Question

The graph below shows the percentage returns of Stock X and Mutual Fund Y over sixteen days of a month. Study the graph and pick the statement that correctly describes the relationship between the returns of Stock X and Mutual Fund Y.

• A. Returns of Stock X are directly proportional to Mutual Fund Y.
• B. Average returns from Stock X and Mutual Fund Y are the same.
• C. Stock X is less volatile than Mutual Fund Y.
• D. Stock X is more volatile than Mutual Fund Y.

Hint:

Volatility means how widely a series swings up and down; compare the highest and lowest points each line reaches on the graph.

Answer 1

The Correct Option is D

Step 1: Understand what the graph shows.
The graph plots percentage return on the y-axis against the day of the month (1 to 16) on the x-axis, with two lines: Stock X and Mutual Fund Y.

Step 2: Read the range each line covers.
Stock X swings widely across the 16 days, touching about \(1.0\) on some days and dropping close to \(0\) on other days.
Mutual Fund Y stays inside a much narrower band, roughly between \(0.2\) and \(0.75\), across the same 16 days.

Step 3: Compare the two lines using the idea of volatility.
Volatility means how much a value moves up and down over time; a line that jumps between a high peak and a low dip is more volatile than a line that stays fairly flat.
Stock X's lowest value is below Mutual Fund Y's lowest value, and Stock X's highest value is above Mutual Fund Y's highest value, so Stock X's entire range is wider than Mutual Fund Y's range.
This wider range is exactly what more volatile means, so Stock X is more volatile than Mutual Fund Y.

Step 4: Check the wrong options.
Direct proportionality would need the two lines to rise and fall together in a fixed ratio; the graph shows the two lines moving independently, often in opposite directions, so that option is wrong.
The same average option cannot be confirmed just by looking at a graph like this without adding up all 16 values for both lines; the visual spread of Stock X versus the tighter band of Mutual Fund Y does not support equal averages.
Saying Stock X is less volatile is the exact opposite of what the graph shows since Stock X's swings are clearly wider.
Inverse proportionality would require one line to consistently go up exactly when the other goes down, in a fixed ratio, and the graph does not show this fixed inverse pattern either.

Final Answer:
Stock X shows much bigger swings from day to day than Mutual Fund Y, so Stock X is more volatile than Mutual Fund Y.
\[ \boxed{\text{Stock X is more volatile than Mutual Fund Y}} \]