The Beta-Return Relationship of the Companies on a Stock Exchange for the US Market - Research Proposal Example

THE BETA-RETURN RELATIONSHIP OF THE LISTED COMPANIES ON A STOCK EXCHANGE FOR THE US MARKET By Name University April, 2014 DECLARATION This thesis is my original work and has not been presented for a degree or any other award in any other university. ………………………………… ……………………………… Admin No. DATE This thesis has been submitted with our approval as the university supervisors. …………………………. ……… ………………………… Name of the Professor DATE Department of 1.0 Introduction Portfolio managers and investors are some special group of people who are very much interested in the risk return relationship a fundamental concepts in finance as one of their main function is to estimated risk in investments (Karacabey, 2001). One of the most popular approach of risk analysis known as Capital Asset Pricing Model (CAPM) argues that the systematic risk or what is known as beta is the only valid measure for investment and a positive trade-off between beta and expected return should exist(Karacabey, 2001).. Due to its important to both investors and portfolio managers, this concept is one of the most tested models in financial literature. The CAPM model states that there is linear relationship between the return on any asset and its market beta where beta is defined as the ratio of the covariance of each asset with the market portfolio to the variance of the market portfolio (Karacabey, 2001). This means, during the model test on the return on asset only the market beta will be priced. Fama (1992) in his major contribution showed that beta alone is not capable of explaining the cross-section of US asset return more so in the recent turbulent market condition. Similar evidence was also found by Miles and Timmermann (1996) in their study of United Kingdom (UK) stock returns. Due to these findings, the asset pricing research is changing to a quest for more comprehensive multifactor models that are capable of providing more comprehensive result on multi-factor models in explaining the relationship between beta and the stock market returns. Ross (1976) came up with Arbitrage Pricing Theory (APT) in which he explained and proofed that beta is not only the model and cannot verify beta on its own and there are other components of the that could be used to measure the systematic risk or undiversified of stock returns and other securities. Pettengill et al (1995) came up with a conditional relationship between beta and realized returns by separating periods of positive and negative market excess returns; this was done using stock exchange data between 1936 through 1990. The main aim of this study is to determine whether beta has a role to play in explaining the cross sectional differences in the returns of the United States stock exchange market for the listed companies price index. 2.0 Literature Review Most of the available empirical literature is mostly based on the Fama and MacBeth (1973) methodology which uses a three step approach. In his study, Reinganum (1981) found out that the cross-sectional differences in the betas portfolio and the differences in average portfolio returns are not reliably related. This was to mean that the portfolio returns on higher-beta are not significantly higher than the returns on low-beta portfolios, and this finding brings doubt in the empirical content on CAPM. Lakonishock and Shapiro (1986) examined the monthly returns of all stocks which were being traded in New York Stock Exchange (NYSE), they found that the return on individual securities is not directly related to its degree of systematic risk, though it was significantly related to the market capitalization values. In their conclusion, the stated that the traditional beta and the alternative residuals risk measures is not able to explicitly explain the cross-sectional variation in return and the size of the stock is what can significantly explain it. Haugen and Baker (1991) in their study examined the risk return and the characteristics of 1000 US stock that have the largest market capitalization over all US exchanges and markets in the period between 1972 and 1989 price indexes. In their findings, they realized that the market portfolio is not efficient because low risk stocks seems to have abnormally high returns, a position which was contradicting the earlier relationship between beta and returns as stated by CAPM. Fletcher (2000) in his study using the monthly return of the MSCI indices of over 18countries and the world MSCI index, he found that a consistent result exists. In the study, there was a significant positive relationship between beta and returns more so in periods when the world market excess returns are positive and a significant negative relationship during periods when the world market excess returns are negative. A part from this relationship, the relationship is a symmetrical and there is, on average, a positive means excess returns on the index. The literature and brief survey suggest that the traditional method of CAPM beta lacks some basic efficiency and completeness as a measure of risk or that there is no risk return trade off when only beta is used as a risk measurement. 2.1 Conational nature of the beta-return relationship Though, the current empirical evidence shows that there is no compensation for beta, this does not means that beta is no longer in useful in making investment decisions. Chan 1993 argued that as long as beta still behaves in a stable manner in more so in exposure to the market movement, investors and portfolio managers should be in a position to consider the sensitivity of stocks to the prevailing market factor. Most scholars define risk as a chance that ex post realized returns differ from expected ones. Therefore, the variance dispersion on return outcomes around their average values is important as a risk measurement tool in the market. Many studies have been done to help in hypothesis testing in determining the relationship between beta and return and they have conditioned the relationship between beta and return in market movement direction. The market model helps in providing overall prediction indicating positive relationship between beta and expected returns. Tudor (2008) studied the explanatory power of beta for the stock market of Romanian employing stochastic model for returns which is similar to the one which was used by Fama and Makbeth in 1973. He concluded that beta is not capable of explaining future stock return in the Romanian Stock market. Several studies have found out that there are other several factors which are important in explaining risk factor of expected return on individual assets and most of the results are against the CAPM. Banz (1981) as reported by Fletcher, discussed the effect of the stock size as one of the factors which influences the return on the stock. He found that average returns on the stocks which are having low market equity are too high taking into consideration that the betas returns on those stocks with high market equity are too high given their beta. Bhandari (1988) I his investigation found that there is positive linear relationship between expected return and the skewness coefficient. A positive linear relationship between expected return and skewness was also noted in study by Litzenberge, Sear and Wei. In Their study, Fama and French 1998 found that the similar ratios which were found to be the risk factors on the US market have similar explanatory characteristics on stock returns on the twelve non Us major markets and also on the emerging markets. In their discussion in 2004, the capital Asset theory pricing model; theory and its evidence all these findings are evidence that the contradictions of the CAPM associated with prices rations in most cases are not specific samples. Importance of global risk factors and their impact on stock market was done by Mateus (2004), he concluded that global instruments have stronger predictive power than the local variables in the case of Romania. Kothari, Shanken and Sloan (1995) in their study found that using betas which have been generated from annual reports as opposed to monthly reports will give more concrete result which is positively related with the returns. They propose that that the relationship between average returns and BE/ME observed by Fama and French in 1992 and many other scholars. Another research which was done in U.S and Japan relating to the cross sectional behavior of stock returns to the market risk and firm characteristics, but on emerging markets, the research is still limited. 2.3 Summary In summary, international investors have been attracted so much with lucrative international markets and they are hoping to get abnormal return as well as diversifying their market portfolios. Due to this, the study of the relationship between betas and stock return is of greater importance of more immense interest both to scholars and investors. 3.0 Data methodology Research design is defined as the plan, structure and strategy of investigation conceived so as to obtain answers to research questions and control variance (Kerlinger, 1964). According to Orodho (2004), research design refers to all the procedures selected by a researcher for studying a particular set of questions or hypotheses. He summarizes it as a programme to guide the researcher in collecting, analyzing and interpreting observed facts. For this study, Descriptive survey method is appropriate. Descriptive survey is a method of collecting information by interviewing or administering a questionnaire to a sample of individuals (Orodho, 2003). Kerlinger (1969) states that descriptive studies are not only restricted to facts finding, but might often results in the formulation of important principles of knowledge and solution to significant problems. The data to be used here are monthly price indexes of the common stock traded in the U.S stock exchange. The data is row in that they exclude the dividends but are adjusted for split in capital and stock dividends. The data was picked from US stock exchange data base. The market return was obtained from ASE composite share price index. The time series of excess returns in the market of individual company securities are taken. The monthly returns for the market index was calculated and for the individual companies separately using the following formula: Rt =Ln (Pt/Pt-1) or Ln (Pt) - Ln (Pt-1), only for the companies which have complete data from 1 January 2000 was taken, while those which did not have were ignored in the process. The beta for individual companies was estimated using the CAPM model and regression of individual company’s return on the relevant market return (the return on the stock exchange index) was done using the following regression: Rjt = a + bRmt + e. The coefficient ‘b’ here is the beta The equally weighted average beta and equally weighted average return of all the companies used for the analysis was calculated. Based on the results of the risk and return analysis, a Table of Risk-Return Matrix classifying the companies was drawn. Data Result DATE PIt PIt-1 PIt/PIt-1 LN(Pit/PIt-1) 2000-01-01 1425.59 1425.59 1 0 2000-02-01 1388.87 36.72 37.82326 3.63292418 2000-03-01 1442.21 -53.34 -27.0381 3.29724542 2000-04-01 1461.36 -19.15 -76.3112 4.33482007 2000-05-01 1418.48 42.88 33.08022 3.49893564 2000-06-01 1461.96 -43.48 -33.6237 3.51523222 2000-07-01 1473.00 -11.04 -133.424 4.89353138 2000-08-01 1485.46 -12.46 -119.218 4.78095625 2000-09-01 1468.05 17.41 84.32223 4.43464551 2000-10-01 1390.14 77.91 17.8429 2.88160543 2000-11-01 1375.04 15.10 91.06225 4.51154336 2000-12-01 1330.93 44.11 30.17298 3.40694671 2001-01-01 1335.63 -4.70 -284.177 5.64959586 2001-02-01 1305.75 29.88 43.6998 3.77734351 2001-03-01 1185.85 119.90 9.890325 2.29155703 2001-04-01 1189.84 -3.99 -298.206 5.69778289 2001-05-01 1270.37 -80.53 -15.7751 2.75843369 2001-06-01 1238.71 31.66 39.12539 3.66677174 2001-07-01 1204.45 34.26 35.15616 3.55979982 2001-08-01 1178.51 25.94 45.43215 3.81622003 2001-09-01 1044.64 133.87 7.803391 2.05455843 2001-10-01 1076.59 -31.95 -33.6961 3.51738174 2001-11-01 1129.68 -53.09 -21.2786 3.0577011 2001-12-01 1144.93 -15.25 -75.0774 4.31851928 2002-01-01 1140.21 4.72 241.5699 5.48715894 2002-02-01 1100.67 39.54 27.83687 3.32636155 2002-03-01 1153.79 -53.12 -21.7204 3.07825395 2002-04-01 1112.03 41.76 26.62907 3.28200351 2002-05-01 1079.27 32.76 32.94475 3.49483191 2002-06-01 1014.05 65.22 15.54814 2.74394132 2002-07-01 903.59 110.46 8.180246 2.10172225 2002-08-01 912.55 -8.96 -101.847 4.62347265 2002-09-01 867.81 44.74 19.39674 2.96510484 2002-10-01 854.63 13.18 64.84294 4.1719681 2002-11-01 909.93 -55.30 -16.4544 2.80059476 2002-12-01 899.18 10.75 83.64465 4.42657748 2003-01-01 895.84 3.34 268.2156 5.59179102 2003-02-01 837.62 58.22 14.38715 2.6663356 2003-03-01 846.62 -9.00 -94.0689 4.54402737 2003-04-01 890.03 -43.41 -20.5029 3.02056534 2003-05-01 935.96 -45.93 -20.378 3.01445424 2003-06-01 988.00 -52.04 -18.9854 2.94367004 2003-07-01 992.54 -4.54 -218.621 5.3873403 2003-08-01 989.53 3.01 328.7475 5.79529 2003-09-01 1019.44 -29.91 -34.0836 3.52881586 2003-10-01 1038.73 -19.29 -53.8481 3.98616727 2003-11-01 1049.90 -11.17 -93.9928 4.54321859 2003-12-01 1080.64 -30.74 -35.1542 3.559744 2004-01-01 1132.52 -51.88 -21.8296 3.08326716 2004-02-01 1143.36 -10.84 -105.476 4.65848358 2004-03-01 1123.98 19.38 57.9969 4.06038963 2004-04-01 1133.08 -9.10 -124.514 4.82442045 2004-05-01 1102.78 30.30 36.39538 3.59444183 2004-06-01 1132.76 -29.98 -37.7839 3.63188192 2004-07-01 1105.85 26.91 41.09439 3.71587158 2004-08-01 1088.94 16.91 64.39622 4.16505486 2004-09-01 1117.66 -28.72 -38.9157 3.66139875 2004-10-01 1118.07 -0.41 -2727 7.91095738 2004-11-01 1168.94 -50.87 -22.979 3.13457928 2004-12-01 1199.21 -30.27 -39.6171 3.67926116 2005-01-01 1181.41 17.80 66.37135 4.19526546 2005-02-01 1199.63 -18.22 -65.8414 4.18724856 2005-03-01 1194.90 4.73 252.6216 5.53189258 2005-04-01 1164.42 30.48 38.20276 3.64290766 2005-05-01 1178.28 -13.86 -85.013 4.44280403 2005-06-01 1202.26 -23.98 -50.1359 3.91473825 2005-07-01 1222.24 -19.98 -61.1732 4.11370875 2005-08-01 1224.27 -2.03 -603.089 6.40206423 2005-09-01 1225.91 -1.64 -747.506 6.61674246 2005-10-01 1191.96 33.95 35.10928 3.55846544 2005-11-01 1237.37 -45.41 -27.2488 3.30501109 2005-12-01 1262.07 -24.70 -51.096 3.93370527 2006-01-01 1278.72 -16.65 -76.8 4.34120464 2006-02-01 1276.65 2.07 616.7391 6.42444613 2006-03-01 1293.74 -17.09 -75.7016 4.32679903 2006-04-01 1302.18 -8.44 -154.287 5.03881275 2006-05-01 1290.00 12.18 105.9113 4.66260224 2006-06-01 1253.12 36.88 33.97831 3.52572232 2006-07-01 1260.24 -7.12 -177 5.17614973 2006-08-01 1287.15 -26.91 -47.8317 3.86768779 2006-09-01 1317.81 -30.66 -42.9814 3.76076767 2006-10-01 1363.38 -45.57 -29.9184 3.39847258 2006-11-01 1388.63 -25.25 -54.9952 4.00724677 2006-12-01 1416.42 -27.79 -50.9687 3.9312116 2007-01-01 1424.16 -7.74 -184 5.21493576 2007-02-01 1444.79 -20.63 -70.0334 4.24897293 2007-03-01 1406.95 37.84 37.18155 3.61581278 2007-04-01 1463.65 -56.70 -25.8139 3.25091438 2007-05-01 1511.14 -47.49 -31.8202 3.46010045 2007-06-01 1514.49 -3.35 -452.087 6.11387368 2007-07-01 1520.70 -6.21 -244.879 5.50076514 2007-08-01 1454.62 66.08 22.01301 3.09163385 2007-09-01 1497.12 -42.50 -35.2264 3.56179447 2007-10-01 1539.66 -42.54 -36.1932 3.58887208 2007-11-01 1463.39 76.27 19.18697 2.95423126 2007-12-01 1479.23 -15.84 -93.3857 4.53673857 2008-01-01 1378.76 100.47 13.7231 2.61908065 2008-02-01 1354.87 23.89 56.71285 4.03800083 2008-03-01 1316.94 37.93 34.72027 3.54732379 2008-04-01 1370.47 -53.53 -25.6019 3.24266678 2008-05-01 1403.22 -32.75 -42.8464 3.75762191 2008-06-01 1341.25 61.97 21.64354 3.0747069 2008-07-01 1257.33 83.92 14.98248 2.70688174 2008-08-01 1281.47 -24.14 -53.0849 3.97189292 2008-09-01 1217.01 64.46 18.88008 2.93810743 2008-10-01 968.80 248.21 3.903147 1.36178303 2008-11-01 883.04 85.76 10.29664 2.3318178 2008-12-01 877.56 5.48 160.1387 5.07604023 2009-01-01 865.58 11.98 72.25209 4.28016121 2009-02-01 805.23 60.35 13.34267 2.590967 2009-03-01 757.13 48.10 15.74075 2.75625279 2009-04-01 848.15 -91.02 -9.31828 2.23197824 2009-05-01 902.41 -54.26 -16.6312 2.81128166 2009-06-01 926.12 -23.71 -39.0603 3.66510692 2009-07-01 935.82 -9.70 -96.4763 4.56929726 2009-08-01 1009.72 -73.90 -13.6633 2.61471552 2009-09-01 1044.55 -34.83 -29.99 3.40086237 2009-10-01 1067.66 -23.11 -46.199 3.83295919 2009-11-01 1088.07 -20.41 -53.3106 3.97613579 2009-12-01 1110.38 -22.31 -49.7705 3.90742257 2010-01-01 1123.58 -13.20 -85.1197 4.44405847 2010-02-01 1089.16 34.42 31.64323 3.45452425 2010-03-01 1152.05 -62.89 -18.3185 2.90791107 2010-04-01 1197.32 -45.27 -26.4484 3.27519644 2010-05-01 1125.06 72.26 15.56961 2.74532092 2010-06-01 1083.36 41.70 25.97986 3.25732147 2010-07-01 1079.80 3.56 303.3146 5.71477057 2010-08-01 1087.28 -7.48 -145.358 4.97920165 2010-09-01 1122.08 -34.80 -32.2437 3.473322 2010-10-01 1171.58 -49.50 -23.6683 3.16413587 2010-11-01 1198.89 -27.31 -43.8993 3.78189847 2010-12-01 1241.53 -42.64 -29.1166 3.37130699 2011-01-01 1282.62 -41.09 -31.2149 3.44089536 2011-02-01 1321.12 -38.50 -34.3148 3.5355769 2011-03-01 1304.49 16.63 78.44197 4.36235915 2011-04-01 1331.51 -27.02 -49.2787 3.89749158 2011-05-01 1338.31 -6.80 -196.81 5.28224029 2011-06-01 1287.29 51.02 25.23109 3.2280768 2011-07-01 1325.18 -37.89 -34.9744 3.55461635 2011-08-01 1185.31 139.87 8.474369 2.1370462 2011-09-01 1173.88 11.43 102.7017 4.6318283 2011-10-01 1207.22 -33.34 -36.2094 3.5893176 2011-11-01 1226.41 -19.19 -63.9088 4.15745717 2011-12-01 1243.32 -16.91 -73.5257 4.29763534 2012-01-01 1300.58 -57.26 -22.7136 3.1229633 2012-02-01 1352.49 -51.91 -26.0545 3.26019117 2012-03-01 1389.24 -36.75 -37.8024 3.63237389 2012-04-01 1386.43 2.81 493.3915 6.20130289 2012-05-01 1341.27 45.16 29.7004 3.39116047 2012-06-01 1323.48 17.79 74.3946 4.30938341 2012-07-01 1359.78 -36.30 -37.4595 3.62326046 2012-08-01 1403.44 -43.66 -32.1448 3.47024929 2012-09-01 1443.42 -39.98 -36.1036 3.58639125 2012-10-01 1437.82 5.60 256.7536 5.54811676 2012-11-01 1394.51 43.31 32.19834 3.47191482 2012-12-01 1422.29 -27.78 -51.1983 3.93570719 2013-01-01 1480.40 -58.11 -25.4758 3.23772983 2013-02-01 1512.31 -31.91 -47.393 3.85847412 2013-03-01 1550.83 -38.52 -40.2604 3.69536796 2013-04-01 1570.70 -19.87 -79.0488 4.3700656 2013-05-01 1639.84 -69.14 -23.7177 3.16622052 2013-06-01 1618.77 21.07 76.82819 4.34157165 2013-07-01 1668.68 -49.91 -33.4338 3.50956679 2013-08-01 1670.09 -1.41 -1184.46 7.07704309 2013-09-01 1687.17 -17.08 -98.7804 4.59289966 2013-10-01 1720.03 -32.86 -52.3442 3.9578409 2013-11-01 1783.54 -63.51 -28.0828 3.33515806 2013-12-01 1807.78 -24.24 -74.5784 4.31185069 2014-01-01 1822.36 -14.58 -124.99 4.82823692 2014-02-01 1817.03 5.33 340.9062 5.83160734 2014-03-01 1863.52 -46.49 -40.0843 3.69098522 3.0 Result and discussion From the statistical result in the table below giving the R-square and adjusted R-square showing close relationship between the variables Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics R Square Change F Change df1 1 .176a .031 .025 221.26635 .031 5.406 1 Coefficients Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 1100.274 65.041 16.917 .000 LNPitPit1 37.528 16.141 .176 2.325 .021 The result shows positive relationship between beta and the returns as can be seen in the coefficient table above. Beta is 0.178 while t-test gives 2.325. According to CAPM, the return on stock should be equal to the expected excess return on the market portfolio. The result shows a positive relationship between beta and return on capital in US stock exchange. Based on Mean Security Return Mean = 0.68 High Low Total Based on Mean Security Risk (Beta) Mean= 0.45 High 0.56 1 0.75 Low 0.23 3 4 Total Based on Market index return =1.93 High Low Total Based on Market Risk (Beta) =1 High Low 11 23 Total 23 The results are similar and support the findings by Fama and French 1998 and Tudor (2008) which will supports the CAPM principles. 4.0 Conclusion Most of the past empirical studies have supported the CAPM theory and methods while the recent studies have disputed the method. In our result, the result shows positive relationship between beta and the return on stock hence can be positively used by the investors and portfolio managers. References Fama, Eugene F., and James MacBeth (1973) / “Risk, return and equilibrium: Empirical tests”, Journal of Political Economy ,81, pp 607-636. Fletcher, J., (2000), “On the Conditional Relationship Between Beta and Return in International Stock Returns”, International Review of Financial Analysis 9, pp.235-245. Karacabey, A., (2001) , “Beta and Return: Istanbul Stock Exchange Evidence” ,Working Paper Series, SSRN Pettengill, G. N., Sundaram, S., & Mathur, I. (1995), “The conditional relation between beta and returns”, Journal of Financial and Quantitative Analysis 30(1), 101-116 Reinganum, M. (1981), “A new empirical perspective on the CAPM”, Journal of Financial and Quantitative Analysis, 16, 439–462 Ross, S. , (1976), “The arbitrage theory of capital asset pricing”, Journal of Economic Theory ,13(6):341-360 Read More