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 = Bj (Rm - Rf), (equation 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 Bj 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 = Aj + Bj (Rm - Rf) + e, (equation 0.2)

RAW DATA

obs	dis	ge	gm	ibm	msft	xom	mkt	riskfree
1998:01:00	0.080884	0.056218	-0.046296	-0.056153	0.154255	-0.030644	0.004529	0.004188
1998:02:00	0.047368	0.003226	0.19849	0.05962	0.136154	0.081728	0.07323	0.004268
1998:03:00	-0.046343	0.112379	-0.017226	-0.005386	0.056047	0.060784	0.051322	0.004358
1998:04:00	0.168337	-0.011603	-0.005535	0.115523	0.006983	0.080407	0.010862	0.00394
1998:05:00	-0.090818	-0.021277	0.074212	0.015922	-0.058946	-0.029461	-0.025755	0.003806
1998:06:00	-0.072296	0.089955	-0.070435	-0.022872	0.277819	0.012411	0.031954	0.003919
1998:07:00	-0.015158	-0.012517	0.08232	0.154056	0.014418	-0.015762	-0.023264	0.003954
1998:08:00	-0.203267	-0.105521	-0.189283	-0.14834	-0.127345	-0.062669	-0.157667	0.003909
1998:09:00	-0.075171	-0.001719	-0.055914	0.140954	0.147231	0.079274	0.063836	0.003357
1998:10:00	0.063645	0.099764	0.151481	0.155642	-0.038047	0.014159	0.074357	0.00296
1998:11:00	0.194896	0.032857	0.113749	0.113434	0.152302	0.052845	0.061986	0.003702
1998:12:00	-0.067961	0.132503	0.02415	0.116578	0.136783	-0.025	0.063053	0.003662
1999:01:00	0.1	0.028186	0.254148	-0.006102	0.26183	-0.039316	0.038346	0.003674
1999:02:00	0.066288	-0.043504	-0.074513	-0.072469	-0.142143	-0.046655	-0.038105	0.003755
1999:03:00	-0.115453	0.106293	0.054353	0.044183	0.194005	0.060094	0.037862	0.003798
1999:04:00	0.02008	-0.047458	0.023707	0.180183	-0.092748	0.177148	0.049	0.00371
1999:05:00	-0.082677	-0.034994	-0.071253	0.1102	-0.007686	-0.033439	-0.02072	0.003683
1999:06:00	0.05794	0.111248	-0.043478	0.114224	0.117738	-0.034429	0.05102	0.003698
1999:07:00	-0.105477	-0.032301	-0.073864	-0.027563	-0.04851	0.029173	-0.030635	0.003708
1999:08:00	0.006803	0.03039	0.092025	-0.007996	0.07866	-0.001134	-0.009983	0.00375
1999:09:00	-0.063063	0.058765	-0.05	-0.0286	-0.021607	-0.03645	-0.022867	0.003751
1999:10:00	0.019231	0.142857	0.119166	-0.188017	0.022084	-0.025493	0.062048	0.003638
1999:11:00	0.059811	-0.039668	0.029281	0.050204	-0.016374	0.076827	0.036856	0.003809
1999:12:00	0.049327	0.192392	0.009549	0.046695	0.282306	0.01576	0.083925	0.004252
2000:01:00	0.241453	-0.136511	0.108341	0.040556	-0.16167	0.035687	-0.039753	0.004488
2000:02:00	-0.077453	-0.009355	-0.049651	-0.083563	-0.086845	-0.092105	0.03177	0.004428
2000:03:00	0.231343	0.178735	0.088743	0.148418	0.188811	0.034855	0.053552	0.00488
2000:04:00	0.05	0.010442	0.130566	-0.055085	-0.343529	-0.003208	-0.059467	0.004392
2000:05:00	-0.031746	0.005167	-0.24032	-0.03583	-0.103047	0.078069	-0.039047	0.003896
2000:06:00	-0.074516	0.005931	-0.177876	0.020373	0.278721	-0.057764	0.051649	0.004691
2000:07:00	-0.003221	-0.026903	-0.019376	0.026241	-0.127344	0.019108	-0.017105	0.004896
2000:08:00	0.006462	0.140948	0.276619	0.175142	0	0.025812	0.075811	0.005195
2000:09:00	-0.017657	-0.014711	-0.099567	-0.147727	-0.136079	0.091884	-0.051139	0.004933
2000:10:00	-0.063725	-0.049837	-0.044231	-0.124444	0.141969	0.000701	-0.024564	0.005023
2000:11:00	-0.191972	-0.095781	-0.195171	-0.049442	-0.166969	-0.008381	-0.102546	0.005099
2000:12:00	0.007257	-0.029559	0.02904	-0.090909	-0.244009	-0.012074	0.020346	0.004808
2001:01:00	0.052268	-0.040834	0.054233	0.317647	0.407781	-0.032063	0.039533	0.004023
2001:02:00	0.01642	0.011309	0.002235	-0.106875	-0.033777	-0.03161	-0.099267	0.004178
2001:03:00	-0.075929	-0.096344	-0.027569	-0.037237	-0.073093	-0.000617	-0.07029	0.003693
2001:04:00	0.057692	0.159341	0.057088	0.19713	0.238857	0.093827	0.083904	0.003118
2001:05:00	0.045289	0.009685	0.047254	-0.027792	0.021107	0.006659	0.010561	0.002871
2001:06:00	-0.086338	-0.005102	0.130931	0.010733	0.055218	-0.015549	-0.017481	0.002846
2001:07:00	-0.08792	-0.10441	-0.011655	-0.068938	-0.093288	-0.043847	-0.018321	0.003033
2001:08:00	-0.034915	-0.057931	-0.131289	-0.048665	-0.138087	-0.033046	-0.05908	0.002812
2001:09:00	-0.267794	-0.088336	-0.216438	-0.082341	-0.103068	-0.01868	-0.09154	0.001982
2001:10:00	-0.001611	-0.021237	-0.03683	0.17826	0.136408	0.001269	0.027967	0.001744
2001:11:00	0.10113	0.057402	0.214908	0.07088	0.104213	-0.046134	0.078734	0.00144
2001:12:00	0.022472	0.045714	-0.022133	0.046457	0.031771	0.050802	0.017841	0.001363
2002:01:00	0.016409	-0.073104	0.052263	-0.108052	-0.03834	-0.006361	-0.01606	0.001408
2002:02:00	0.092118	0.041184	0.045757	-0.089258	-0.084288	0.063508	-0.021705	0.001444
2002:03:00	0.003478	-0.027273	0.140997	0.059927	0.033768	0.061259	0.044693	0.001425
2002:04:00	0.004333	-0.157543	0.061208	-0.194615	-0.133477	-0.083505	-0.049649	0.001461
2002:05:00	-0.011648	-0.012995	-0.023383	-0.037727	-0.025832	-0.000249	-0.010458	0.001408
2002:06:00	-0.175033	-0.061336	-0.139984	-0.105034	0.074445	0.024793	-0.070243	0.001389
2002:07:00	-0.061905	0.108434	-0.129093	-0.022222	-0.122852	-0.101662	-0.081137	0.001417
2002:08:00	-0.115623	-0.063665	0.038883	0.072869	0.022926	-0.02938	0.007984	0.00138
2002:09:00	-0.034439	-0.176451	-0.187213	-0.226453	-0.108802	-0.100141	-0.099975	0.001308
2002:10:00	0.103038	0.024341	-0.145244	0.353799	0.222451	0.055172	0.074958	0.001183
2002:11:00	0.186826	0.074059	0.209023	0.10299	0.078736	0.040701	0.061276	0.001014
2002:12:00	-0.166498	-0.095133	-0.071537	-0.108375	-0.103675	0.004023	-0.053309	0.000947
2003:01:00	0.072961	-0.049692	-0.014379	0.009032	-0.082012	-0.02261	-0.02343	0.000955
2003:02:00	-0.025143	0.047537	-0.056702	-0.001279	0.002107	0.002928	-0.015408	0.000996
2003:03:00	-0.002345	0.060291	-0.004442	0.006158	0.021519	0.027337	0.010333	0.000951
2003:04:00	0.096357	0.154902	0.072278	0.082494	0.055762	0.007153	0.082797	0.000911
2003:05:00	0.053055	-0.025467	-0.006103	0.038869	-0.037167	0.041193	0.063507	0.000934
2003:06:00	0.005089	0.005923	0.018964	-0.062926	0.041853	-0.013462	0.016332	0.000662
2003:07:00	0.109873	-0.008368	0.039722	-0.015152	0.030031	-0.00919	0.02313	0.000733
2003:08:00	-0.064781	0.039733	0.111408	0.011323	0.004165	0.06661	0.024908	0.000809
2003:09:00	-0.016098	0.014542	-0.004136	0.077064	0.048265	-0.029178	-0.009102	0.00071
2003:10:00	0.122459	-0.026837	0.042512	0.013019	-0.053957	-0.000546	0.060331	0.000763
2003:11:00	0.019876	-0.01172	0.014296	0.013634	-0.01645	-0.003554	0.016607	0.00075
2003:12:00	0.019489	0.087548	0.248247	0.023636	0.064566	0.132597	0.045532	0.000689
2004:01:00	0.028718	0.085539	-0.069663	0.070673	0.01023	-0.005122	0.023064	0.000689
2004:02:00	0.105417	-0.027059	-0.021337	-0.025899	-0.040506	0.039961	0.015467	0.000778
2004:03:00	-0.058048	-0.061501	-0.021197	-0.04829	-0.060309	-0.013754	-0.010685	0.000769
2004:04:00	-0.078431	-0.018676	0.006794	-0.039961	0.048135	0.023082	-0.02423	0.000674
2004:05:00	0.019105	0.039065	-0.032265	0.006805	0.003827	0.022797	0.014127	0.000757
2004:06:00	0.086067	0.047558	0.026438	-0.004967	0.08883	0.026821	0.021563	0.000941
2004:07:00	-0.094155	0.026235	-0.07405	-0.012252	-0.002451	0.042558	-0.037681	0.001065
2004:08:00	-0.027718	-0.013835	-0.03083	-0.025267	-0.038961	0.001512	0.002714	0.001201
2004:09:00	0.004454	0.030192	0.028322	0.012398	0.012821	0.048373	0.020555	0.001215
2004:10:00	0.118404	0.016081	-0.092514	0.046769	0.011573	0.018415	0.01781	0.001457
2004:11:00	0.065821	0.036342	0.014008	0.052033	0.068645	0.046729	0.048243	0.001693
2004:12:00	0.043155	0.038462	0.038093	0.046053	-0.003357	0.000195	0.03518	0.00159
2005:01:00	0.029856	-0.010137	-0.081128	-0.052343	-0.016467	0.006633	-0.026557	0.001802
2005:02:00	-0.024101	-0.019651	-0.01793	-0.007065	-0.039574	0.232171	0.022695	0.002081
2005:03:00	0.028275	0.024432	-0.175596	-0.012962	-0.039348	-0.058601	-0.016937	0.002166
2005:04:00	-0.0811	0.003882	-0.092208	-0.16415	0.046752	-0.043121	-0.025182	0.002259
2005:05:00	0.039394	0.007735	0.200525	-0.008248	0.022925	-0.009469	0.037916	0.002293
2005:06:00	-0.082362	-0.044134	0.078338	-0.017869	-0.037209	0.022598	0.011531	0.002488
2005:07:00	0.018268	-0.004329	0.082941	0.124798	0.030998	0.022272	0.043331	0.002691
2005:08:00	-0.017551	-0.025797	-0.057849	-0.031632	0.072237	0.024511	-0.005943	0.002784
2005:09:00	-0.04208	0.008331	-0.104709	-0.004962	-0.060263	0.060768	0.010609	0.002655
2005:10:00	0.009946	0.007128	-0.104868	0.020693	-0.001166	-0.116462	-0.020784	0.00308
2005:11:00	0.022979	0.053377	-0.182482	0.088178	0.080156	0.038831	0.040406	0.003309
2005:12:00	-0.027678	-0.011758	-0.113242	-0.075366	-0.055275	-0.032052	0.003476	0.003288
2006:01:00	0.055903	-0.065621	0.238929	-0.010949	0.076482	0.117144	0.040112	0.003606
2006:02:00	0.105887	0.011298	-0.14547	-0.010578	-0.042273	-0.048765	-0.001644	0.003687
2006:03:00	-0.003573	0.058108	0.047267	0.027792	0.012653	0.025097	0.01906	0.003828
2006:04:00	0.00251	-0.005463	0.075693	-0.001576	-0.112459	0.036477	0.012968	0.003844
2006:05:00	0.090844	-0.00954	0.187937	-0.02599	-0.058385	-0.029328	-0.031042	0.003913
2006:06:00	-0.016393	-0.030648	0.106201	-0.038548	0.028698	0.007224	-0.000396	0.003903
2006:07:00	-0.010333	-0.008192	0.081907	0.00768	0.032618	0.104156	-0.001902	0.0042
2006:08:00	-0.001347	0.041909	-0.086876	0.049864	0.071904	0.003691	0.025085	0.004138
2006:09:00	0.042496	0.043746	0.139822	0.01198	0.064202	-0.008423	0.019452	0.003874
2006:10:00	0.017794	-0.005382	0.04991	0.1268	0.049726	0.064382	0.037086	0.004293
2006:11:00	0.05054	0.004842	-0.155785	-0.001191	0.026123	0.07995	0.023716	0.00415
2006:12:00	0.046294	0.062642	0.050975	0.056897	0.01703	-0.002343	0.010823	0.003973
2007:01:00	0.026262	-0.031174	0.06901	0.020587	0.03349	-0.033016	0.019438	0.004168
2007:02:00	-0.026159	-0.023856	-0.021011	-0.059607	-0.083927	-0.02834	-0.013998	0.004286
2007:03:00	0.005255	0.01289	-0.039498	0.014203	-0.01065	0.052595	0.012949	0.004209
2007:04:00	0.015974	0.042421	0.019256	0.084341	0.074273	0.052087	0.039893	0.003963
2007:05:00	0.01315	0.019533	-0.0317	0.046864	0.028393	0.052154	0.038894	0.003913
2007:06:00	-0.023082	0.026078	0.26042	-0.012664	-0.039756	0.008537	-0.014758	0.003776
2007:07:00	-0.033392	0.012539	-0.142857	0.051306	-0.016288	0.014902	-0.031753	0.004254
2007:08:00	0.018182	0.002838	-0.043519	0.058202	-0.005519	0.011159	0.011623	0.00346
2007:09:00	0.023512	0.072292	0.193884	0.009512	0.025409	0.079669	0.040903	0.002869
2007:10:00	0.006979	-0.005797	0.067847	-0.014261	0.249491	-0.006158	0.025842	0.003318
2007:11:00	-0.042737	-0.069728	-0.232457	-0.090768	-0.084216	-0.026959	-0.049279	0.002683
2007:12:00	-0.015686	-0.023766	-0.165605	0.027762	0.059524	0.050808	-0.004342	0.002382
2008:01:00	-0.075589	-0.046129	0.133387	-0.009158	-0.08427	-0.07781	-0.062305	0.001387
2008:02:00	0.086126	-0.054016	-0.165899	0.066754	-0.162273	0.011111	-0.02204	0.001725
2008:03:00	-0.03178	0.116777	-0.181701	0.011242	0.043386	-0.027928	-0.01047	0.001032
2008:04:00	0.033461	-0.116455	0.217848	0.048289	0.004933	0.100378	0.051144	0.001048
2008:05:00	0.036078	-0.060551	-0.252155	0.076471	-0.003156	-0.042011	0.023825	0.001623
2008:06:00	-0.071429	-0.121094	-0.327485	-0.084215	-0.028602	-0.007098	-0.078625	0.001412
2008:07:00	-0.027244	0.059948	-0.037391	0.079727	-0.065067	-0.087371	-0.01315	0.001319
2008:08:00	0.065898	-0.006716	-0.096658	-0.044929	0.065319	-0.000249	0.011042	0.001387
2008:09:00	-0.051314	-0.081495	-0.055	-0.039185	-0.021986	-0.029371	-0.09806	0.000803
2008:10:00	-0.155751	-0.234902	-0.387302	-0.205113	-0.163357	-0.045583	-0.184726	0.000212
2008:11:00	-0.130837	-0.119939	-0.094991	-0.116919	-0.08867	0.086751	-0.085206	0.000025
2008:12:00	0.023091	-0.038439	-0.389313	0.031373	-0.038576	-0.003993	0.021482	0.000025

DATA DESCRIPTION

Variable Name	Descriptive Label
date	year/month/day
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

Questions (SHOW YOUR WORK)

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 six firms (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 132 observations cover January 1998 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 ?