Chapter 7, Problem 20PS

Summary Introduction

(a)

To determine:

The spreadsheet of the given data and estimate the index model for full five-year period and compare the betas of each firm

Introduction:

The net loss or the net gain on any investment over a certain time period which is expressed as the investment's initial cost percentage is the rate of return or ROR.

Answer to Problem 20PS

The beta is 1.81, 0.86 and 0.71 for Ford, GM and Toyota respectively.

Explanation of Solution

Given Information:

The data is available in the given website for GM, Ford, Toyota, S&P 500 and Treasury bills.

The excel snippet given here shows the calculation of betas of GM, Ford, Toyota and S&P 500.

Here the beta for each of the companies is calculated for the five year period. The beta is obtained as:

For Ford, it is obtained using the formula in Excel SLOPE (G4:G63, $J$4:$J$63)

For GM, it is obtained using the formula in Excel SLOPE (H4:H63, $J$4:$J$63)

For Toyota, it is obtained using the formula in Excel SLOPE (I4:I63, $J$4:$J$63)

	Rates of Return					Excess rates of return
Month	Ford	GM	Toyota	S&P	T-bills	Ford	GM	Toyota	S&P
Jan-04	-5.44	0.56	4.11	1.28	0.07	-5.51	0.49	4.04	1.21
Feb-04	-1.28	0.00	8.34	-1.38	0.06	-1.34	-0.06	8.28	-1.44
Mar-04	13.92	-3.19	-1.74	-1.98	0.09	13.83	-3.28	-1.83	-2.07
Apr-04	-3.34	0.00	-1.17	1.62	0.08	-3.42	-0.08	-1.25	1.54
May-04	5.36	-0.25	12.81	1.79	0.06	5.30	-0.31	12.75	1.73
Jun-04	-5.30	2.39	-1.99	-3.30	0.08	-5.38	2.31	-2.07	-3.38
Jul-04	-4.12	1.69	-1.01	0.15	0.1	-4.22	1.59	-1.11	0.05
Aug-04	-0.46	1.51	-2.97	0.89	0.11	-0.57	1.40	-3.08	0.78
Sep-04	-6.48	0.08	1.59	1.18	0.11	-6.59	-0.03	1.48	1.07
Oct-04	8.75	-1.17	-3.71	4.35	0.11	8.64	-1.28	-3.82	4.24
Nov-04	3.26	1.97	9.59	2.86	0.15	3.11	1.82	9.44	2.71
Dec-04	-9.33	-3.02	-4.50	-2.40	0.16	-9.49	-3.18	-4.66	-2.56
Jan-05	-3.97	-0.24	-0.53	1.93	0.16	-4.13	-0.40	-0.69	1.77
Feb-05	-10.38	-15.28	-3.74	-1.99	0.16	-10.54	-15.44	-3.90	-2.15
Mar-05	-18.74	-7.84	-2.25	-2.08	0.21	-18.95	-8.05	-2.46	-2.29
Apr-05	9.50	2.25	-1.37	3.01	0.21	9.29	2.04	-1.58	2.80
May-05	2.65	4.91	-0.31	-0.09	0.24	2.41	4.67	-0.55	-0.33
Jun-05	5.77	5.44	6.12	3.59	0.23	5.54	5.21	5.89	3.36
Jul-05	-7.12	-8.88	8.07	-1.17	0.24	-7.36	-9.12	7.83	-1.41
Aug-05	-1.15	-5.37	13.59	0.50	0.3	-1.45	-5.67	13.29	0.20
Sep-05	-14.54	-7.77	0.48	-2.65	0.29	-14.83	-8.06	0.19	-2.94
Oct-05	-2.24	-7.52	4.25	4.12	0.27	-2.51	-7.79	3.98	3.85
Nov-05	-5.08	-4.31	8.13	-0.50	0.31	-5.39	-4.62	7.82	-0.81
Dec-05	12.45	12.61	-0.87	2.09	0.32	12.13	12.29	-1.19	1.77
Jan-06	-7.14	-3.43	3.05	0.22	0.35	-7.49	-3.78	2.70	-0.13
Feb-06	-0.13	6.04	1.90	1.31	0.34	-0.47	5.70	1.56	0.97
Mar-06	-11.42	1.23	7.56	0.89	0.37	-11.79	0.86	7.19	0.52
Apr-06	3.04	6.39	-8.32	-3.37	0.36	2.68	6.03	-8.68	-3.73
May-06	-3.23	5.18	-2.60	-0.17	0.43	-3.66	4.75	-3.03	-0.60
Jun-06	-3.05	4.63	0.60	0.05	0.4	-3.45	4.23	0.20	-0.35
Jul-06	25.49	-1.41	2.97	1.78	0.4	25.09	-1.81	2.57	1.38
Aug-06	-3.35	6.11	0.52	2.28	0.42	-3.77	5.69	0.10	1.86
Sep-06	2.35	3.60	8.36	2.75	0.41	1.94	3.19	7.95	2.34
Oct-06	-1.81	0.61	1.74	1.58	0.41	-2.22	0.20	1.33	1.17
Nov-06	-7.63	0.52	11.88	0.35	0.42	-8.05	0.10	11.46	-0.07
Dec-06	8.26	6.70	-1.88	1.11	0.4	7.86	6.30	-2.28	0.71
Jan-07	-2.71	-0.16	1.38	-2.40	0.44	-3.15	-0.60	0.94	-2.84
Feb-07	-0.25	-0.73	-4.07	0.78	0.38	-0.63	-1.11	-4.45	0.40
Mar-07	1.90	-0.08	-5.26	3.99	0.43	1.47	-0.51	-5.69	3.56
Apr-07	3.73	1.87	-0.54	2.95	0.44	3.29	1.43	-0.98	2.51
May-07	12.95	-0.24	4.24	-1.87	0.41	12.54	-0.65	3.83	-2.28
Jun-07	-9.66	-6.32	-4.17	-3.53	0.4	-10.06	-6.72	-4.57	-3.93
Jul-07	-8.23	-4.78	-4.10	0.88	0.4	-8.63	-5.18	-4.50	0.48
Aug-07	8.71	8.79	1.02	3.46	0.42	8.29	8.37	0.60	3.04
Sep-07	4.48	-0.25	-2.07	1.03	0.32	4.16	-0.57	-2.39	0.71
Oct-07	-15.33	-6.86	-1.74	-4.19	0.32	-15.65	-7.18	-2.06	-4.51
Nov-07	-10.39	-5.59	-5.58	-1.47	0.34	-10.73	-5.93	-5.92	-1.81
Dec-07	-1.34	11.18	2.03	-6.31	0.27	-1.61	10.91	1.76	-6.58
Jan-08	-1.66	-3.13	0.21	-2.79	0.21	-1.87	-3.34	0.00	-3.00
Feb-08	-12.40	-9.60	-7.06	-1.03	0.13	-12.53	-9.73	-7.19	-1.16
Mar-08	44.41	8.78	0.60	4.60	0.17	44.24	8.61	0.43	4.43
Apr-08	-17.68	-6.48	0.54	1.34	0.17	-17.85	-6.65	0.37	1.17
May-08	-29.26	-15.56	-7.89	-8.52	0.17	-29.43	-15.73	-8.06	-8.69
Jun-08	-0.21	-11.01	-8.46	-1.07	0.17	-0.38	-11.18	-8.63	-1.24
Jul-08	-7.08	-4.92	4.11	1.40	0.15	-7.23	-5.07	3.96	1.25
Aug-08	16.59	-29.61	-4.23	-9.54	0.12	16.47	-29.73	-4.35	-9.66
Sep-08	-57.88	-13.77	-11.32	-16.67	0.15	-58.03	-13.92	-11.47	-16.82
Oct-08	22.83	-26.04	-17.07	-7.04	0.08	22.75	-26.12	-17.15	-7.12
Nov-08	-14.87	-25.44	3.71	0.97	0.02	-14.89	-25.46	3.69	0.95
Dec-08	-18.34	23.02	-2.95	-8.31	0.09	-18.43	22.93	-3.04	-8.40
						Ford	GM	Toyota	S&P
					Beta for 5 years	1.81	0.86	0.71	1.00

Summary Introduction

(b)

Requirement 2 To Determine:

The betas for the firms for the first two years and for the last two years and to see how stable the betas obtained for these shorter subperiods are.

Introduction:

The net loss or the net gain on any investment over a certain time period which is expressed as the investment's initial cost percentage is the rate of return or ROR.

Answer to Problem 20PS

The betas for first 2 years is 2.01, 1.05 and 0.47 for Ford, GM and Toyota respectively.

Explanation of Solution

Given Information:

The data is available in the given website for GM, Ford, Toyota, S&P 500 and Treasury bills.

The excel snippet given here shows the calculation of betas of GM, Ford, Toyota and S&P 500.

Here the beta for each of the companies is calculated for the first 2 year period. The beta is obtained as:

For Ford, it is obtained using the formula in excel SLOPE (G4:G27, $J$4:$J$27)

For GM, it is obtained using the formula in excel SLOPE (H4:H27, $J$4:$J$27)

For Toyota, it is obtained using the formula in excel SLOPE (I4:I27, $J$4:$J$27)

For the last two year period, the beta of the stocks is calculated as:

For Ford, it is obtained using the formula in excel SLOPE (G40:G63, $J$40:$J$63)

For GM, it is obtained using the formula in excel SLOPE (H40:H63, $J$40:$J$63)

For Toyota, it is obtained using the formula in excel SLOPE (I40:I63, $J$40:$J$63)

	Rates of Return					Excess rates of return
Month	Ford	GM	Toyota	S&P	T-bills	Ford	GM	Toyota	S&P
Jan-04	-5.44	0.56	4.11	1.28	0.07	-5.51	0.49	4.04	1.21
Feb-04	-1.28	0.00	8.34	-1.38	0.06	-1.34	-0.06	8.28	-1.44
Mar-04	13.92	-3.19	-1.74	-1.98	0.09	13.83	-3.28	-1.83	-2.07
Apr-04	-3.34	0.00	-1.17	1.62	0.08	-3.42	-0.08	-1.25	1.54
May-04	5.36	-0.25	12.81	1.79	0.06	5.30	-0.31	12.75	1.73
Jun-04	-5.30	2.39	-1.99	-3.30	0.08	-5.38	2.31	-2.07	-3.38
Jul-04	-4.12	1.69	-1.01	0.15	0.1	-4.22	1.59	-1.11	0.05
Aug-04	-0.46	1.51	-2.97	0.89	0.11	-0.57	1.40	-3.08	0.78
Sep-04	-6.48	0.08	1.59	1.18	0.11	-6.59	-0.03	1.48	1.07
Oct-04	8.75	-1.17	-3.71	4.35	0.11	8.64	-1.28	-3.82	4.24
Nov-04	3.26	1.97	9.59	2.86	0.15	3.11	1.82	9.44	2.71
Dec-04	-9.33	-3.02	-4.50	-2.40	0.16	-9.49	-3.18	-4.66	-2.56
Jan-05	-3.97	-0.24	-0.53	1.93	0.16	-4.13	-0.40	-0.69	1.77
Feb-05	-10.38	-15.28	-3.74	-1.99	0.16	-10.54	-15.44	-3.90	-2.15
Mar-05	-18.74	-7.84	-2.25	-2.08	0.21	-18.95	-8.05	-2.46	-2.29
Apr-05	9.50	2.25	-1.37	3.01	0.21	9.29	2.04	-1.58	2.80
May-05	2.65	4.91	-0.31	-0.09	0.24	2.41	4.67	-0.55	-0.33
Jun-05	5.77	5.44	6.12	3.59	0.23	5.54	5.21	5.89	3.36
Jul-05	-7.12	-8.88	8.07	-1.17	0.24	-7.36	-9.12	7.83	-1.41
Aug-05	-1.15	-5.37	13.59	0.50	0.3	-1.45	-5.67	13.29	0.20
Sep-05	-14.54	-7.77	0.48	-2.65	0.29	-14.83	-8.06	0.19	-2.94
Oct-05	-2.24	-7.52	4.25	4.12	0.27	-2.51	-7.79	3.98	3.85
Nov-05	-5.08	-4.31	8.13	-0.50	0.31	-5.39	-4.62	7.82	-0.81
Dec-05	12.45	12.61	-0.87	2.09	0.32	12.13	12.29	-1.19	1.77
Jan-06	-7.14	-3.43	3.05	0.22	0.35	-7.49	-3.78	2.70	-0.13
Feb-06	-0.13	6.04	1.90	1.31	0.34	-0.47	5.70	1.56	0.97
Mar-06	-11.42	1.23	7.56	0.89	0.37	-11.79	0.86	7.19	0.52
Apr-06	3.04	6.39	-8.32	-3.37	0.36	2.68	6.03	-8.68	-3.73
May-06	-3.23	5.18	-2.60	-0.17	0.43	-3.66	4.75	-3.03	-0.60
Jun-06	-3.05	4.63	0.60	0.05	0.4	-3.45	4.23	0.20	-0.35
Jul-06	25.49	-1.41	2.97	1.78	0.4	25.09	-1.81	2.57	1.38
Aug-06	-3.35	6.11	0.52	2.28	0.42	-3.77	5.69	0.10	1.86
Sep-06	2.35	3.60	8.36	2.75	0.41	1.94	3.19	7.95	2.34
Oct-06	-1.81	0.61	1.74	1.58	0.41	-2.22	0.20	1.33	1.17
Nov-06	-7.63	0.52	11.88	0.35	0.42	-8.05	0.10	11.46	-0.07
Dec-06	8.26	6.70	-1.88	1.11	0.4	7.86	6.30	-2.28	0.71
Jan-07	-2.71	-0.16	1.38	-2.40	0.44	-3.15	-0.60	0.94	-2.84
Feb-07	-0.25	-0.73	-4.07	0.78	0.38	-0.63	-1.11	-4.45	0.40
Mar-07	1.90	-0.08	-5.26	3.99	0.43	1.47	-0.51	-5.69	3.56
Apr-07	3.73	1.87	-0.54	2.95	0.44	3.29	1.43	-0.98	2.51
May-07	12.95	-0.24	4.24	-1.87	0.41	12.54	-0.65	3.83	-2.28
Jun-07	-9.66	-6.32	-4.17	-3.53	0.4	-10.06	-6.72	-4.57	-3.93
Jul-07	-8.23	-4.78	-4.10	0.88	0.4	-8.63	-5.18	-4.50	0.48
Aug-07	8.71	8.79	1.02	3.46	0.42	8.29	8.37	0.60	3.04
Sep-07	4.48	-0.25	-2.07	1.03	0.32	4.16	-0.57	-2.39	0.71
Oct-07	-15.33	-6.86	-1.74	-4.19	0.32	-15.65	-7.18	-2.06	-4.51
Nov-07	-10.39	-5.59	-5.58	-1.47	0.34	-10.73	-5.93	-5.92	-1.81
Dec-07	-1.34	11.18	2.03	-6.31	0.27	-1.61	10.91	1.76	-6.58
Jan-08	-1.66	-3.13	0.21	-2.79	0.21	-1.87	-3.34	0.00	-3.00
Feb-08	-12.40	-9.60	-7.06	-1.03	0.13	-12.53	-9.73	-7.19	-1.16
Mar-08	44.41	8.78	0.60	4.60	0.17	44.24	8.61	0.43	4.43
Apr-08	-17.68	-6.48	0.54	1.34	0.17	-17.85	-6.65	0.37	1.17
May-08	-29.26	-15.56	-7.89	-8.52	0.17	-29.43	-15.73	-8.06	-8.69
Jun-08	-0.21	-11.01	-8.46	-1.07	0.17	-0.38	-11.18	-8.63	-1.24
Jul-08	-7.08	-4.92	4.11	1.40	0.15	-7.23	-5.07	3.96	1.25
Aug-08	16.59	-29.61	-4.23	-9.54	0.12	16.47	-29.73	-4.35	-9.66
Sep-08	-57.88	-13.77	-11.32	-16.67	0.15	-58.03	-13.92	-11.47	-16.82
Oct-08	22.83	-26.04	-17.07	-7.04	0.08	22.75	-26.12	-17.15	-7.12
Nov-08	-14.87	-25.44	3.71	0.97	0.02	-14.89	-25.46	3.69	0.95
Dec-08	-18.34	23.02	-2.95	-8.31	0.09	-18.43	22.93	-3.04	-8.40

	Ford	GM	Toyota	S&P
Beta for 5 years	1.81	0.86	0.71	1.00
Beta for frst 2 years	2.01	1.05	0.47
Beta for last 2 years	1.97	0.69	0.49
SE of residual	12.01	8.34	5.14
SE beta 5 years	0.42	0.29	0.18
Intercept 5 years	-0.93	-1.44	0.45
Intercept 2 years	-2.37	-1.82	1.8
Intercept last 2 years	0.81	-3.41	-1.91

It is clear from the above table that there is a deviation in the sub-period approximation from the overall estimate. This deviation is more than 2 standard deviations. It is clearly evident in the case of Toyota where for the first two years; the intercept shows a positive value of 1.8 while for the last two years it is a negative value.

The results of Toyota are surprising as the negative performance is beyond the expectation from the index. This shows that 0.5 beta is more trustworthy.

The explanation of the behavior for GM and Ford are also on the same lines.