Question



2.2. The return on a stock is the change in its market price plus any dividend payments made. Return is usually expressed as a percent of the beginning price. The figure shows a histogram of the distribution of monthly returns for the U.S. stock market over a 273-month period.

Which statement about the overall shape of the distribution of monthly returns is true?
A)The shape of the distribution is slightly skewed to the left with a single peak.
B)The shape of the distribution is slightly skewed to the right with two peaks.
C)The shape of the distribution is slightly skewed to the right with a single peak.
D)The shape of the distribution is slightly skewed to the left with two peaks.
E)The shape of the distribution is roughly symmetric with a single peak

Answer 1

The distribution of monthly returns in the U.S. stock market over a 273-month period is slightly skewed to the right with a single peak, especially evident in the interval
`\(0 \text{ to } 2.5\).`

To determine the overall shape of the distribution of monthly returns, we can analyze the information provided in the histogram. The key information is the number of months within each interval.

The intervals with their respective frequencies are as follows:

-
`\(-25 \text{ to } -22.5\)`: 2 months

-
`\(-17.5 \text{ to } -15\)`: 1 month

-
`\(-12.5 \text{ to } -10\)`: 5 months

-
`\(-10 \text{ to } -7.5\)`: 7 months

-
`\(-7.5 \text{ to } -5\)`: 12 months

-
`\(-5 \text{ to } -2.5\)`: 29 months

-
`\(-2.5 \text{ to } 0\)`: 50 months

-
`\(0 \text{ to } 2.5\)`: 80 months

-
`\(2.5 \text{ to } 5\)`: 60 months

-
`\(5 \text{ to } 7.5\)`: 23 months

-
`\(7.5 \text{ to } 10\)`: 10 months

-
`\(10 \text{ to } 12.5\)`: 3 months

Now, let's interpret the information:

- The highest frequency occurs in the interval
`\(0 \text{ to } 2.5\)`, indicating a peak.

- The distribution is not perfectly symmetric; it is slightly skewed to the right because the tail on the right (positive side) is longer.

- There is a single peak, suggesting a unimodal distribution.

Based on this analysis, the correct statement is:

**C) The shape of the distribution is slightly skewed to the right with a single peak.**