Use the uploaded price data to answer the questions that follow. Assume that the S&P 500...

Use the uploaded price data to answer the questions that follow. Assume that the S&P 500 is the proxy for the market portfolio. • A: Price data for the American Funds Growth Fund of America (ticker symbol AGTHX) and S&P 500 is given in the Excel Upload file. Each month, calculate the excess returns for both AGTHX and the S&P 500.

• B: Using the excess returns, estimate the fund’s alpha and beta (assume that the CAPM is the appropriate benchmark model). What is the 95% confidence interval for beta?

• C: Does AGTHX significantly outperform, significantly underperform, or perform as expected (again using CAPM as the benchmark model)? Why?

	AGTHX	S&P 500	Risk-free rate
Month	Price	Price
1	22.147606	1400.380005	0.01%
2	20.705042	1280	0.00%
3	19.993551	1267.380005	0.00%
4	19.980497	1282.829956	0.00%
5	17.591454	1166.359985	0.00%
6	14.510504	968.75	0.00%
7	13.309449	896.23999	0.00%
8	13.368198	903.25	0.00%
9	12.783327	825.880005	0.00%
10	11.957958	735.090027	0.00%
11	12.981416	797.869995	0.00%
12	14.242583	872.809998	0.00%
13	15.180202	919.140015	0.00%
14	15.15379	919.320007	0.00%
15	16.131027	987.47998	0.00%
16	16.461176	1020.619995	0.00%
17	17.180901	1057.079956	0.00%
18	16.778114	1036.189941	0.00%
19	17.709133	1095.630005	0.00%
20	18.045885	1115.099976	0.00%
21	17.382166	1073.869995	0.00%
22	17.901236	1104.48999	0.00%
23	18.946026	1169.430054	0.00%
24	19.072468	1186.689941	0.00%
25	17.521915	1089.410034	0.00%
26	16.730003	1030.709961	0.00%
27	17.768139	1101.599976	0.00%
28	16.989536	1049.329956	0.00%
29	18.520124	1141.199951	0.00%
30	19.298727	1183.26001	0.00%
31	19.205561	1180.550049	0.00%
32	20.257013	1257.640015	0.00%
33	20.770506	1286.119995	0.00%
34	21.468224	1327.219971	0.00%
35	21.501766	1325.829956	0.00%
36	22.092144	1363.609985	0.00%
37	21.716448	1345.199951	0.01%
38	21.354174	1320.640015	0.01%
39	21.052277	1292.280029	0.01%
40	19.609879	1218.890015	0.01%
41	17.892424	1131.420044	0.01%
42	19.764179	1253.300049	0.00%
43	19.656843	1246.959961	0.00%
44	19.274439	1257.599976	0.01%
45	20.819939	1312.410034	0.00%
46	21.739561	1365.680054	0.00%
47	22.260225	1408.469971	0.00%
48	22.219656	1397.910034	0.00%
49	20.684702	1310.329956	0.00%
50	21.327084	1362.160034	0.00%
51	21.509653	1379.319946	0.00%
52	22.179085	1406.579956	0.00%
53	22.895847	1440.670044	0.01%
54	22.611847	1412.160034	0.00%
55	23.08518	1416.180054	0.00%
56	23.22718	1426.189941	0.00%
57	24.466576	1498.109985	0.00%
58	24.602913	1514.680054	0.01%
59	25.420967	1569.189941	0.01%
60	25.85726	1597.569946	0.01%
61	26.59351	1630.73999	0.01%
62	26.218565	1606.280029	0.01%
63	27.677425	1685.72998	0.01%
64	27.22068	1632.969971	0.01%
65	28.638636	1681.550049	0.01%
66	29.729378	1756.540039	0.01%
67	30.465618	1805.810059	0.01%
68	29.313528	1848.359985	0.01%
69	30.721369	1782.589966	0.01%
70	32.347878	1859.449951	0.01%
71	31.654972	1872.339966	0.00%
72	31.31946	1883.949951	0.00%
73	32.420818	1923.569946	0.01%
74	33.223133	1960.22998	0.00%
75	32.66151	1930.670044	0.00%
76	34.061916	2003.369995	0.01%
77	33.369007	1972.290039	0.01%
78	34.018154	2018.050049	0.01%
79	34.579773	2067.560059	0.01%
80	31.129822	2058.899902	0.00%
81	33.938644	1994.98999	0.01%
82	35.813839	2104.5	0.02%
83	35.508015	2067.889893	0.01%
84	36.07943	2085.51001	0.00%
85	36.594501	2107.389893	0.00%
86	35.998943	2063.110107	0.03%
87	36.843987	2103.840088	0.08%
88	34.856125	1972.180054	0.15%
89	33.58453	1920.030029	0.13%
90	36.361111	2079.360107	0.15%
91	36.747417	2080.409912	0.17%
92	33.230415	2043.939941	0.18%
93	33.495281	1940.23999	0.18%
94	33.144459	1932.22998	0.17%
95	35.293278	2059.73999	0.13%
96	35.880913	2065.300049	0.21%
97	36.635193	2096.949951	0.27%
98	36.310677	2098.860107	0.34%
99	37.89817	2173.600098	0.32%
100	38.126209	2170.949951	0.32%
101	38.661224	2168.27002	0.42%
102	37.950798	2126.149902	0.40%
103	39.055901	2198.810059	0.40%
104	36.872002	2238.830078	0.41%
105	41.057636	2278.870117	0.44%
106	42.029194	2363.639893	0.43%
107	42.458923	2362.719971	0.38%
108	43.290348	2384.199951	0.44%
109	44.252563	2411.800049	0.40%
110	44.121777	2423.409912	0.42%
111	45.588455	2470.300049	0.41%
112	45.597801	2471.649902	0.41%
113	46.335808	2519.360107	0.42%
114	48.045376	2575.26001	0.40%
115	48.96088	2584.840088	0.40%
116	46.279758	2673.610107	0.43%
117	53.580002	2823.810059	0.36%
118	52.119999	2713.830078	0.37%
119	51	2640.870117	0.34%
120	51.41	2656.300049	0.35%

Expert Solution

Step 1 Calculate Return of AGTHX using formula = (b4-B3)/B3 and return of S&P 500 using formula = (c4-c3)/c3

Step 2 Calculate Excess of Market Return over Risk free Return (Variable X) (=F4 - D4)

Step 2 Calcualte Excess of AGTHX Return over Risk free Return (Variable Y) (=E4-D4)

Step 4 Open data analysis in Data Tab, and select Regression

Step 5 Y variable should be excess of AGTHX return over Risk free Return & X variable should be excess of Market Return over Risk Free Return

Step 6 Click Ok and result will be displayed in a new Worksheet

Now you will get output as shown below:

Alpha is Intercept and Beta is X variable

95% confidence level is highlighted

Sice alpha is positive (0.00228) the security has outperformed the market

jeff jeffy answered 1 year ago

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