Homework Sourse13 Segregate the return data in the above table into bull an
13. Segregate the return data in the above table into bull and bear markets, using the S&P 500 index as the proxy for the market. a) What was the average return for the two companies during these two types of markets? What was the return for the S&P 500 index during those times? b) Using the average return measures in a), compute the beta for Yahoo and Google. c) According to these beta estimates, which company is riskier?
Month
Monthly Returns (%)
Month
Monthly Returns (%)
Month
Monthly Returns (%)
Ended
Yahoo
S&P500
Ended
Yahoo
S&P500
Ended
Yahoo
S&P500
Dec-07
-13.241
-0.219
-0.692
Dec-06
-5.442
-5.018
1.403
Dec-05
-2.610
2.457
0.036
Nov-07
-13.794
-1.980
-4.182
Nov-06
2.544
1.767
1.899
Nov-05
8.818
8.806
3.778
Oct-07
15.861
24.632
1.590
Oct-06
4.193
18.534
3.257
Oct-05
9.249
17.595
-1.668
Sep-07
18.093
10.096
3.736
Sep-06
-12.314
6.174
2.575
Sep-05
1.561
10.650
0.810
Aug-07
-2.237
1.029
1.497
Aug-06
6.227
-2.087
2.376
Aug-05
-0.060
-0.612
-0.912
Jul-07
-14.302
-2.430
-3.097
Jul-06
-17.758
-7.805
0.616
Jul-05
-3.781
-2.172
3.717
Jun-07
-5.470
4.979
-1.660
Jun-06
4.463
12.778
0.133
Jun-05
-6.855
6.088
0.143
May-07
2.354
5.628
3.486
May-06
-3.630
-11.035
-2.875
May-05
7.826
26.032
3.179
Apr-07
-10.387
2.885
4.428
Apr-06
1.612
7.164
1.342
Apr-05
1.770
21.877
-1.896
Mar-07
1.393
1.938
1.116
Mar-06
0.624
7.551
1.244
Mar-05
5.051
-3.979
-1.769
Feb-07
9.007
-10.379
-1.950
Feb-06
-6.735
-16.188
0.271
Feb-05
-8.350
-3.900
2.103
Jan-07
10.846
8.908
1.511
Jan-06
-12.264
4.291
2.648
Jan-05
-6.555
1.468
-2.437
| Month | Monthly Returns (%) | Month | Monthly Returns (%) | Month | Monthly Returns (%) | ||||||
| Ended | Yahoo | | S&P500 | Ended | Yahoo | | S&P500 | Ended | Yahoo | | S&P500 |
| Dec-07 | -13.241 | -0.219 | -0.692 | Dec-06 | -5.442 | -5.018 | 1.403 | Dec-05 | -2.610 | 2.457 | 0.036 |
| Nov-07 | -13.794 | -1.980 | -4.182 | Nov-06 | 2.544 | 1.767 | 1.899 | Nov-05 | 8.818 | 8.806 | 3.778 |
| Oct-07 | 15.861 | 24.632 | 1.590 | Oct-06 | 4.193 | 18.534 | 3.257 | Oct-05 | 9.249 | 17.595 | -1.668 |
| Sep-07 | 18.093 | 10.096 | 3.736 | Sep-06 | -12.314 | 6.174 | 2.575 | Sep-05 | 1.561 | 10.650 | 0.810 |
| Aug-07 | -2.237 | 1.029 | 1.497 | Aug-06 | 6.227 | -2.087 | 2.376 | Aug-05 | -0.060 | -0.612 | -0.912 |
| Jul-07 | -14.302 | -2.430 | -3.097 | Jul-06 | -17.758 | -7.805 | 0.616 | Jul-05 | -3.781 | -2.172 | 3.717 |
| Jun-07 | -5.470 | 4.979 | -1.660 | Jun-06 | 4.463 | 12.778 | 0.133 | Jun-05 | -6.855 | 6.088 | 0.143 |
| May-07 | 2.354 | 5.628 | 3.486 | May-06 | -3.630 | -11.035 | -2.875 | May-05 | 7.826 | 26.032 | 3.179 |
| Apr-07 | -10.387 | 2.885 | 4.428 | Apr-06 | 1.612 | 7.164 | 1.342 | Apr-05 | 1.770 | 21.877 | -1.896 |
| Mar-07 | 1.393 | 1.938 | 1.116 | Mar-06 | 0.624 | 7.551 | 1.244 | Mar-05 | 5.051 | -3.979 | -1.769 |
| Feb-07 | 9.007 | -10.379 | -1.950 | Feb-06 | -6.735 | -16.188 | 0.271 | Feb-05 | -8.350 | -3.900 | 2.103 |
| Jan-07 | 10.846 | 8.908 | 1.511 | Jan-06 | -12.264 | 4.291 | 2.648 | Jan-05 | -6.555 | 1.468 | -2.437 |
Solution
Answer
Answer (b)
Figures in $
Number
Month
Monthly Returns (%)
Ended
Yahoo
S&P500
Y
X
X*Y
X*X
dependent
Independent
1
Dec-07
-13.241
-0.692
9.162772
0.478864
2
Nov-07
-13.794
-4.182
57.68651
17.48912
3
Oct-07
15.861
1.59
25.21899
2.5281
4
Sep-07
18.093
3.736
67.59545
13.9577
5
Aug-07
-2.237
1.497
-3.34879
2.241009
6
Jul-07
-14.302
-3.097
44.29329
9.591409
7
Jun-07
-5.47
-1.66
9.0802
2.7556
8
May-07
2.354
3.486
8.206044
12.1522
9
Apr-07
-10.387
4.428
-45.9936
19.60718
10
Mar-07
1.393
1.116
1.554588
1.245456
11
Feb-07
9.007
-1.95
-17.5637
3.8025
12
Jan-07
10.846
1.511
16.38831
2.283121
13
Dec-06
-5.442
1.403
-7.63513
1.968409
14
Nov-06
2.544
1.899
4.831056
3.606201
15
Oct-06
4.193
3.257
13.6566
10.60805
16
Sep-06
-12.314
2.575
-31.7086
6.630625
17
Aug-06
6.227
2.376
14.79535
5.645376
18
Jul-06
-17.758
0.616
-10.9389
0.379456
19
Jun-06
4.463
0.133
0.593579
0.017689
20
May-06
-3.63
-2.875
10.43625
8.265625
21
Apr-06
1.612
1.342
2.163304
1.800964
22
Mar-06
0.624
1.244
0.776256
1.547536
23
Feb-06
-6.735
0.271
-1.82519
0.073441
24
Jan-06
-12.264
2.648
-32.4751
7.011904
25
Dec-05
-2.61
0.036
-0.09396
0.001296
26
Nov-05
8.818
3.778
33.3144
14.27328
27
Oct-05
9.249
-1.668
-15.4273
2.782224
28
Sep-05
1.561
0.81
1.26441
0.6561
29
Aug-05
-0.06
-0.912
0.05472
0.831744
30
Jul-05
-3.781
3.717
-14.054
13.81609
31
Jun-05
-6.855
0.143
-0.98027
0.020449
32
May-05
7.826
3.179
24.87885
10.10604
33
Apr-05
1.77
-1.896
-3.35592
3.594816
34
Mar-05
5.051
-1.769
-8.93522
3.129361
35
Feb-05
-8.35
2.103
-17.5601
4.422609
36
Jan-05
-6.555
-2.437
15.97454
5.938969
Sum Total
-34.293
25.756
150.0298
195.2605
Beta of yahoo = N*(SUM of XY) – (SUM of X)(SUM of Y) / N*( SUM of X2) – ( SUM of X)2
= 36*(150.0298) – (25.756)( -34.293) / 36*(195.2605)- (25.756)2
= 5401.073 – (-883.251) / 7029.379 - 663.3715
= 6284.324 / 6366.007
Beta of Yahoo = 0.987
Number
Month
Monthly Returns (%)
Ended
S&P500
Y
X
dependent
Independent
X*Y
X*X
1
Dec-07
-0.219
-0.692
0.151548
0.478864
2
Nov-07
-1.98
-4.182
8.28036
17.48912
3
Oct-07
24.632
1.59
39.16488
2.5281
4
Sep-07
10.096
3.736
37.71866
13.9577
5
Aug-07
1.029
1.497
1.540413
2.241009
6
Jul-07
-2.43
-3.097
7.52571
9.591409
7
Jun-07
4.979
-1.66
-8.26514
2.7556
8
May-07
5.628
3.486
19.61921
12.1522
9
Apr-07
2.885
4.428
12.77478
19.60718
10
Mar-07
1.938
1.116
2.162808
1.245456
11
Feb-07
-10.379
-1.95
20.23905
3.8025
12
Jan-07
8.908
1.511
13.45999
2.283121
13
Dec-06
-5.018
1.403
-7.04025
1.968409
14
Nov-06
1.767
1.899
3.355533
3.606201
15
Oct-06
18.534
3.257
60.36524
10.60805
16
Sep-06
6.174
2.575
15.89805
6.630625
17
Aug-06
-2.087
2.376
-4.95871
5.645376
18
Jul-06
-7.805
0.616
-4.80788
0.379456
19
Jun-06
12.778
0.133
1.699474
0.017689
20
May-06
-11.035
-2.875
31.72563
8.265625
21
Apr-06
7.164
1.342
9.614088
1.800964
22
Mar-06
7.551
1.244
9.393444
1.547536
23
Feb-06
-16.188
0.271
-4.38695
0.073441
24
Jan-06
4.291
2.648
11.36257
7.011904
25
Dec-05
2.457
0.036
0.088452
0.001296
26
Nov-05
8.806
3.778
33.26907
14.27328
27
Oct-05
17.595
-1.668
-29.3485
2.782224
28
Sep-05
10.65
0.81
8.6265
0.6561
29
Aug-05
-0.612
-0.912
0.558144
0.831744
30
Jul-05
-2.172
3.717
-8.07332
13.81609
31
Jun-05
6.088
0.143
0.870584
0.020449
32
May-05
26.032
3.179
82.75573
10.10604
33
Apr-05
21.877
-1.896
-41.4788
3.594816
34
Mar-05
-3.979
-1.769
7.038851
3.129361
35
Feb-05
-3.9
2.103
-8.2017
4.422609
36
Jan-05
1.468
-2.437
-3.57752
5.938969
Sum total
145.523
25.756
319.12
195.2605
Beta of Google = N*(SUM of XY) – (SUM of X)(SUM of Y) / N*( SUM of X2) – ( SUM of X)2
= 36 * (319.12) – (25.756)( 145.523) / 36 * (195.2605) – (25.756)2
= 11488.32 - 3748.09 / 7029.379 - 663.3715
= 7740.23 / 6366.007
Beta of Google = 1.216
Answer (C)
Beta of the google is 1.216 which is greater than beta of Yahoo (0.987). So According to these beta estimates, Google is more riskier than yahoo.
| Figures in $ | |||||
| Number | Month | Monthly Returns (%) | |||
| Ended | Yahoo | S&P500 | |||
| Y | X | X*Y | X*X | ||
| dependent | Independent | ||||
| 1 | Dec-07 | -13.241 | -0.692 | 9.162772 | 0.478864 |
| 2 | Nov-07 | -13.794 | -4.182 | 57.68651 | 17.48912 |
| 3 | Oct-07 | 15.861 | 1.59 | 25.21899 | 2.5281 |
| 4 | Sep-07 | 18.093 | 3.736 | 67.59545 | 13.9577 |
| 5 | Aug-07 | -2.237 | 1.497 | -3.34879 | 2.241009 |
| 6 | Jul-07 | -14.302 | -3.097 | 44.29329 | 9.591409 |
| 7 | Jun-07 | -5.47 | -1.66 | 9.0802 | 2.7556 |
| 8 | May-07 | 2.354 | 3.486 | 8.206044 | 12.1522 |
| 9 | Apr-07 | -10.387 | 4.428 | -45.9936 | 19.60718 |
| 10 | Mar-07 | 1.393 | 1.116 | 1.554588 | 1.245456 |
| 11 | Feb-07 | 9.007 | -1.95 | -17.5637 | 3.8025 |
| 12 | Jan-07 | 10.846 | 1.511 | 16.38831 | 2.283121 |
| 13 | Dec-06 | -5.442 | 1.403 | -7.63513 | 1.968409 |
| 14 | Nov-06 | 2.544 | 1.899 | 4.831056 | 3.606201 |
| 15 | Oct-06 | 4.193 | 3.257 | 13.6566 | 10.60805 |
| 16 | Sep-06 | -12.314 | 2.575 | -31.7086 | 6.630625 |
| 17 | Aug-06 | 6.227 | 2.376 | 14.79535 | 5.645376 |
| 18 | Jul-06 | -17.758 | 0.616 | -10.9389 | 0.379456 |
| 19 | Jun-06 | 4.463 | 0.133 | 0.593579 | 0.017689 |
| 20 | May-06 | -3.63 | -2.875 | 10.43625 | 8.265625 |
| 21 | Apr-06 | 1.612 | 1.342 | 2.163304 | 1.800964 |
| 22 | Mar-06 | 0.624 | 1.244 | 0.776256 | 1.547536 |
| 23 | Feb-06 | -6.735 | 0.271 | -1.82519 | 0.073441 |
| 24 | Jan-06 | -12.264 | 2.648 | -32.4751 | 7.011904 |
| 25 | Dec-05 | -2.61 | 0.036 | -0.09396 | 0.001296 |
| 26 | Nov-05 | 8.818 | 3.778 | 33.3144 | 14.27328 |
| 27 | Oct-05 | 9.249 | -1.668 | -15.4273 | 2.782224 |
| 28 | Sep-05 | 1.561 | 0.81 | 1.26441 | 0.6561 |
| 29 | Aug-05 | -0.06 | -0.912 | 0.05472 | 0.831744 |
| 30 | Jul-05 | -3.781 | 3.717 | -14.054 | 13.81609 |
| 31 | Jun-05 | -6.855 | 0.143 | -0.98027 | 0.020449 |
| 32 | May-05 | 7.826 | 3.179 | 24.87885 | 10.10604 |
| 33 | Apr-05 | 1.77 | -1.896 | -3.35592 | 3.594816 |
| 34 | Mar-05 | 5.051 | -1.769 | -8.93522 | 3.129361 |
| 35 | Feb-05 | -8.35 | 2.103 | -17.5601 | 4.422609 |
| 36 | Jan-05 | -6.555 | -2.437 | 15.97454 | 5.938969 |
| Sum Total | -34.293 | 25.756 | 150.0298 | 195.2605 |
