The mean of 1,000 quarterly returns is calculated as 4.52%. The standard deviation of these returns is calculated as 1.84%. An investor can be 95% certain that the return for any particular quarter will be at least:
Question
The mean of 1,000 quarterly returns is calculated as 4.52%. The standard deviation of these returns is calculated as 1.84%. An investor can be 95% certain that the return for any particular quarter will be at least:
Solution
To answer this question, we need to understand the concept of a confidence interval in statistics. A 95% confidence interval is defined as a range of values such that with 95% probability, the range will contain the true unknown value of the parameter. In a normal distribution, a 95% confidence interval corresponds to a range that is 1.96 standard deviations away from the mean on both sides.
Here are the steps to calculate it:
-
Calculate the standard deviation range: Multiply the standard deviation by 1.96. In this case, 1.84% * 1.96 = 3.6064%.
-
Subtract this range from the mean to get the lower bound of the confidence interval. In this case, 4.52% - 3.6064% = 0.9136%.
So, an investor can be 95% certain that the return for any particular quarter will be at least 0.9136%.
Similar Questions
The quarterly returns on a portfolio are as follows:Quarter 1 2 3 4Return 20% -20% 10% -10%The time-weighted rate of return of the portfolio is closest to:A.−5.0%.B.−1.3%.C.0.0%.
If you invest on average $10,000, and project profits of negative $2,000 in thefirst year, followed by positive $4,000 for years 2 and 3, what is your Average Accounting Rate of Return?
Over a period of 18 months, an investor has earned a return of 28.4%. The investor's annualized return is closest to:Question 70Answera.18.13%b.20.43%c.25.53%
With an initial payment of Rs 1,000 for 1 year, the redeemable value at the end is Rs 1,028. What is the average annual return after the given time period?Options 2.34% 2.60% 2.83% 2.90%
You buy 50 stocks of Company A, 30 of Company B, and 20 of Company C. The annual returns of these companies are 8%, 12%, and 10% respectively. The average return for one year is the closest to __________.Multiple Choice9.1%10.0%10.5%9.6%
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.