Chapter 7, Problem 3WM

Summary Introduction

In this problem we have to regress initial period betas with final period betas. Then find out for alphas also. Then we have to find whether betas and alphas in one period predicts in other period also.

Explanation of Solution

In this problem we have to first select six different firms from New York Stock exchange and then find out their price for 60 months from 2014 to 2018. Then after that we have to find out their returns. In the same way and for same period we have to calculate the returns of S&P 500. Then we have to regress each company's returns against returns of S&P one by one for initial 30 months and then for last 30 months. After that we will get trend line /regression equation. The slope of that will be beta and its intercept will be its alpha.

After that we have to regress betas and alphas between their initial and final values. Our objective will be to find out whether initial betas and alphas can predict final betas and alphas.

This is how we can do it.

Below is the return series of six companies and one for S&P:

Date	Adj Close	Returns Alcoa	Returns Google	Returns-Apple	Returns-Genpact	Returns-Barnes	Returns-Dominion Energy	Returns S&P
12/1/2013	0	0	0	0	0	0	0	0
1/1/2014	26.764509	0	0	0	0	0	0	0
2/1/2014	27.299334	0.019785587	0.028942704	0.049950158	-0.017236623	0.026618819	0.021703693	0.042213375
3/1/2014	30.005569	0.094520691	-0.083634406	0.062299587	0.043408574	0.003489558	0.03110756	0.006908249
4/1/2014	31.404423	0.045565745	-0.058697919	0.094761463	-0.03267496	0.001298835	0.021599142	0.006181643
5/1/2014	31.730831	0.010340052	0.061185151	0.070195596	-0.000593355	-0.03004163	-0.050611455	0.020812196
6/1/2014	34.793423	0.09213958	0.027116555	0.066942336	0.039563099	0.033501511	0.045130671	0.018878997
7/1/2014	38.298481	0.09598186	-0.006417389	0.0283262	0.003985146	-0.118010188	-0.055777316	-0.015194687
8/1/2014	38.81255	0.013333413	0	0.069690025	-0.011428696	-0.000291905	0.03743368	0.036963644
9/1/2014	37.666203	-0.029980428	0.010026461	-0.012258668	-0.064078857	-0.117433796	-0.007543735	-0.015635436
10/1/2014	39.23465	0.040797065	-0.032173337	0.069488813	0.072662543	0.186158259	0.031486272	0.022936399
11/1/2014	40.475365	0.031133233	-0.031340335	0.09640405	0.026428359	0.004638781	0.017379601	0.024237474
12/1/2014	37.030998	-0.088938172	-0.028890843	-0.070279209	0.049265713	0.010829715	0.066477476	-0.004197385
1/1/2015	36.702663	-0.008906032	0.015303224	0.059611491	0.058478198	-0.074586256	-0.000129919	-0.031532779
2/1/2015	34.685776	-0.056519624	0.043706445	0.092077102	0.101766576	0.152777625	-0.064460726	0.053438876
3/1/2015	30.355043	-0.133367024	-0.018800259	-0.027935582	0.045312393	0.014693692	-0.008286693	-0.017549197
4/1/2015	31.529776	0.037969704	-0.01415627	0.005769732	-0.061646604	-0.009678683	0.011364534	0.008484722
5/1/2015	29.368273	-0.071017427	-0.009780885	0.040172924	0.028412237	0.003982009	-0.016315448	0.01043673
6/1/2015	26.253988	-0.112097041	-0.022041087	-0.03376979	-0.052956233	-0.029118173	-0.044049855	-0.021235559
7/1/2015	23.24008	-0.121939527	0.18391803	-0.033480898	0.04042806	-0.001540222	0.0697402	0.019549683
8/1/2015	22.251133	-0.043485446	0.018999638	-0.071587231	0.037556879	-0.007736167	-0.027573409	-0.064624731
9/1/2015	22.815954	0.025067099	-0.046861383	-0.018959507	0.023570922	-0.065945949	0.018254345	-0.026798731
10/1/2015	21.091766	-0.078577301	0.155539757	0.080112519	0.048366523	0.041831121	0.014808634	0.079719379
11/1/2015	22.107386	0.047029033	0.043752347	-0.010092653	0.016807118	0.024439605	-0.058518172	0.000504742
12/1/2015	23.386749	0.056257819	0.021686159	-0.112518832	-0.00876853	-0.08163468	0.013428105	-0.017685659
1/1/2016	17.273497	-0.302996218	-0.021214905	-0.078223553	-0.043360576	-0.084881608	0.064824876	-0.052067617
2/1/2016	21.159441	0.202912827	-0.0627392	-0.00669983	0.0997848	0.053889285	-0.031672503	-0.004136906
3/1/2016	22.797729	0.074574737	0.065427554	0.125157661	0.028349567	0.024325562	0.071734885	0.06390499
4/1/2016	26.581484	0.153553957	-0.072272675	-0.150731294	0.02541887	-0.075272242	-0.039751319	0.002695762
5/1/2016	22.060013	-0.18644828	0.059805129	0.063244269	0.010699175	0.027323785	0.01085441	0.015208367
6/1/2016	22.124142	0.002902807	-0.061119153	-0.0375264	-0.049074028	-0.004133087	0.075678867	0.000910506
7/1/2016	25.346104	0.135955619	0.105087403	0.086235342	-0.002611455	0.135604929	0.010889578	0.034990433
8/1/2016	24.05732	-0.052185714	-0.002265849	0.017973961	-0.123495999	0.086088281	-0.050739825	-0.001219987
9/1/2016	24.271074	0.008845955	0.01326151	0.068850678	0.012182507	-0.016136784	0.010865356	-0.001235213
10/1/2016	21.356104	-0.12794767	0.009284048	0.004325015	-0.040909027	-0.017664271	0.01244423	-0.019616837
11/1/2016	28.856638	0.301002453	-0.034361405	-0.026958767	0.040073563	0.148108262	-0.025727056	0.033603545
12/1/2016	28.08	-0.027282474	0.018015246	0.051961825	0.016988186	0.028963126	0.026017384	0.018037111
1/1/2017	36.450001	0.260883907	0.031839757	0.046641712	0.013872111	0.014861852	0.023208989	0.017726315
2/1/2017	34.59	-0.052376863	0.032620231	0.121229169	-0.017989038	0.040314694	0.017672147	0.036523001
3/1/2017	34.400002	-0.005508	0.007684078	0.051867607	0.021225287	0.026841103	-0.000902183	-0.000389273
4/1/2017	33.73	-0.019668973	0.088099742	-6.97027E-05	-0.013826979	0.068317391	0.00796546	0.009050132
5/1/2017	32.939999	-0.023699955	0.062987818	0.061488192	0.112216566	0.0290447	0.042231233	0.011509759
6/1/2017	32.650002	-0.008842777	-0.059934999	-0.054796572	0.018495541	0.036270822	-0.04325434	0.004802226
7/1/2017	36.400002	0.108723913	0.023674078	0.032180261	0.041181254	0.027800531	0.007151595	0.019164018
8/1/2017	43.880001	0.186889829	0.009444797	0.097733907	-0.019147634	0.038146557	0.020391816	0.000546284
9/1/2017	46.619999	0.060570954	0.020838882	-0.058215715	0.010489572	0.121605758	-0.014182302	0.019119039
10/1/2017	47.779999	0.024577509	0.05825261	0.092403878	0.05744826	-0.078990285	0.053280052	0.02194556
11/1/2017	42.299999	-0.121820059	0.004680912	0.016486687	0.057121953	0.017966188	0.036187151	0.003713141
12/1/2017	53.869999	0.241786656	0.024171725	-0.011774791	-0.015630265	-0.044130157	-0.027964775	0.033766015
1/1/2018	52.02	-0.034945458	0.11159669	-0.010693473	0.067016515	0.039056666	-0.058683265	0.054657399
2/1/2018	44.970001	-0.145632637	-0.057351472	0.061892173	-0.078742176	-0.086970075	-0.031495563	-0.039726108
3/1/2018	44.959999	-0.00022244	-0.068305747	-0.055735076	0.0195713	-0.004765425	-0.093920608	-0.027252497
4/1/2018	51.200001	0.129966368	-0.014113631	-0.015133669	-0.003130904	-0.075586213	-0.001649225	0.002715086
5/1/2018	48.07	-0.06308127	0.064389196	0.122893282	-0.060095534	0.067707536	-0.036256238	0.021378191
6/1/2018	46.880001	-0.025067115	0.027866455	-0.00561427	-0.037317796	-0.006142484	0.073330067	0.004830749
7/1/2018	43.27	-0.080131612	0.087165223	0.027598914	0.048905345	0.141458235	0.050478792	0.035387951
8/1/2018	44.669998	0.031842536	0.000763663	0.179172357	0.008521848	0.003090296	-0.013194962	0.029814315
9/1/2018	40.400002	-0.100472256	-0.020501096	-0.004836665	-0.000979527	0.045052207	-0.006947889	0.004285093
10/1/2018	34.990002	-0.143767471	-0.102899168	-0.030951643	-0.110418875	-0.227093407	0.027682832	-0.071929346
11/1/2018	31.809999	-0.095281689	0.016267891	-0.203395539	0.102876554	0.059168624	0.042221156	0.017701752
12/1/2018	28.82	-0.098711084	-0.054306939	-0.048110855	-0.073399222	-0.083111766	0.023480489	-0.047137951
12/7/2018	28.82	0	0	0	0	0	0.011147998	0

Then after regression we get the following betas:

For First 30 months
Company	Beta
1	0.6203
2	0.8168
3	1.4091
4	0.3297
5	1.1642
6	0.2102
For Last 30 months
Company	Beta
1	1.9944
2	1.4553
3	0.6336
4	1.1791
5	2.0042
6	-0.0233

After regression we find that there is no connection between initial and final betas.

This is the regression output.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.418118819
R Square	0.174823347
Adjusted R Square	-0.100235538
Standard Error	0.815328585
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.422512042	0.422512042	0.635585166	0.483580805
Residual	3	1.994282106	0.664760702
Total	4	2.416794148
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	0.556326592	0.718371622	0.774427294	0.495111817	-1.729852522	2.842505705	-1.729852522	2.842505705
0.6203	0.627803319	0.787474919	0.797235954	0.483580805	-1.878293329	3.133899966	-1.878293329	3.133899966

By looking at this out we get that p value is more than 0.05 (0.49 approx). So there no significant relationship between initial and final betas for six firms.

Similarly, we get Alphas from the trend line. In the trend line the alphas are intercept of liner equation.

So, for six firms:

For First 30 months
Company	Alpha
1	-0.0098
2	0.0016
3	0.0073
4	0.0155
5	-0.0098
6	0.0035
For Last 30 months
Company	Alpha
1	-0.0058
2	0.0004
3	0.0152
4	-0.0083
5	0.0023
6	0.0054

After regression we find that there is no connection between initial and final betas.

This is the regression output.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.239405316
R Square	0.057314905
Adjusted R Square	-0.25691346
Standard Error	0.009538432
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.6595E-05	1.6595E-05	0.18239889	0.698117037
Residual	3	0.000272945	9.09817E-05
Total	4	0.00028954
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	0.00380109	0.004659903	0.815701506	0.474412779	-0.011028802	0.018631	-0.011028802	0.018630982
-0.0098	-0.221295608	0.518157392	-0.427081831	0.698117037	-1.870303685	1.427712	-1.870303685	1.42771247

Conclusion

There is no significant relationship between initial betas and alphas with their final values for all the six firms chosen.