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

This question checks whether you can read a line graph and connect the shape of a curve to the idea of volatility, which is just a word for how much a value bounces around.

1. Returns of Stock X are directly proportional to Mutual Fund Y: two quantities are directly proportional only if one is always a fixed multiple of the other, so plotting one against the other would give a straight line through the origin. The two curves here rise and fall at different times and by different amounts, so there is no fixed multiplying factor linking them. This option fails.
2. Average returns from Stock X and Mutual Fund Y are the same: checking averages would need every one of the 16 daily values added up and divided by 16 for each line, which is not something that can simply be read off a graph. Nothing here points to equal averages, so this option is not the intended reading of the graph.
3. Stock X is less volatile than Mutual Fund Y: volatility is about the size of the swing between the lowest and highest points a line touches. Stock X's swing runs from near $0$ up to about $1.0$, a spread of roughly $1.0$. Mutual Fund Y only moves between about $0.2$ and $0.75$, a spread of roughly $0.55$. Since Stock X's spread is clearly bigger, calling it less volatile is backwards.
4. Stock X is inversely proportional to Mutual Fund Y: an inverse relationship would mean the product of the two values stays constant, so whenever one line goes up sharply the other must go down by just enough to keep that product fixed. The graph does not show this tight, matched swinging between the two curves.

Working out the spread confirms the right reading: Stock X's range (about $1.0 - 0 = 1.0$) is almost double Mutual Fund Y's range (about $0.75 - 0.2 = 0.55$). A bigger range over the same 16 days means bigger swings day to day, which is the definition of higher volatility.

Let's summarize:

• Volatility is measured by how wide a line's swing is between its lowest and highest points, not by whether it moves with or against another line.
• Stock X's swing (about $0$ to $1.0$) is wider than Mutual Fund Y's swing (about $0.2$ to $0.75$).

So Stock X is more volatile than Mutual Fund Y, which is the correct reading of the graph.