correlated with actual values and coefficient of correlation was measured. Mean of rate of return and standard deviation characterized the distribution graph of values of rate of return. T test was done to identify if the null hypothesis holds: the market is unpredictable. P value was measured to find the probability of committing type I error and rejecting null hypothesis. Coefficient of autocorrelation was calculated to identify how efficiently the data (given and calculated) fits the pattern. UK STOCKS RETURNS Horizon 3 6 12 24 Coefficient of correlation 0.699309 0.699309 0.699309 0.699309 Mean 0.096069 0.096243 0.099035 0.099967 Standard Deviation 0.104809 0.102259 0.099203 0.096459 T Value 0.0137 0.0325 0.3333 0.4372 Standard error of difference 0.009 0.009 0.009 0.009 P Value 0.9891 0.9741 0.739 0.6621 Coefficient of autocorrelation 0.994774 0.994773 0.994723 0.994708 The coefficient of correlation was 0.699309 between the UK stocks and the horizons. The P value of the horizon 3 (P= 98.91%) and 6 (97.41%) with respect to original data showed that both the data belonged to same population. Coefficient of autocorrelation indicated that the data was highly synchronized and with limited randomness. US STOCK ROI Horizon 3 6 12 24 Coefficient of correlation 0.845571 0.845571 0.845571 0.845571 Mean 0.309877 0.310594 0.313005 0.324033 Standard Deviations 0.354881 0.349338 0.337963 0.331443 T value 0.0117 0.0373 0.1248 0.5269 standard error of difference 0.028 0.028 0.028 0.027 P value 0.9907 0.9703 0.9007 0.5984 Coefficient of Autocorrelation 0.99471 0.99471 0.99471 0.99471 The coefficient of correlation was 0.845571 between the US stocks and the horizons. The P value of the horizon 3 (P= 99.07%) and 6 (97.03%) with respect to original data showed that both the data belonged to same population. Coefficient of autocorrelation indicated that the data was highly synchronized and with limited randomness. The coefficient of correlation was 0.699309 between the UK stocks and the horizons. The P value of the horizon 3 (P= 98.91%) and 6 (97.41%) with respect to original data showed that both the data belonged to same population. Coefficient of autocorrelation indicated that the data was highly synchronized and with limited randomness. Conclusion Time series analysis of the indices revealed that the two stocks are correlated to each other in terms of rate of returns. Higher correlation was observed in volatility of the two stocks. Globalization, open economy and integrated mutual interests of the two economies can be attributed for such correlation. The UK stock is more volatile than the US stock though it has higher average rate of return. The Other January effect was observed in both the US and the UK stocks. It was more prominent in the UK stocks. The long horizon regression analysis of the US and the UK stocks delivered that the markets are predictable. All horizons were correlated with the stocks. The high P value indicated that the calculated data and original data belonged to same population hence establishing the fact that the markets were predictable. The Autocorrelation coefficient examined the periodicity of the markets. References 1. ‘New York Stock Exchange’, 23 April 2011, retrieved from http://en.wikipedia.org/wiki/New_York_Stock_Exchange 2. ‘Investment Risks’. From Retail Investor.org. n.d. retrieved from http://www.retailinvestor.org/risk.html#volatility 3. Gregory C. Chow, Caroline C. Lawler. ‘A Time-Series Analysis of the Shanghai and New York Stock Price Indices’ EconWPA ‘General Economics and Teaching’. 10 Jun 2003 Number 0306008 4. Michael J. Cooper. John J. McConnell. Alexei V. Ovtchinnikov. ‘The Other January Effect’. AFA 2006 Boston Meetings Paper. September 19, 2005 5. Martin. T. Bohl. Christian. A. Salm. ‘The Other January E?ect: Nothing More than a Statistical Artifact’ Westf?alische Wilhelms –University M?unster, Germany. October2007 6. ‘The Other January Effect: international evidence’. Article provided by Taylor and Francis Journals in journal ‘The European Journal of Finance’. 16 (2010). Pages: 173-182 7. Qingqing Chen. Yongmiao Hong. ‘Predictability of Equity Returns over Different Time Horizons: A Non parametric Approach (Preliminary Version)’ March 2009 8. Ralph S. J. Koijen. Stijn Van Nieuwerburgh. ‘Market Efficiency and Return Predictability’ February 10, 2007 9. Estimating Future Returns. March 17 2011. retrieved from http://gestaltu.blogspot.com/2011/03/estimating-future-returns.html 10. ‘Linear Regression’ Clemson University. Last Modified on 04/28/2011. retrieved from http://phoenix.phys.clemson.edu/tutorials/excel/regression.html 11. Skewness, Kurtosis, and the Normal Curve. Retrieved from http://core.ecu.edu/psyc/wuenschk/docs30/Skew-Kurt.doc Appendix Code For Calculating Rate of Return and Mean and variance of rate of return: package javaapplication1; public class java { public static void main(String args[]){ double ABC[][]=new double[10][3]; ABC[0][0]=4.2; ABC[1][0]=14.2; ABC[2][0]=42.2; ABC[3][0]=45.2; ABC[4][0]=67.2; ABC[5][0]=482; ABC[6][0]=211; ABC[7][0]=653; ABC[8][0]=4234; ABC[9][0]=786; for(int i=0;i Read More