CONNECT WITH LEARNSMART FOR BODIE: ESSE
CONNECT WITH LEARNSMART FOR BODIE: ESSE
11th Edition
ISBN: 2819440196246
Author: Bodie
Publisher: MCG
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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.

Expert Solution & Answer
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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.

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Chapter 7 Solutions

CONNECT WITH LEARNSMART FOR BODIE: ESSE

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