Question

The term "beta" refers to a measure of a stock's price volatility relative to the stock market as a whole. A beta of 1 means the stock's price moves exactly with the market. A beta of 1.6 means the stock's price would increase by 1.6% for an increase of 1% in the stock market. A larger beta means the stock price is more volatile. The beta values for the stocks of certain companies are shown in the following table.

Company	Beta
Company 1	1.24
Company 2	0.99
Company 3	1.2
Company 4	1.36
Company 5	1.11
Company 6	1.36
Company 7	0.97
Company 8	1.18
Company 9	1.79
Company 10	1.22
Company 11	0.92
Company 12	0.9
Company 13	0.84
Company 14	1.84
Company 15	0.68

Company	Beta
Company 16	0.62
Company 17	1.23
Company 18	0.56
Company 19	0.69
Company 20	0.47
Company 21	0.72
Company 22	0.73
Company 23	0.18
Company 24	0.86
Company 25	0.88
Company 26	1.22
Company 27	0.82
Company 28	0.04
Company 29	0.26
Company 30	1.1

(a)

Construct a frequency distribution and percent frequency distribution. (Round your answers to percent frequency to one decimal place.)

Beta	Frequency	Percent Frequency
0.00–0.09		%
0.10–0.19		%
0.20–0.29		%
0.30–0.39		%
0.40–0.49		%
0.50–0.59		%
0.60–0.69		%
0.70–0.79		%
0.80–0.89		%
0.90–0.99		%
1.00–1.09		%
1.10–1.19		%
1.20–1.29		%
1.30–1.39		%
1.40–1.49		%
1.50–1.59		%
1.60–1.69		%
1.70–1.79		%
1.80–1.89		%
Total		%

(b)

Construct a histogram.

A histogram with 19 class labels along the horizontal axis is given.

• The horizontal axis is labeled: Beta.
• The vertical axis is labeled: Frequency.

Centered over the leftmost label, 0.00-0.09, a bar is drawn 5 units tall. Moving to the right, information about the remaining bars (beginning with class label) is listed.

• 0.10-0.19: 4 units tall, 0.20-0.29: 4 units tall, 0.30-0.39: 3 units tall, and 0.40-0.49: 3 units tall
• 0.50-0.59: 2 units tall, 0.60-0.69: 2 units tall, 0.70-0.79: 1 unit tall, and 0.80-0.89: 1 unit tall
• 0.90-0.99: 1 unit tall, 1.00-1.09: 1 unit tall, 1.10-1.19: 1 unit tall, and 1.20-1.29: 1 unit tall
• 1.30-1.39: 1 unit tall, 1.40-1.49: no bar, 1.50-1.59: no bar, and 1.60-1.69: no bar
• 1.70-1.79: no bar and 1.80-1.89: no bar

A histogram with 19 class labels along the horizontal axis is given.

• The horizontal axis is labeled: Beta.
• The vertical axis is labeled: Frequency.

Centered over the leftmost label, 0.00-0.09, a bar is drawn 1 unit tall. Moving to the right, information about the remaining bars (beginning with class label) is listed.

• 0.10-0.19: 1 unit tall, 0.20-0.29: no bar, 0.30-0.39: no bar, and 0.40-0.49: no bar
• 0.50-0.59: 2 units tall, 0.60-0.69: 5 units tall, 0.70-0.79: 3 units tall, and 0.80-0.89: no bar
• 0.90-0.99: 4 units tall, 1.00-1.09: 4 units tall, 1.10-1.19: 2 units tall, and 1.20-1.29: 3 units tall
• 1.30-1.39: 1 unit tall, 1.40-1.49: 1 unit tall, 1.50-1.59: no bar, and 1.60-1.69: 1 unit tall
• 1.70-1.79: 1 unit tall and 1.80-1.89: 1 unit tall

A histogram with 19 class labels along the horizontal axis is given.

• The horizontal axis is labeled: Beta.
• The vertical axis is labeled: Frequency.

There is no bar centered over the leftmost label, 0.00-0.09. Moving to the right, information about the remaining bars (beginning with class label) is listed.

• 0.10-0.19: no bar, 0.20-0.29: no bar, 0.30-0.39: no bar, and 0.40-0.49: no bar
• 0.50-0.59: 1 unit tall, 0.60-0.69: 1 unit tall, 0.70-0.79: 1 unit tall, and 0.80-0.89: 1 unit tall
• 0.90-0.99: 1 unit tall, 1.00-1.09: 1 unit tall, 1.10-1.19: 1 unit tall, and 1.20-1.29: 2 units tall
• 1.30-1.39: 2 units tall, 1.40-1.49: 3 units tall, 1.50-1.59: 3 units tall, and 1.60-1.69: 4 units tall
• 1.70-1.79: 4 units tall and 1.80-1.89: 5 units tall

A histogram with 19 class labels along the horizontal axis is given.

• The horizontal axis is labeled: Beta.
• The vertical axis is labeled: Frequency.

Centered over the leftmost label, 0.00-0.09, a bar is drawn 1 unit tall. Moving to the right, information about the remaining bars (beginning with class label) is listed.

• 0.10-0.19: 1 unit tall, 0.20-0.29: 1 unit tall, 0.30-0.39: no bar, and 0.40-0.49: 1 unit tall
• 0.50-0.59: 1 unit tall, 0.60-0.69: 3 units tall, 0.70-0.79: 2 units tall, and 0.80-0.89: 4 units tall
• 0.90-0.99: 4 units tall, 1.00-1.09: no bar, 1.10-1.19: 3 units tall, and 1.20-1.29: 5 units tall
• 1.30-1.39: 2 units tall, 1.40-1.49: no bar, 1.50-1.59: no bar, and 1.60-1.69: no bar
• 1.70-1.79: 1 unit tall and 1.80-1.89: 1 unit tall

(c)

Comment on the shape of the distribution.

The distribution is somewhat skewed to the right.The distribution is almost perfectly symmetric.    The distribution is somewhat skewed to the left.

(d)

Which stock has the highest beta?

Company 1Company 9    Company 14Company 23Company 28

Which stock has the lowest beta?

Company 1Company 9    Company 14Company 23Company 28

Answer 1

a) frequency distribution and percent frequency distribution :

Beta	Frequency	Percent frequency
0 - 0.09	1	1 / 30*100 = 3.3%
0.1 - 0.19	1	1 / 30*100 = 3.3%
0.2 - 0.29	1	1 / 30*100 = 3.3%
0.3 - 0.39	0	0 / 30*100 = 0%
0.4 - 0.49	1	1 / 30*100 = 3.3%
0.5 - 0.59	1	1 / 30*100 = 3.3%
0.6 - 0.69	3	3 / 30*100 = 10%
0.7 - 0.79	2	2 / 30*100 = 6.7%
0.8 - 0.89	4	4 / 30*100 = 13.3%
0.9 - 0.99	4	4 / 30*100 = 13.3%
1 - 1.09	0	0 / 30*100 = 0%
1.1 - 1.19	3	3 / 30*100 = 10%
1.2 - 1.29	5	5 / 30*100 = 16.7%
1.3 - 1.39	2	2 / 30*100 = 6.7%
1.4 - 1.49	0	0 / 30*100 = 0%
1.5 - 1.59	0	0 / 30*100 = 0%
1.6 - 1.69	0	0 / 30*100 = 0%
1.7 - 1.79	1	1 / 30*100 = 3.3%
1.8 - 1.89	1	1 / 30*100 = 3.3%

b) Histogram:

6 5 Beta Frequency 0.00-0.09 0.10-0.19 0.20-0.29 0.30-0.39 0.40-0.49 0.50-0.59 0.60-0.69 0.70-0.79 0.80-0.89 0.90-0.99 1.00-1.09 1.10-1.19 1.20-1.29 1.30-1.39 140-1.49 1.50-1.59 1.60-1.69 1.70-1.79 1.80-1.89

c) Shape of the distribution:

The distribution is somewhat skewed to the left.

(d) Highest beta : Company 14

Lowest beta : Company 28