Final answer:
To calculate the confidence interval for a stock with an expected return of 13.86% and a standard deviation of 14.30%, you can use the formula CI = X ± (Z * σ / √n), where X is the expected return, Z is the z-score based on the confidence level, σ is the standard deviation, and n is the sample size. The upper range and lower range of the confidence intervals at different confidence levels can be calculated using this formula.
Step-by-step explanation:
To calculate the confidence interval, we need to use the formula: CI = X ± (Z * σ / √n), where X is the expected return, Z is the z-score based on the confidence level, σ is the standard deviation, and n is the sample size.
For the given stock with an expected return of 13.86% and a standard deviation of 14.30%:
a. To find the upper range of a 68% confidence interval, we use a z-score of 1 (standard deviation equivalent) and a sample size of 1. The upper range is therefore 13.86 + (1 * 14.30 / √1) = 27.16%.
b. To find the lower range of a 68% confidence interval, we use the same parameters as above. The lower range is 13.86 - (1 * 14.30 / √1) = 0.56%.
c. To find the upper range of a 95% confidence interval, we use a z-score of 1.96 (standard deviation equivalent) and a sample size of 1. The upper range is 13.86 + (1.96 * 14.30 / √1) = 40.58%.
d. To find the lower range of a 95% confidence interval, we use the same parameters as above. The lower range is 13.86 - (1.96 * 14.30 / √1) = -12.86%.
e. To find the upper range of a 99% confidence interval, we use a z-score of 2.58 (standard deviation equivalent) and a sample size of 1. The upper range is 13.86 + (2.58 * 14.30 / √1) = 52.99%.
f. To find the lower range of a 99% confidence interval, we use the same parameters as above. The lower range is 13.86 - (2.58 * 14.30 / √1) = -26.27%.