To determine the maximum return an asset could achieve with a 2.5% probability, we can use the concept of z-scores and the normal distribution.

Steps:

1. Understanding the problem:

   • Mean ($\mu$) = 10.91%
   • Standard deviation ($\sigma$) = 23.55%
   • We are looking for the return at the top 2.5% of the distribution.

2. Find the z-score: The cumulative probability at the top 2.5% corresponds to the 97.5th percentile of a standard normal distribution. The z-score for this percentile is approximately 1.96.

3. Calculate the return: Using the formula: $X = \mu + z \cdot \sigma$ Substituting the values: $X = 10.91 + (1.96 \cdot 23.55)$ $X = 10.91 + 46.16 = 57.07\%$

4. Closest multiple-choice answer: The closest option is 58.01%.

Final Answer:

58.01%

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Would you like a detailed explanation of how the z-score is determined or why the normal distribution is used?

Related Questions:

1. What is the expected return at the bottom 2.5% of the distribution?
2. How does increasing the standard deviation affect the calculated return?
3. What is the z-score for a probability of 5% instead of 2.5%?
4. Can this approach be applied to distributions that are not normal?
5. What assumptions underlie the use of the normal distribution for asset returns?

Tip:

Remember, extreme events (like 2.5% probabilities) often assume normality in financial models, but real-world distributions may have "fat tails," where extreme outcomes occur more frequently than predicted.