To answer this question, we need to calculate the 95% confidence interval based on the given information.

Step 1: Understanding the confidence interval

The 95% confidence interval is given by: $\text{Confidence Interval} = \text{Mean} \pm 1.96 \times \text{Standard Deviation}$ Where:

• The mean return of the portfolio is 12.01%.
• The standard deviation is 19.28%.

Step 2: Calculate the lower and upper bounds of the 95% confidence interval

$\text{Lower Bound} = 12.01\% - 1.96 \times 19.28\%$ $\text{Upper Bound} = 12.01\% + 1.96 \times 19.28\%$

Let me compute that.The 95% confidence interval for the portfolio's returns is:

• Lower bound: -25.78%
• Upper bound: 49.80%

Part 1: The lower end of the 95% prediction interval is -25.78% (rounded to two decimal places).

Part 2: Would a 30% loss next year be outside the 95% confidence interval?

A 30% loss means a return of -30%. Since the lower bound of the interval is -25.78%, a -30% return is lower than the lower bound. Therefore, it would fall outside the 95% confidence interval.

Thus, the correct answer is:

D. No, you cannot be confident that the portfolio will not lose more than 30% of its value next year. This is because the low end of the prediction interval is less than -30%.

Would you like more details or further clarification?

Here are five related questions you may find useful:

1. How is a confidence interval constructed in statistics?
2. What does the 95% confidence interval mean in practical terms?
3. How do changes in the standard deviation affect the confidence interval?
4. What is the significance of a 1.96 Z-score in confidence intervals?
5. How can a portfolio's risk be mitigated if the confidence interval suggests potential large losses?

Tip: A wide confidence interval suggests high uncertainty in predictions, so diversifying your portfolio might help reduce the risk.