CAPM Test for FTSE 100 Stocks - Statistics Project Example

CAPM Test on FTSE 100 Stocks by Teacher’s CAPM Test for FTSE 100 Stocks Stock Trading is a significant financial activity of Capitalist economy. From this viewpoint, stocks are considered as a commodity or assets; it can be purchased and sold. The stock purchasers are called investors. The goal of investors is to make money from stock trading. One can make as well as lose money from stock trading. The trivial question every investor would ask if there is a way to predict profit or losses from stock trading? Financial researchers (Fama & French 2004; Marling & Emanuelson 2012; Allen, Kumar Singh, & Powel 2009) have developed a model and claim prediction is possible. The model is called CAPM (Capital Asset Pricing Model). Researchers emphasise that the model explains the relationship between risk and reward of stock trading (Diether n.d.). This study presents the results of a test on the validity of the CAPM model on FTSE 100 Stocks. Methodology and Data The test was conducted using bivariate regression technique. The bivariate regression method studies dependency of two variables in the form of y = a + mx. The CAPM defines return on an investment using the formula E(ri)= rf + βi(rm – rf); where E(ri) is expected return on a stock, rf is risk-free return, and rm is the market return. The formula implies that the regression analysis requires three sets of data: ri, rm, and rf. We collected data for ri from the FTSE 100 stocks (Yahoo Finance UK n.d.), rm from FTSE index values (Yahoo Finance UK n.d.), and rf from10-year U.K. government bond (Data.Okfn.org. n.d). The data set presents weekly values of three variables for periods: January 2006 – December 2008, January 2009 – December 2011, and January 2012 – December 2014. The study conducted 30 time-series regression and four cross-sectional analyses. All regression analyses were performed at the 95% confidence level. Company Selection As of February 27, 2015 fact sheet (FTSE Factsheet, n.d), the total market capitalization of FTSE 100 was 1.8 trillion GBP. The Oil & Gas Producer and Banking sectors respectively contributed 14.45% and 12.6% of weighted capital to the FTSE 100. We selected five companies from each of these sectors (UK Stock Challenge n.d; The Telegraph n.d.). Table1. List of ten companies selected for the study Oil & Gas producer Sector Company name Ticker Market capitalization (in million GBP) British Petroleum BP 81,381.50 Royal Dutch Shell RDSA 80,609.58 (128.07 b) BG Group BG 30,104.85 Dragon Oil DGO 2,881.39 Tullow Oil TLW 2,807.57 Banks Sector HSBC Holding HSBA 111, 79.78 Lloyds Banking Group LLOY 56,906.28 Barclays BARC 41,255.87 Standard Chartered STAN 27,199.61 Royal Bank of Scotland RBS 22,299.73 Results of Time-Series Regression Analysis Coefficient and Slope tests The original CAPM formula, E(ri)= rf + β(rm – rf) is rearranged for the time regression analysis in the form of (rit-rft) = α + β(rm,t – rft). In this model, α is a constant and β is the slope on the (rt-rft) - (rmkt,t – rft) plane; where (rmkt,t – rft) and (rt-rft) are respectively independent and dependent variables (Therion, Aggelidis & Spiridis n.d). The Overall stability of the models is determined through the significance of F test. It conducts hypothesis test H0: α = 0 and β = 0 versus Ha: at least one of the parameters of the equation (rit-rft) = α + β(rm,t – rft) is not equal to zero. The Excell results of F-test allow to reject Null of all 30 models (Sage n.d.). This fact implies that there is a linear dependency between the tested variables (rit-rft) and (rmkt,t – rft). The regression analysis also returned the values of α coefficients and β slopes of 30 equations. Table2. Regression coefficient test results (Jan. 2006-Dec.2008) Note: Oil and gas sector of FTSE 100 Note: Bank sector of FTSE 100; t-critical is evaluated for probability 0.05 and df= 155 Table3. Regression coefficient test results (Jan. 2009-Dec.2011) Note: Oil & gas sector of FTSE 100 Note: Bank sector of FTSE 100; t-critical is evaluated for probability 0.05 and df= 155 Table4. Regression coefficient test results (Jan. 2012-Dec.2014) Note: Oil & gas sector of FTSE 100 Note: Bank sector of FTSE 100; t-critical is evaluated for probability 0.05 and df= 155 Table 2, 3, and 4 illustrate values of coefficients of α and β of the equation (rit-rft) = α + β(rm,t – rft). For CAPM to be valid, the regression analysis must return α = 0 and β ≠ 0. The CAPM expresses that Expected rate of return on a security = Rate of risk-free investment + (Volatility of a security relative to the market) x (market premium). The coefficient β of the above regression equation expresses the volatility of a security relative to the market. The value of β = 1.00 indicates that return on the security moves with the market; β > 1 implies that it is more volatile than the market, and β < 1 states that the return on that security moves against the market and is less than the risk-free return. Table 2, 3, and 4 contain β values of 30 time-series regression analyses. The statistical significance of β was tested for H0=0 and Ha ≠ 0. For t-stat > t-critical and p – value < alpha=0.05, the Null is rejected. All thirty β values reported in Table 2, 3, and 4 are statistically significant. The tests t-stat > t-critical for α demonstrated the coefficient is insignificant for all cases; except for TLW and RSB for time-series January 2006-December 2008; TLW and LLOYDS for time-series January 2012-Decemeber 2014. However, considering the lower and upper values of α at 95% confidence interval level, the values of the coefficient α for above cases may be accepted as zero. Thirty time-series regression analyses for periods from January 2006 to December 2014 on ten different stocks of FTSE 100 confirms the validity of the CAPM equation (ri)= rf + βi(rm – rf). Goodness of Fit The goodness of fit of a regression equation is expressed through the value of R^2. For R^2 = 1, the line passes through all observed points. For any other values of R^2, it describes the percentage of total variance that can be explained by the regression model (Therion, Aggelidis & Spiridis n.d.) The regression analysis of the CAPM equation of the BP stock for time-series January 2006-December, 2014 returned R^2=0.68. It implies that this regression model explains 68% of the variance. Table 5 illustrates R^2 values for thirty regression analyses. Table5. Goodness of fit values, R^2 Cross-Sectional Regression The time-series analyses returned thirty β values. The coefficient β measures volatility of a stock relative to the market (Ashgarian & Hanson n.d.). The CAPM implies that the expected return of a stock depends linearly on β; Furthermore, it states that in the equilibrium position all expected returns lie on a straight line called Security Market Line (SML). In other words, the SML is a linear function of β (Boundless.com n.d.). This statement allows to express the CAPM equation (ri)= rf + βi(rm – rf) for regression model as E(ri) = ϒ+λβi. For CAPM to be valid, the regression must return ϒ = rf and λ=rm-rf >0. Table6. F-test of models for oil & gas and banks sectors for different periods The results of F-test results in Table 6 indicates that the regressor βi for 30 observations does not explain a larger part of the variance observed in E(ri) compared to the null model. Hence, the hypothesis H0=rm-rf = 0 cannot be rejected. Table7. The values t-test for the coefficient λ and ϒ The statistical significance of was tested for H0=0 and Ha ≠ 0. For t-stat < t-critical and p – value > alpha=0.05, the Null cannot be rejected. The tests of both coefficients are reported in Table 7. The above analysis shows that cross-sectional regression model E(ri) = ϒ+λβi for 10 selected stocks of FTSE 100 failed to confirm the validity of the CAPM model for selected periods. We studied correlation of all 30 values of E (ri) and β by drawing the trend line on the scatter plat. The result is illustrated in Figure 2: linear Correlation between these variables does not exist. The two principal parameters of CAPM is risk-free (rf) and capital market return (rm). The risk-free return is substituted by the yield on Government bond. Furthermore, the model considers that risk-free return is a fixed value. However, in the real world, it is not true; it changes on a daily basis depending on economic circumstances (ACCA n.d.). In the CAPM, the market premium (rm-rf) is calculated using the value of the capital market return. On the other hand, the capital market return is calculated using the sum of the average of capital gain and the dividend yield. The formula uses the market premium value (rm-rf) as a positive number. However, the market can provide a negative value of return if the effect of falling share prices outweighs the dividend yield (ACCA n.d). The SML concept is developed for a perfect capital market: with no taxes and transaction cost, all investors are risk averse, and there are large numbers of sellers and buyers with same expectations. However, a real capital market is far from the perfect one, and it creates uncertainty about the market premium (rm-rf), which in turn makes an impact on the expected return (Researchomatic n.d). Contrary to the above-discussed drawbacks of CAPM; it is a familiar concept that is used to predict the return on stocks trading. The test on the CAPM of 10 FTSE 100 stocks shows that there exists a linear dependency between market premium and excess return, and it can be measured. Sensitivity to Sector The study conducted time-series and cross-sectional analyses. The time-series analyses showed that the oil and gas sector is less volatile than the banking sector. Moreover, oil & gas sector over the period from 2006 – 2014 remained stable while the banking sector reflected instability. The above conclusion is drawn from the analysis of average β of these sectors. The cross-sectional analysis of ten companies of FTSE 100 for three different periods failed to confirm SML equation E(ri)=Rf+β(Rm-Rf). The companies belong to oil & gas and bank sectors. We conducted sector wise cross-sectional analysis for the same periods. The analysis for oil & gas sector for the period of January 2006 – December 2008 confirmed SML concept that the stock return linearly depends on the risk β. The R^2 of this analysis is 0.99; the f-test rejected the null, tests on coefficients ϒ and λ showed that they were statically significant. The regression equation is E(Ri) = -0.02+0.02 β. The rest of the cross-sectional analyses failed to confirm SML equation through regression analysis. Scatter plots of different sectors for different periods are attached below. Conclusion The current report presented results and analysis of CAPM test on ten companies selected from oil & gas and banking sectors of FTSE 100 index. Time-series regression analysis confirmed the validity of the CAPM on these stocks; however, the cross-sectional regression failed to confirm the validity. Reference List ACCA n.d., CAPM: Theory, Advantages and Disadvantages. [ONLINE] Available at: http://www.accaglobal.com/an/en/student/acca-qual-student-journey/qual-resource/acca-qualification/f9/technical-articles/CAPM-theory.html [Accessed 07 April 2015] Allen, D.E, Kumar Singh, A & Powel, 2009, Asset Pricing, the Fama-French Factor Model and the Implications of Quantile Regression Analysis, School of Accounting, Finance and Economics, Edith Cowan University. [ONLINE] Available at: [Accessed 07 April 2015]. Ashgarian H & Hanson B n.d., Cross-Sectional Analysis of the Swedish Market. [ONLINE] Available at: < http://econpapers.repec.org/paper/hhslunewp/2002_5f019.htm > [Accessed 07 April 2015] Boundless.com n.d., The SML Approah. [ONLINE] Available at: < https://www.boundless.com/finance/textbooks/boundless-finance-textbook/introduction-to-the-cost-of-capital-10/calculation-approaches-89/the-sml-approach-381-3908/ > [Accessed 07 April 2015]. Data.Okfn.Org. n.d., 10 Y UK Government Bond Yields. [ONLINE] Available at: [Accessed 07 April 215] Diether K..B. n.d., Testing the CAPM. [ONLINE] Available at: < http://www.ewp.rpi.edu/hartford/~youneh/INVII/Week%204/test_capm_2up.pdf > [Accessed 07 April 2015] Fama, E.f., & French, K.R. 2004, The Capital Asset Pricing Model: Theory and Evidence, Journal of Economic Prospective, volume 18, number 3, pages 25 – 46. [ONLINE] Available at: < http://www-personal.umich.edu/~kathrynd/JEP.FamaandFrench.pdf > [Accessed 07 April 2015]. FTSE Factsheet, n.d., UKX_20150331.pdf.[ONLINE] Available at: [Accessed 07 April 2015]. Marling, H & Emanuelson, S. 2012, The Markowitz Portfolio Theory. [ONLINE] Available at: [Accessed 07 April 2015]. Researchomatic n.d., Disadvantages Of Capital Asset Pricing Model. [ONLINE] Available at: http://www.researchomatic.com/Disadvantages-Of-Capital-Asset-Pricing-Model-16399.html [Accessed 07 April 2015]. Sage n.d., Introduction to Hypothesis Testing. [ONLINE] Available at: < http://www.sagepub.com/upm-data/40007_Chapter8.pdf > [Accessed 07 April 2015] The Telegraph n.d., Indicies. [ONLINE] Available at < http://shares.telegraph.co.uk/indices/> [Accesses 07 April 2015]. Therion N, Aggelidis V & Spiridis T n.d., Empirical Testing of Capital Asset Pricing Model. [ONLINE] Available at: < http://abd.teikav.edu.gr/articles_th/capital_asset_pricing_model.pdf > [Accesses 07 April 2015]. UK Stock Challenge, n.d., FTSE All Share Index Ranking. [ONLINE] Available at: [Accessed 07 April 2015]. Yahoo Finance Uk & Ireland n.d. FTSE 100. [ONLINE] Available at: < https://uk.finance.yahoo.com/q?s=^FTSE&ql=0> [Accessed 07 April 2015]. Read More