The 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 rj rf = j(rm rf), (0.1) where rj and rf are the returns to security j and the risk-free rate, respectively, rm is the return on the market portfolio, and j is the jth securitys beta value. A stocks beta is important to investors since it reveals the stocks volatility. It measures the sensitivity of security js 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 markets. A beta greater than 1 indicates an aggressive stock. Investors usually want an estimate of a stocks beta before purchasing it. The CAPM model shown above is the economic model in this case. The econometric model is obtained by including an intercept in the model (even though theory says it should be zero) and an error term rj rf = j + j(rm rf) + e, (0.2)

Questions :

1. Explain why the econometric model in equation 0.2 is a simple regression model.

2. In the data file Case2.xlsx are data on the monthly returns of seven firms (Apple, Microsoft, GE, GM, IBM, Disney, and Mobil-Exxon), the rate of return on the market portfolio (MKT), and the rate of return on the risk free asset (RISKFREE). The 120 observations cover January 1999 to December 2008. Estimate the CAPM model for each firm, and comment on their estimated beta values. Which firm appears most aggressive ? Which firm appears most defensive ?

3. Finance theory says that the intercept parameter j should be zero. Does this seem correct given your estimates ? For the Microsoft stock, plot the fitted regression line along with the data scatter.

4. Estimate the model for each firm under the assumption that j = 0. Do the estimates of the beta values change much ?

Variable Name	Descriptive Label
date	year/month/day
aapl	Apple monthly rate of return
dis	Disney monthly rate of return
ge	General Electric monthly rate of return
gm	General Motors monthly rate of return
ibm	IBM monthly rate of return
msft	Microsoft monthly rate of return
xom	Exxon-Mobil monthly rate of return
mkt	Market Portfolio monthly rate of return
riskfree*	Risk free rate, monthly rate based on 30 day T-bill

obs aapl dis ge gm ibm msft xom mkt riskfree 1999:01:00 0.006109 0.1 0.0281861 0.254148 -0.0061 0.26183 -0.03932 0.038346 0.003674 1999:02:00 -0.15478 0.066288 -0.0435 -0.07451 -0.07247| -0.14214 -0.04666 -0.03811 0.003755 1999:03:00 0.032317| -0.11545 0.106293 0.054353 0.044183 0.194005 0.060094 0.037862 0.003798 1999:04:00 0.279997 0.02008 -0.04746 0.0237071 0.180183 -0.09275 0.177148 0.049 0.00371 1999:05:00 -0.04212 -0.08268 -0.03499 -0.07125 0.11021 -0.00769 -0.03344 -0.02072 0.003683 1999:06:00 0.051063 0.05794 0.111248 -0.04348 0.114224 0.117738 -0.03443 0.05102 0.003698 1999:07:00 0.202431 -0.10548 -0.0323 -0.07386 -0.02756 -0.04851 0.029173 -0.03064 0.003708 1999:08:00 0.171716 0.006803 0.03039 0.092025 -0.008 0.07866 -0.00113 -0.00998 0.00375 1999:09:00 -0.02969 -0.063061 0.058765 -0.05 -0.0286 -0.02161 -0.03645 -0.02287 0.003751 1 1999:10:00 0.265549 0.019231 0.142857 0.119166 -0.18802 0.022084 -0.02549 0.062048 0.003638 2 1999:11:00 0.221529 0.059811 -0.03967 0.029281 0.050204 -0.01637| 0.0768271 0.036856 0.003809 8 1999:12:00 0.050447 0.049327 0.192392 0.009549 0.046695 0.282306 0.01576 0.083925 0.004252 4 2000:01:00 0.009118 0.241453 -0.13651 0.108341 0.040556 -0.16167 0.035687 -0.03975 0.004488 5 2000:02:00 0.10482 -0.07745 -0.00936 -0.04965 -0.08356 -0.08685 -0.09211 0.03177| 0.004428 6 2000:03:00 0.184842 0.231343 0.178735 0.088743 0.148418 0.188811 0.034855 0.053552 0.00488 7 2000:04:00 -0.08652 0.05 0.010442 0.130566 -0.05509 -0.34353 -0.00321 -0.05947 0.004392 B 2000:05:00 -0.32292 -0.03175 0.005167 -0.24032 -0.03583 -0.10305 0.078069 -0.03905 0.003896 9 2000:06:00 0.247024 -0.07452 0.005931 -0.17788 0.020373 0.278721 -0.05776 0.051649 0.004691 2000:07:00 -0.02983 -0.00322 -0.0269 -0.01938 0.026241 -0.12734 0.019108 -0.01711 0.004896 1 2000:08:00 0.199262 0.006462 0.140948 0.276619 0.175142 0 0.025812 0.075811 0.005195 2 2000:09:00 -0.57744 -0.01766 -0.01471 -0.09957 -0.14773 -0.13608 0.091884 -0.05114 0.004933 23 2000:10:00 -0.24029| -0.06373 -0.04984 -0.04423 -0.1244 0.141969 0.000701 -0.02456 0.005023 24 2000:11:00 -0.15655 -0.1919 -0.09578 -0.19517 -0.0494 -0.16697 -0.00838| -0.10255 0.005099 25 2000:12:00 -0.09849| 0.007257 -0.02956 0.02904 -0.09091 -0.24401 -0.01207 0.020346| 0.004808 26 | 2001:01:00| 0.453783 0.052268 -0.04083| 0.054233| 0.317647 0.407781 -0.03206| 0.039533| 0.004023 27 2001:02:00 -0.15607 0.01642 0.011309 0.002235 -0.10688| -0.03378 -0.03161 -0.09927 0.004178|| 28 | 2001:03:00| 0.209314 -0.07593 -0.09634 -0.0275 -0.03724 -0.07309| -0.00062] -0.07029 0.003693 29 2001:04:00| 0.154963 0.057692 0.159341| 0.057088 0.19713| 0.238857 0.093820.083904| 0.003118 30 2001:05:00 -0.21734 0.045289 0.009685 0.047254 -0.02779 0.021107 0.006659 0.010561| 0.002871 31 | 2001:06:00 0.165415 -0.08634 -0.0051 0.130931 0.010733 0.055218 -0.01555 -0.01748 0.002846| 32 2001:07:00 -0.19183 -0.087921 -0.10441 -0.01166 -0.06894 -0.09329| -0.04385 -0.018321 0.003033| 3 2001:08:00 -0.012 -0.034921 -0.05793 -0.13129| -0.04861 -0.13809| -0.03305 -0.05908 0.002812 34 2001:09:00 -0.16388 -0.26779 -0.08834 -0.2164 -0.08234 -0.10307 -0.01868 -0.09154 0.001982 35 2001:10:00 0.132172 -0.00161 -0.02124 -0.03683 0.17826 0.136408] 0.001269 0.027967 0.00174 2001:11:00 0.212985 01011| 0.057402 0.214908 0.07088| 0.104213 -0.04613| 0.078734 0.0014 37 2001:12:00| 0.028168| 2.022472 0.045714] -0.02213| 0.046457 0.031771| 0.050802 0.017841| 0.001363 38 2002:01:00 0.128769 0.016409 -0.0731| 0.052263 -0.10805 -0.0384 -0.00636 -0.01606 0.001408 9 2002:02:00 -0.1221 0.092118| 0.04114 0.045757 -0.08926 -0.08429 0.063508 -0.02171| 0.0014 40 | 2002:03:00| 0.090785 0.003478 -0.02727 0.140997 0.05992 0.033768| 0.061259 0.044693 0.001425 41 2002:04:00 0.025348 0.004333 -0.15754| 0.061208 -0.19462 -0.13348 -0.08351 -0.04965 0.00 1461 42 2002:05:00 -0.03997 -0.01165 -0.013 -0.02338 -0.03773 -0.02583 -0.00025 -0.01046 0.001408 43 2002:06:00 -0.23948 -0.17503 -0.06134 -0.13998 -0.10503 0.07445 0.024793 -0.07024 0.001389 4 2002:07:00 -0.13883| -0.06191 0.108434 -0.1290 -0.02222 -0.12285 -0.10166 -0.08114] 0.001417 45 2002:08:00 -0.03342 -0.11562 -0.06367 0.038883 0.072869 0.022926 -0.02938 0.007984 0.00138 6 2002:09:00 -0.01695 -0.0344 -0.17645 -0.18721 -0.22645 -0.1088 -0.10014 -0.09998 0.001308 47 2002:10:00 0.108273| 0.103038 0.024341 -0.14524 0.353799 0.222451| 0.055172 0.074958| 0.001183 82002:11:00 -0.0354 0.186826 0.074059 0.209023 0.10299 0.078736 0.040701 0.061276 0.001014 9 2002:12:00 -0.07548 -0.1665 -0.09513| -0.07154 -0.10838| -0.10368| 0.004023 -0.05331 0.000947 50 2003:01:00 0.002095 0.072961 -0.04969| -0.01438 0.009032] -0.08201 -0.02261 -0.02343] 0.000955 5 2003:02:00 0.045264 -0.02514| 0.047537 -0.056 -0.00128| 0.00210 0.002928 -0.01541| 0.000996 52 2003:03:00 -0.05796 -0.00235 0.060291 -0.0044 0.006158 0.021519 0.027337 0.010333| 0.000951 53 | 2003:04:00 0.005659| 0.096357 0.154902 0.072278| 0.082494 0.055762 0.007153| 0.082797 0.000911 54 | 2003:05:00 0.262306 0.053055 -0.02547 -0.0061| 0.038869 -0.0371 0.041193 0.06350 0.00094 55 | 2003:06:00 0.06183 0.005089 0.005923 0.018964 -0.06293 0.041853 -0.01346 0.016332 0.000662 56 2003:07:00| 0.105983| 0.109873| -0.0083 0.039722 -0.01515 0.0300311 -0.00919 0.02313 0.000733 57 2003:08:00 0.072579 -0.06478 0.039733| 0.111408 0.011323] 0.004165 0.06661| 0.024908| 0.000809 58| 2003:09:00 -0.08359 -0.0161| 0.014542 -0.00414| 0.077064 0.048265 -0.02918 -0.0091 0.00071 59 | 2003:10:00 0.10473| 0.122459 -0.02684| 0.042512| 0.013019| -0.05396 -0.00055| 0.060331| 0.000763| 60 2003:11:00 -0.0865 0.019876 -0.01172 0.014296 0.213634 -0.01645 -0.00355| 0.216607 0.00075 61 2003:12:00 0.021998| 0.019489 0.087548 0.248247 0.023636 0.064566 0.132597 0.045532| 0.000689 62 2004:01:00 0.055686 0.028718 0.085539 -0.06966| 0.070673 0.01023 -0.005121 0.023064 0.000689 63| 2004:02:00 0.060284 0.10541 -0.02706| -0.02134 -0.025 -0.04051| 0.039961| 0.015461 0.000778 64 | 2004:03:00 0.130434 -0.05805 -0.0615 -0.0212 -0.04829 -0.06031 -0.01375 -0.01069 0.000769 65 | 2004:04:00 -0.0466 -0.07843] -0.01868 0.006794 -0.03996 0.048135 0.023082 -0.02423 0.000674 6 2004:05:00 0.0884| 0.019105| 0.039065 -0.03227 0.006805 0.003827 0.02279 0.01412 0.000757 67 | 2004:06:00 0.159658 0.086067 0.047558 0.026438 -0.00497 0.08883| 0.026821| 0.021563| 0.000941 68 2004:07:00 -0.00615 -0.09416 0.026235 -0.07405 -0.01225 -0.00245| 0.042558 -0.03768| 0.001065 69 | 2004:08:00 0.066481 -0.027721 -0.01384 -0.03083 -0.02527 -0.03896 0.001512 0.002714 0.001201 70 | 2004:09:00 0.123513 0.004454| 0.0301921 0.028322] 0.012398 0.012821 0.048373 0.020555 0.001215 71 2004:10:00 | 0.352258 0.118404 0.016081 -0.09251| 0.046769 0.011573| 0.018415 0.01781| 0.001457 72 2004:11:00 0.27958 0.065821 0.0363421 0.014008 0.052033 0.068645 0.046729 0.048243 0.001693 3 2004:12:00 -0.03952 0.043155 0.038462| 0.038093 0.046053 -0.00336 0.00015 0.03518 0.00159 4 2005:01:00 0.194099 0.029856 -0.01014 -0.08113 -0.05234 -0.01647 0.006633 -0.02656 0.001802 75 2005:02:00 0.16671 -0.0241 -0.01965| -0.01793] -0.007 -0.03950.232171) 0.022695 0.002081) 6 2005:03:00 -0.07111| 0.028275 0.024432 -0.1756 -0.01296 -0.03935 -0.0586 -0.01694 0.002166| 7 2005:04:00 -0.13463 -0.0811| 0.003882 -0.09221 -0.16415| 0.046752 -0.043121 -0.02518| 0.002259 8 2005:05:00 0.10260 0.039394 0.007735| 2.200525 -0.00825] 2.022925 -0.009 0.037916| 0.002293 9 | 2005:06:00 -0.07421 -0.08236 -0.0413| 0.078338 -0.0178 -0.03721| 0.022598 0.011531| 0.002488 80 2005:07:00| 0.1586520| 0.018268 -0.00433| 0.082941| 0.124798 0.030998 0.022272 | 0.04333|| 0.002691 81 2005:08:00 0.099414] -0.01755 -0.0258 -0.05785 -0.03163| 0.07223 0.024511] -0.00594 0.002784 82 2005:09:00 0.143314 -0.04208| 0.008331 -0.10471 -0.00496 -0.06026 0.060768 0.010609 0.002655 83 | 2005:10:00 0.07424 0.009946| 0.007128 -0.1048 0.020693 -0.0011 -0.11646| -0.02078 0.00308 84 2005:11:00 0.177635 0.022979 0.05337 -0.18248 0.088178| 0.080156 0.038831 0.040406 0.003309 85 2005:12:00 0.060012 -0.02768 -0.01176 -0.11324 -0.07537 -0.05528 -0.03205 0.003476 0.003288 82 2005:09:00 0.143314 -0.04208] 0.008331 -0.1471 -0.0046 -0.06026 0.060768| 0.010609 0.002655 83 2005:10:00 0.07424 0.009946| 0.007128 -0.10487 0.020693 -0.0011 -0.11646 -0.02078 0.00308 84 2005:11:00| 0.177635 0.022979 0.0533 -0.18248 0.088178 0.080156 0.038831 0.040406 0.003309 85 2005:12:00 0.060012 -0.02768 -0.01176 -0.11324 -0.07537 -0.05528 -0.03205 0.003476 0.003288 86 2006:01:00 0.050355 0.055903 -0.06562 0.238929 -0.01095 0.076482 0.11714 0.040112| 0.003606 87 2006:02:00 -0.0929 0.10588 0.011298 -0.1454 -0.01058 -0.0422 -0.048 -0.00164 0.003687 88 2006:03:00 -0.08425 -0.00357 0.058108 0.047267 0.027792 0.012653 0.025097 0.01906 0.003828 89 | 2006:04:00 0.12229 0.00251 -0.00546 0.075693 -0.00 158 -0.11246| 0.0364 0.012968| 0.00384 98 | 2006:05:00 -0.15087 0.09084 -0.00954 0.187937 -0.02599 -0.05839 -0.02933 -0.03104 0.003913 91 2006:06:00 -0.04183 -0.01639| -0.03065| 0.106201 -0.03855| 0.028698 0.007224 -0.004 0.003903 2 2006:07:00 0.18666 -0.01033 -0.00819 0.081907 0.00768| 0.032618| 0.104156| -0.0019 0.0042 93 2006:08:00 -0.00162 -0.00135| 0.041909 -0.08688 0.04984 0.0719M] 0.003691| 0.025085 0.004138 94 2006:09:00 0.134562 0.042496] 0.043746| 0.139822 0.01198 0.064202 -0.008421 0.019452 0.003874 95 2006:10:00 0.05326 0.017794 -0.00538 0.04991 0.1268| 0.049726| 0.064382] 2.037086 0.004293 6 2006:11:00 0.13048 0.05054 0.004842 -0.15579 -0.0011 0.026123 0.07995 0.023716 0.00415 97 2006:12:00 -0.07441| 0.046294| 0.062642 0.050975 0.056897 0.01703] -0.00234 0.010823] 0.003973 98 | 2007:01:00 0.0104 0.026262 -0.0311 0.06901 0.020587 0.0334 -0.03302] 0.019438| 0.004168 99 2007:02:00 -0.01306 -0.02616 -0.02386 -0.02101 -0.05961 -0.08393 -0.02834 -0.014 0.004286 100 2007:03:00 0.098097 0.005255 0.01289 -0.0395 0.014203 -0.01065| 0.052595 0.012949 0.004209 101 2007:04:00| 0.074158| 0.015974| 0.042421| 0.019256 0.084341| 0.074273 0.052087 0.039893 0.003963 102 2007:05:00| 0.214328 0.01315 0.019533 -0.0317] 0.046864 0.028393 0.052154| 0.038894 0.003913 103 2007:06:00 0.007014| -0.02308 0.026078 0.26042] -0.01266 -0.03976 0.00853 -0.01476 0.003776 104 2007:07:00 0.079646 -0.03339 0.012539 -0.14286 0.051306 -0.01629 0.014902| -0.03175 0.004254 105 2007:08:00 0.0510021 0.018182| 0.002838| -0.04352 0.058202 -0.005521 0.011159 0.011623 0.00346 106 2007:09:00 0.108247 0.023512| 0.072292 0.193884 0.009512| 0.02540| 0.0796691 0.040903| 0.002869 107 2007:10:00| 0.237701 0.006979 -0.0058| 0.067847 -0.01426 0.249491 -0.00616 0.025842 0.003318 108 2007:11:00 -0.04069| -0.04274 -0.06973| -0.23246 -0.090 -0.08422] -0.02696 -0.04928| 0.002683 109 2007:12:00| 0.087038 -0.01569 -0.023 -0.16561 0.027762| 0.059524| 0.050808 -0.00434| 0.002382 110 2008:01:00 -0.31664 -0.07559 -0.04613 0.133387 -0.00916 -0.08427 -0.07781 -0.06231| 0.001387 111 2008:02:00 -0.0763| 0.086126 -0.05402 -0.1659 0.066754 -0.16227 0.011111 -0.02204 0.001725 112 2008:03:00| 0.147816 -0.03178 0.11677 -0.1817 0.011242] 0.043386 -0.02793 -0.01047 0.001032 113 2008:04:00| 0.212195 0.033461 -0.11646| 0.217848 0.048289| 0.004933 | 0.100378 0.05114 0.001048 114 2008:05:00| 0.085082| 0.036078 -0.06055 -0.25216 0.076471 -0.00316 -0.04201 0.023825 0.001623 115 2008:06:00 -0.1129| -0.07143 -0.12109 -0.32749| -0.08422 -0.0286 -0.0071 -0.07863| 0.001412 116 2008:07:00 -0.0500 -0.02724 0.059948 -0.03739 0.079727 -0.06507 -0.08737 -0.01315 0.001319 117 2008:08:00 0.066562 0.065898| -0.00672 -0.09666 -0.04493 0.06531 -0.00025 0.011042 0.001387 118 2008:09:00 -0.32956 -0.05131 -0.0815 -0.055| -0.03919 -0.02199| -0.02937 -0.09806 0.000803 119 2008:10:00 -0.0534 -0.15575 -0.2349 -0.3873 -0.20511 -0.16336 -0.04558| -0.18473| 0.000212 120 2008:11:00 -0.13867 -0.13084| -0.11994] -0.09499 -0.11692 -0.0886 0.086751 -0.08521 0.000025 121 2008:12:00 -0.07899 | 0.023091 -0.03844| -0.38931 0.031373 -0.03858 -0.00399 0.021482| 0.000025