Reference no: EM131133277
The capital asset pricing model (CAPM) is an important model in the field of finance. It explains variations in the rate of return on a security as a function of the rate of return on a portfolio consisting of all publicly traded stocks, which is called the market portfolio. Generally the rate of return on any investment is measured relative to its opportunity cost, which is the return on a risk free asset. The resulting difference is called the risk premium since it is the reward or punishment for making a risky investment. The CAPM says that the risk premium on security j is proportional to the risk premium on the market portfolio. That is,
(1) rj - rrf = βj(rm - rrf)
where rj is the return to security j, rjf is the risk free rate, rm is the return on the market portfolio and βj is the "beta" of security j. A stock's beta is important to investors since it reveals the stock's volatility. It measures the sensitivity of security j return to variation in the whole stock market. As such, values of beta less than 1 indicate that the stock is "defensive" since its variation is less than the market's. A beta greater than 1 indicates an "aggressive" stock. Investors usually want an estimate of the stock's beta before purchasing it. The CAPM model is the theoretical model. The econometric model is obtained by including an intercept (even though the theoretical model says that it should be zero) and an error term in the model:
(2) rj - rrf = αj + βj(rm - rrf) + ε
PART 1
1. Explain why the econometric model (equation 2) is a simple regression model like those discussed in class.
2. Choose a public corporation whose stocks are traded in the NYSE. For example, you may choose MICROSOFT, GE, GM, IBM, DISNEY, and MOBIL-EXXON. Using the Finance portal in Yahoo, download monthly data on the stock of your chosen public corporation for the period December 1997 to December 2008 and construct the monthly returns (January 1998 to December 2008) as log differences (not in percent).I attach at the end of this file the return series on the market portfolio (represented by the S&P 500) MKT and the return series on the risk free asset RISKFREE. The 132 observations cover the period January 1998 to December 2008. Estimate the CAPM model for each corporation and comment on their estimated beta values. Interpret your estimates. Does your stock appear aggressive? Defensive?
3. Finance theory (equation 1) says that the intercept parameter should be zero. Does this seem correct given your estimates? Draw a scatter diagram of your data and plot the fitted regression line along with the scatter diagram.
4. Estimate the model (equation 2) under the assumption that the intercept is zero. Do the estimates of beta change much?
5. What is the standard error of βj? Test the null that βj is zero (at alpha = 0.01). What is RSS, ESS, TSS, R-square? Construct the ANOVA test.
PART 2-
There are, however, potential problems with the previous econometric findings.
6. The beta may not be constant through time. Use the dummy variable approach and the Chow test approach to determine whether the assumption of parameter constancy is valid. Use 2001m10 as the break date.
7. The error variance may not be constant through time. This is known as heteroskedasticity. Use the White test to investigate the issue of heteroskedastic disturbances.
8. The errors may be correlated through time. This is known as autocorrelation or serial correlation. Use the Durbin Watson test to test the hypothesis of first order positive autocorrelation.
9. Returns may be non-linearly related to market returns rather than the linear relation that is suggested in the statistical model. Construct a test for linearity.
10. To add some dynamic content, re-estimate the model by including the one month lag of the market risk premium. Is the lagged market risk premium significant?
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date
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MKT
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RISKFREE
|
|
19980130
|
0.004529
|
0.004188
|
|
19980227
|
0.07323
|
0.004268
|
|
19980331
|
0.051322
|
0.004358
|
|
19980430
|
0.010862
|
0.00394
|
|
19980529
|
-0.025755
|
0.003806
|
|
19980630
|
0.031954
|
0.003919
|
|
19980731
|
-0.023264
|
0.003954
|
|
19980831
|
-0.157667
|
0.003909
|
|
19980930
|
0.063836
|
0.003357
|
|
19981030
|
0.074357
|
0.00296
|
|
19981130
|
0.061986
|
0.003702
|
|
19981231
|
0.063053
|
0.003662
|
|
19990129
|
0.038346
|
0.003674
|
|
19990226
|
-0.038105
|
0.003755
|
|
19990331
|
0.037862
|
0.003798
|
|
19990430
|
0.049
|
0.00371
|
|
19990528
|
-0.02072
|
0.003683
|
|
19990630
|
0.05102
|
0.003698
|
|
19990730
|
-0.030635
|
0.003708
|
|
19990831
|
-0.009983
|
0.00375
|
|
19990930
|
-0.022867
|
0.003751
|
|
19991029
|
0.062048
|
0.003638
|
|
19991130
|
0.036856
|
0.003809
|
|
19991231
|
0.083925
|
0.004252
|
|
20000131
|
-0.039753
|
0.004488
|
|
20000229
|
0.03177
|
0.004428
|
|
20000331
|
0.053552
|
0.00488
|
|
20000428
|
-0.059467
|
0.004392
|
|
20000531
|
-0.039047
|
0.003896
|
|
20000630
|
0.051649
|
0.004691
|
|
20000731
|
-0.017105
|
0.004896
|
|
20000831
|
0.075811
|
0.005195
|
|
20000929
|
-0.051139
|
0.004933
|
|
20001031
|
-0.024564
|
0.005023
|
|
20001130
|
-0.102546
|
0.005099
|
|
20001229
|
0.020346
|
0.004808
|
|
20010131
|
0.039533
|
0.004023
|
|
20010228
|
-0.099267
|
0.004178
|
|
20010330
|
-0.07029
|
0.003693
|
|
20010430
|
0.083904
|
0.003118
|
|
20010531
|
0.010561
|
0.002871
|
|
20010629
|
-0.017481
|
0.002846
|
|
20010731
|
-0.018321
|
0.003033
|
|
20010831
|
-0.05908
|
0.002812
|
|
20010928
|
-0.09154
|
0.001982
|
|
20011031
|
0.027967
|
0.001744
|
|
20011130
|
0.078734
|
0.00144
|
|
20011231
|
0.017841
|
0.001363
|
|
20020131
|
-0.01606
|
0.001408
|
|
20020228
|
-0.021705
|
0.001444
|
|
20020328
|
0.044693
|
0.001425
|
|
20020430
|
-0.049649
|
0.001461
|
|
20020531
|
-0.010458
|
0.001408
|
|
20020628
|
-0.070243
|
0.001389
|
|
20020731
|
-0.081137
|
0.001417
|
|
20020830
|
0.007984
|
0.00138
|
|
20020930
|
-0.099975
|
0.001308
|
|
20021031
|
0.074958
|
0.001183
|
|
20021129
|
0.061276
|
0.001014
|
|
20021231
|
-0.053309
|
0.000947
|
|
20030131
|
-0.02343
|
0.000955
|
|
20030228
|
-0.015408
|
0.000996
|
|
20030331
|
0.010333
|
0.000951
|
|
20030430
|
0.082797
|
0.000911
|
|
20030530
|
0.063507
|
0.000934
|
|
20030630
|
0.016332
|
0.000662
|
|
20030731
|
0.02313
|
0.000733
|
|
20030829
|
0.024908
|
0.000809
|
|
20030930
|
-0.009102
|
0.00071
|
|
20031031
|
0.060331
|
0.000763
|
|
20031128
|
0.016607
|
0.00075
|
|
20031231
|
0.045532
|
0.000689
|
|
20040130
|
0.023064
|
0.000689
|
|
20040227
|
0.015467
|
0.000778
|
|
20040331
|
-0.010685
|
0.000769
|
|
20040430
|
-0.02423
|
0.000674
|
|
20040528
|
0.014127
|
0.000757
|
|
20040630
|
0.021563
|
0.000941
|
|
20040730
|
-0.037681
|
0.001065
|
|
20040831
|
0.002714
|
0.001201
|
|
20040930
|
0.020555
|
0.001215
|
|
20041029
|
0.01781
|
0.001457
|
|
20041130
|
0.048243
|
0.001693
|
|
20041231
|
0.03518
|
0.00159
|
|
20050131
|
-0.026557
|
0.001802
|
|
20050228
|
0.022695
|
0.002081
|
|
20050331
|
-0.016937
|
0.002166
|
|
20050429
|
-0.025182
|
0.002259
|
|
20050531
|
0.037916
|
0.002293
|
|
20050630
|
0.011531
|
0.002488
|
|
20050729
|
0.043331
|
0.002691
|
|
20050831
|
-0.005943
|
0.002784
|
|
20050930
|
0.010609
|
0.002655
|
|
20051031
|
-0.020784
|
0.00308
|
|
20051130
|
0.040406
|
0.003309
|
|
20051230
|
0.003476
|
0.003288
|
|
20060131
|
0.040112
|
0.003606
|
|
20060228
|
-0.001644
|
0.003687
|
|
20060331
|
0.01906
|
0.003828
|
|
20060428
|
0.012968
|
0.003844
|
|
20060531
|
-0.031042
|
0.003913
|
|
20060630
|
-0.000396
|
0.003903
|
|
20060731
|
-0.001902
|
0.0042
|
|
20060831
|
0.025085
|
0.004138
|
|
20060929
|
0.019452
|
0.003874
|
|
20061031
|
0.037086
|
0.004293
|
|
20061130
|
0.023716
|
0.00415
|
|
20061229
|
0.010823
|
0.003973
|
|
20070131
|
0.019438
|
0.004168
|
|
20070228
|
-0.013998
|
0.004286
|
|
20070330
|
0.012949
|
0.004209
|
|
20070430
|
0.039893
|
0.003963
|
|
20070531
|
0.038894
|
0.003913
|
|
20070629
|
-0.014758
|
0.003776
|
|
20070731
|
-0.031753
|
0.004254
|
|
20070831
|
0.011623
|
0.00346
|
|
20070928
|
0.040903
|
0.002869
|
|
20071031
|
0.025842
|
0.003318
|
|
20071130
|
-0.049279
|
0.002683
|
|
20071231
|
-0.004342
|
0.002382
|
|
20080131
|
-0.062305
|
0.001387
|
|
20080229
|
-0.02204
|
0.001725
|
|
20080331
|
-0.01047
|
0.001032
|
|
20080430
|
0.051144
|
0.001048
|
|
20080530
|
0.023825
|
0.001623
|
|
20080630
|
-0.078625
|
0.001412
|
|
20080731
|
-0.01315
|
0.001319
|
|
20080829
|
0.011042
|
0.001387
|
|
20080930
|
-0.09806
|
0.000803
|
|
20081031
|
-0.184726
|
0.000212
|
|
20081128
|
-0.085206
|
0.000025
|
|
20081231
|
0.021482
|
0.000025
|
|
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