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Solved: Rates of Return of Stocks Stocks may be
Chapter 3, Problem 27E(choose chapter or problem)
Problem 27E
Rates of Return of Stocks Stocks may be categorized by industry. The data on the following page represent the 5−year rates of return (in percent) for a sample of consumer goods stocks and energy stocks ending November 10, 2010.
(a) Determine the mean and the median rate of return for each industry. Which sector has the higher mean rate of return? Which sector has the higher median rate of return?
(b) Determine the standard deviation for each industry. In finance, the standard deviation rate of return is called risk. Typically, an investor “pays” for a higher return by accepting more risk. Is the investor paying for higher returns in this instance? Do you think the higher returns are worth the cost?
CONSUMER GOODS STOCKS | ||||
9.83 |
10.11 |
11.06 |
9.32 |
7.5 |
8.66 |
13.7 |
15.04 |
17.24 |
16.83 |
6.22 |
8.86 |
11.79 |
9.64 |
−14.12 |
16.83 |
14.85 |
15.24 |
34.17 |
−8.32 |
0.52 |
1.46 |
11.26 |
6.79 |
10.66 |
ENERGY STOCKS | ||||
11.02 |
11.08 |
20.26 |
15.18 |
−0.13 |
4.13 |
1.61 |
1.58 |
16.14 |
−0.42 |
17.11 |
15.32 |
8.49 |
7.44 |
11.01 |
8.53 |
37.83 |
5.21 |
10.68 |
10.27 |
10.76 |
34.32 |
3.97 |
19.3 |
11.28 |
Questions & Answers
QUESTION:
Problem 27E
Rates of Return of Stocks Stocks may be categorized by industry. The data on the following page represent the 5−year rates of return (in percent) for a sample of consumer goods stocks and energy stocks ending November 10, 2010.
(a) Determine the mean and the median rate of return for each industry. Which sector has the higher mean rate of return? Which sector has the higher median rate of return?
(b) Determine the standard deviation for each industry. In finance, the standard deviation rate of return is called risk. Typically, an investor “pays” for a higher return by accepting more risk. Is the investor paying for higher returns in this instance? Do you think the higher returns are worth the cost?
CONSUMER GOODS STOCKS | ||||
9.83 |
10.11 |
11.06 |
9.32 |
7.5 |
8.66 |
13.7 |
15.04 |
17.24 |
16.83 |
6.22 |
8.86 |
11.79 |
9.64 |
−14.12 |
16.83 |
14.85 |
15.24 |
34.17 |
−8.32 |
0.52 |
1.46 |
11.26 |
6.79 |
10.66 |
ENERGY STOCKS | ||||
11.02 |
11.08 |
20.26 |
15.18 |
−0.13 |
4.13 |
1.61 |
1.58 |
16.14 |
−0.42 |
17.11 |
15.32 |
8.49 |
7.44 |
11.01 |
8.53 |
37.83 |
5.21 |
10.68 |
10.27 |
10.76 |
34.32 |
3.97 |
19.3 |
11.28 |
ANSWER:
Solution:
Step 1 of 3:
The given data represents the 5-year rate of return for a sample of consumer goods stocks and energy stocks.
a). We have to determine the mean and the median rate of return for each industry.
- For ‘consumer goods’ industry the mean is calculated by
CONSUMER GOODS STOCKS | ||||
9.83 |
10.11 |
11.06 |
9.32 |
7.5 |
8.66 |
13.7 |
15.04 |
17.24 |
16.83 |
6.22 |
8.86 |
11.79 |
9.64 |
−14.12 |
16.83 |
14.85 |
15.24 |
34.17 |
−8.32 |
0.52 |
1.46 |
11.26 |
6.79 |
10.66 |
= 9.8056
The median for the ‘consumer goods’ industry.
First, we arrange the data in ascending or descending order.
-14.12 |
-8.32 |
0.52 |
1.46 |
6.22 |
6.79 |
7.5 |
8.66 |
8.86 |
9.32 |
9.64 |
9.83 |
10.11 |
10.66 |
11.06 |
11.26 |
11.79 |
13.7 |
14.85 |
15.04 |
15.24 |
16.83 |
16.83 |
17.24 |
34.17 |
Then the middle most value is 10.11 (13th value).
Therefore, the median = 10.11.