- Table G 4 Critical Values Of The Chi Square Distribution Significance Level 10 05 01 1 2 71 3 84 6 63 2 4 61 5 99 9 1 (97.88 KiB) Viewed 48 times
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TABLE G.4 Critical Values of the Chi-Square Distribution Significance Level .10 .05 .01 1 2.71 3.84 6.63 2. 4.61 5.99 9.21 3 6.25 7.81 11.34 4 7.78 9.49 13.28 5 9.24 11.07 15.09 6 10.64 12.59 16.81 7 12.02 14.07 18.48 8 13.36 15.51 20.09 9 14.68 16.92 21.67 10 15.99 18.31 23.21 11 17.28 19.68 24.72 12 18.55 21.03 26.22 13 19.81 22.36 27.69 14 21.06 23.68 29.14 15 22.31 25.00 30.58 16 23.54 26.30 32.00 F 17 24.77 27.59 33.41 r 18 25.99 28.87 34.81 e 19 27.20 30.14 36.19 e 20 28.41 31.41 37.57 d 21 29.62 32.67 38.93 o 22 30.81 33.92 m 40.29 23 32.01 35.17 41.64 24 33.20 36.42 42.98 25 34.38 37.65 44.31 26 35.56 38.89 45.64 27 36.74 40.11 46.96 28 37.92 41.34 48.28 29 39.09 42.56 19.59 30 40.26 43.77 50.89 Example: The 5% critical value with dy = 8 1 15 51 Source: This table was generated using the Stata function invchi2tail. OOOOOO e Fans w V
Current Research Returns In September 2021, we transitioned from using our proprietary links between CRSP and Compustat data to those provided by CRSP after examining their consistency. We also updated the eligible universe through time to apply time-sensitive evaluation of stocks on criteria such as whether they are investment funds. February 2022 Last 3 Months Last 12 Months Fama/French 3 Research Factors Rm-RE SMB 3 HML Fama/French 5 Research Factors (2x3) -2.29 2.19 3.12 -5.55 -5.42 19.31 10.16 -16.75 28.62 Rm-Rf SMB HML RMW CMA -2.29 2.90 3.12 -2.10 3.01 -5.55 -1.86 19.31 3.16 14.81 10.16 -13.52 28.62 24.44 19.03 Fama/French Research Portfolios Size and Book-to-Market Portfolios Small Value Small Neutral Small Growth 2.32 1.12 -0.01 6.00 -4.18 -13.19 19.68 0.49 -20.05 0.34 0.08 Big Value Big Neutral Big Growth 10.52 3.27 -8.90 29.04 9.80 11.54 -3.57 Size and Operating Profitability Portfolios Small Robust Small Neutral Small Weak 1.39 0.69 1.47 -2.69 -1.40 -8.18 10.13 12.39 -17.60 Big Robust Big Neutral Big Weak -3.49 -1.76 0.63 -4.84 -3.92 -5.67 14.88 18.25 -6.27 Size and Investment Portfolios Small Conservative Small Neutral Small Aggressive 4.10 0.46 -0.32 1.40 -0.42 -11.63 3.94 7.39 -15.55 Big Conservativo Big Neutral Big Aggressive -2.09 -1.33 -3.68 3.74 113 -12.85 23.15 17.51 4.59
From Ken French's webpage, https://mba.tuck.dartmouth.edu/pages/fa ... brary.html, download the corresponding data sets containing the monthly Fama-French (FF) market, size and value factors, the risk-free interest rate, and the monthly (Average Value Weighted) re- turns for the five US (United States) industry portfolios: Consumer, Manufacturing, 5 Technology, Health and Other, for the period January 1985 to January 2022. Also, down- load the excel file "Assl_data.xlsx" from the Moodle site which contains monthly closing prices for the following four US securities: Table 4 Symbol BA JNJ Security Boeing Johnson & Johnson CenterPoint Energy Apple Sector Industrials Healthcare Utilities Information Technology CNP AAPL Use these data to answer the following questions: 1 For each security in Table 4, compute its monthly log returns (base e) over the sample period and express them in percentages. Provide a graph of these returns. 2 For each security in Table 4, estimate the CAPM and Fama-French three factor (FF3) models accounting for potential heteroskedasticity in the errors. a Write the two regression equations that you estimate, and clearly denote and define each variable and coefficient in these expressions
b For each regression, neatly report the coefficient estimates and standard errors for the market factor, and the appropriate version of R² of the regression. Comment on the similarities and/or differences of these estimated slope coefficients and R2 across securities and models. Are these results as you would expect? Why? c For each regression, test whether these securities track the market at 1% significance level. Clearly label all testing steps. Comment on your results. Hint: You can collect your results in tables to allow space for commentary in your report. The regression equations and testing steps can be described once. 3 Now use the Technology portfolio and estimate the CAPM and Fama-French three factor models accounting for potential heteroskedasticity in the errors. a Test for the validity of the Fama-French three factor model over CAPM at 5% signifi- cance level. b Comment on the similarities and/or differences of the estimated standard errors for the three risk factors in the FF3 regression with those obtained from the equivalent Apple regression, as well as on the Rºs. How can you justify your observations? 4 Obtain the residuals from each regression in Question 4.2. Group them by the model specification that they have been generated from (i.e. CAPM and FF3). Each group 6 should contain four sets of residuals. Compute the sample correlation matrix for each group and include them in your report. What do you observe when comparing the two matrices? How can you justify your observations? (Hint: you can refer to your results of Question 3.4.c).