Question

Please explain confidence interval of financial modeling in detail.

Answer 1

Step 1 :   Meaning of confidence interval of financial modeling

A confidence interval measures the probability that a population parameter will fall between two set values. It can take any number of probabilities but the most common probabilities is 95% or 99%. A confidence interval is the probability that a value will fall between an upper and lower bound of a probability distribution. For example, given a 95% confidence level, stock ABC's return will fall between -4.5% and +6.8% over the next year. In other terms, an investor is 95% confident that the returns of holding ABC stock over the next year will fall between -4.5% and +6.8%.

Step 2 : Use of Confidence Interval

Statisticians use confidence intervals to measure uncertainty. A higher probability associated with the confidence interval means that there is a greater degree of certainty that the parameter falls within the bounds of the interval. Therefore, a higher confidence level indicates that the parameters must be broader to ensure that level of confidence.

Step 3 : Calculating the confidence interval

Confidence intervals provide more information than point estimates. By establishing a 95% confidence interval using the sample's mean and standard deviation, and assuming a normal distribution as represented by the bell curve, the researchers arrive at an upper and lower bound that contains the true mean 95% of the time. Assume the researchers is studying the height of basket ball players of a school and the interval is 72 inches to 76 inches. If the researchers take 100 random samples from the population of basket ball players of school as a whole, the mean should fall between 72 and 76 inches in 95 of those samples.