What is the most likely value of the correlation coefficient between a stock-index mutual fund and the $S\&P500$ index?

• A. $0$
• B. $0.5$
• C. $1$
• D. $-1$

Answer: (C)

Verified step by step guidance

1. Understand that the correlation coefficient measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1.
2. Recognize that a stock-index mutual fund is designed to track the performance of the S\&P 500 index closely, meaning their returns move very similarly.
3. Recall that when two variables move perfectly together in the same direction, their correlation coefficient is 1.
4. Consider that since the mutual fund aims to replicate the S\&P 500 index, the correlation between them is expected to be very close to 1, indicating a strong positive linear relationship.
5. Therefore, among the given options (0, 0.5, 1, -1), the most likely value of the correlation coefficient is 1.