To find the probability that the one-year return of the stock will be negative, we need to determine the probability that the return is less than 0%. Since the return is normally distributed, we can use the Z-score formula.

Steps:

1. Convert the raw score (0%) to a Z-score: The Z-score formula is: $Z = \frac{X - \mu}{\sigma}$ where:

   • $X$ is the raw score (0% in this case),
   • $\mu$ is the mean (4%),
   • $\sigma$ is the standard deviation (6%).

   Substituting the values: $Z = \frac{0\% - 4\%}{6\%} = \frac{-4\%}{6\%} = -\frac{2}{3} \approx -0.6667$

2. Find the cumulative probability for the Z-score: We need to find $P(Z \leq -0.6667)$, which represents the probability that the return is less than 0%.

   Using a Z-table or a calculator, the cumulative probability for $Z = -0.6667$ is approximately 0.2525.

Thus, the probability that the one-year return of this stock will be negative is approximately 0.2525.

Would you like more details or have any questions about this solution?

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Here are 5 related questions:

1. What is the probability that the one-year return of the stock will be more than 10%?
2. How would the probability change if the mean return were 6% instead of 4%?
3. What is the probability that the return will be between 2% and 8%?
4. How would you calculate the probability if the return distribution were not normal?
5. What is the Z-score for a return of -2%?

Tip: When dealing with normally distributed financial data, understanding how to calculate and interpret Z-scores helps assess the risk and likelihood of various returns.