Capital Asset Pricing Models (CAPM) The CAPM relates the sensitivity of an individual company's stock returns to the returns of the market as a whole. Estimating such a model for a particular firm requires data on the market rate of return (typically a composite index such as the S&P 500), the risk-free rate of return (usually a short-term Treasury bill), and stock returns from the company of interest. The data for this question consist of daily observations on the market return (RM), the risk-free rate (R.F), and the return on the IBM Corporation's common stock (R.IBM). Using a SAS DATA step, we create two new variables, ezretibm = RIBM -RF 2 and erretsp = RM -RF, that correspond to the risk premiums for the IBM Corporation and the Market, respectively. We use the AUTOREG procedure to estimate a linear regression of exretibm on erret sp. Note that a constant term is automatically included in the model. The DWPROB option requests the Durbin-Watson test for autocorrelation of the residuals. The TEST statement enables to perform hypothesis tests on parameter estimates, and the TEST output is obtained after requesting a test that the coefficient of exretsp is equal to 1. Use the SAS outputs provided in the following pages and answer the following questions using the 5% significance level when performing a hypothesis test. Round to four decimals when reporting and/or using values from the SAS output. 1. Test if the IBM Corporation common stock is mispriced according to the CAPM. Under which condition on the constant term in the model can we say that the IBM Corporation common stock is underpriced? 2. Test if the coefficient of the risk premium of the market is significant. 3. Explain using the security market line (SML) why the movement of IBM common stock returns is the same as that of the market as a whole when the beta of IBM stocks equals 1. Test if the movement of IBM common stock returns is the same as that of the market as a whole. 4. What is the percentage of the variance in the excess returns on IBM corporation due to the excess returns on the market. 5. The Durbin-Watson d statistic tests for autocorrelation and lack of independence of residuals, which is a common problem in time series data. The d statistic ranges from 0 to 4. A value close to 2.0, or a p-value larger than the level of the test, indicates that you cannot reject the null hypothesis of no autocorrelation. Test for autocorrelation of the residuals using the Durbin-Watson test. IBM CAPM IBM versus the Market IBM CAPM The AUTOREG Procedure Dependent Variable exretibm IBM CAPM The AUTOREG Procedure Ordinary Least Squares Estimates SSE 0.78123981 DFE MSE 0.0007774 Root MSE SBC -4340.1636 AIC MAE 0.02051775 AICC MAPE 823.888636 HQC Durbin-Watson 1.9498 Regress R-Square Total R-Square 1005 0.02788 -4349.993 -4349.9811 -4346.2584 0.1017 0.1017 Order 1 Durbin-Watson Statistics DW Pr <DW Pr > DW 1.9498 0.2081 0.7919 NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation. Variable DF Estimate t Value Parameter Estimates Standard Error 0.001658 0.0435 Approx Pr>1t| <.0001 <.0001 Intercept exretsp -9.66 1 1 -0.0160 0.4638 10.67 Test 1 Source DF Mean Square F Value Pr>F 152.08 <.0001 Numerator Denominator 1 1005 0.118221 0.000777 Standard Normal Distribution Example: P(Z $ 1.73) = 0(1.73) = 9582 -4 -3 -2 -1 0 1 2 3 4 Z Table 1 Cumulative Probabilities for the Standard Normal Distribution (z) = P(Z <z) 1.0 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.2 0.5793 3199 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.3 0.6179 Wom 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.4 0.6554 0.6591 024 W.. 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.5 0.6915 0.6950 0.6985 07054 0.7019 Wom 02 5.000 0.7054 0.7088 0.7123 0.7157 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 200 0.7422 0.7454 0.7486 0.7 0.7580 0.7611 0.7642 0.7673 2704 *** 0.7704 0.7734 1400 0.7764 0.7794 0.8 0.7881 0.7910 600 0.7939 0.7967 0.7995 . 0.8023 0.8051 0.8078 0.9 0.8159 0.8186 Wow 0.8212 Wood o gogo Wodo 0.8238 Would 0.8264 1.0450 0.8289 0.8315 0.8340 0.8413 0.8438 0.8461 0.8485 4.00 085 0.8508 0.8531 0.8554 Word 0.8577 1.1 0.8643 0.8665 0.8686 0.8708 0.8749 1.000 0.8729 0.8749 Wor 0.8770 0.8790 1.2 0.8849 0.8869 0.8889 0.8907 0.8925 0.00 0.8944 OROK OROM 0.8962 0.8980 1.3 0.9032 0.9049 0.9066 24 0.9082 0.9099 0.9115 0.9131 14 0.9147 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 M 0.9292 1.5 0.9332 0.9345 ws 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 1 1.6 0.9452 0.9463 0.9474 0.9484 ocea 0.9495 0.9505 OSTS 0.9515 0.9525 1.7 0.9554 0.9564 0.9573 ? 0.9582 0.9591 osno 0.9599 nocas wo 0.9608 0.9616 1.8 0.9641 0.9649 0.9656 0414 0.9664 0.9671 2012 0.9678 Ogos 0.9686 0.9713 0.9719 son 0.9693 1.9 0.9726 co 0.9732 0.9738 04 0.9744 09756 0.9750 0.9772 0.9778 0.9756 2.0 0.9783 0.9788 0.9793 0.9798 0.9803 oeng 0.9808 2.1 0.98210.9826 0.9830 0.9834 c 0.9838 0.9842 ges 0.9846 0.9850 2.2 2020 0.9861 0.9864 0.9868 0.9871 0002 0.9875 0.9878 0.9881 0 9884 2.3 0.9893 0.9896 0.9898 0.9901 22 0.9904 0.9906 0.9909 0.9911 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 Source: This table was generated using the SAS10 function PROBNORM 0.08 0.09 0.5319 0.5359 0.5714 0.5753 0.6103 0.6141 0.6480 0.6517 0.6844 0.6879 0.0079 0.7190 0.7224 0.7517 SB 0.7549 0.7823 * 0 0.7852 1034 0.8106 0.8133 0.8365 . 0.8389 0.8599 0.8621 Oce Wow 0.8810 0.8830 Woor 0.9015 0.8997 0.9162 0.9177 0.9306 0.9319 0.9429 0.9441 0.9535 0.9545 0.9625 0.9633 0.9699 0.9706 0.9761 0.9767 0.9812 0.9817 2014 0.9854 0.9857 COM por 0.9887 0.9890 0.9913 2016 0.9916 0.9934 0.9936 0.9951 0.9952 0.9963 0.9964 0.9973 0.9974 0.9980 0.9981 0.9986 0.9986 0.9990 0.9990

pur-new-sol

Related Questions