Using the following annual returns, calculate the estimates of the arithmetic mean returns, the variances, and the standard deviations for assets X and Y. Also calculate the estimates of the covariance and correlation between X and Y. These five years are a sample of the entire population of returns for X and Y. Year 2001 2002 2003 2004 2005 Returns X 11% 6% -8% 28% 13% Y 36% -7% 2% -12% 43% A stock has had returns over the past six years of 29%, 14%, 23%, -18%, 9%, and -14%. What was its arithmetic mean and geometric mean returns over that period? What was the standard deviation of its returns over this six-year period?

Using the following annual returns, calculate the estimates of the arithmetic mean returns, the variances, and the standard deviations for assets X and Y. Also calculate the estimates of the covariance and correlation between X and Y. These five years are a sample of the entire population of returns for X and Y. Year 2001 2002 2003 2004 2005 Returns X 11% 6% -8% 28% 13% Y 36% -7% 2% -12% 43% A stock has had returns over the past six years of 29%, 14%, 23%, -18%, 9%, and -14%. What was its arithmetic mean and geometric mean returns over that period? What was the standard deviation of its returns over this six-year period?

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter8: Time Series Analysis And_forecasting

Section: Chapter Questions

Problem 22P: Consider the following time series: a. Construct a time series plot. What type of pattern exists in...

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Calculate the arithmetic average for the following returns: Year Return O 2.4 % O 2.2% O 3.1% O 3.4% Calculate the geometric average for the following returns: Year Return O 2.2% O 2.4% O 3.1% O 3.4% Calculate the standard deviation for the following returns: Year Return O 8.4% O 8.1% O 7.6% O 7.3% 2017 12.03% 2017 12.03% 2017 12.03% 2018 -8.24% 2018 -8.24% 2018 -8.24% 2019 1.34% 2019 1.34% 2019 1.34% 2020 4.55% 2020 4.55% 2020 4.55%
Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.7 percent and the standard deviation was 18.3 percent. a. What is the probability that your return on this asset will be less than –4.1 percent in a given year? Use the NORMDIST function in Excel® to answer this question. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c. What range of returns would you expect to see 99 percent of the time? (Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations…
uppose the average return on Asset A is 7.1 percent and the standard deviation is 8.3 percent, and the average return and standard deviation on Asset B are 4.2 percent and 3.6 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on Asset B will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. In a particular year, the return on Asset A was −4.38 percent. How likely is it that such a low return will recur at some point in the future? (Do not round…
es Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.7 percent and the standard deviation was 18.3 percent. a. What is the probability that your return on this asset will be less than -4.1 percent in a given year? Use the NORMDIST function in Excel® to answer this question. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c. What range of returns would you expect to see 99 percent of the time? (Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter…
Use the following information to compute the standard deviation of returns: Yearly Returns Year Return (%) 1 19 2 1 3 10 4 26 5 4 a. 12% b. 10.42% c. 0.87% d. 108.5%
Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.2 percent and the standard deviation was 10.6 percent. a. What is the probability that your return on this asset will be less than -9.7 percent in a given year? Use the NORMDIST function in Excel® to answer this question. Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. b. What range of returns would you expect to see 95 percent of the time? Note: Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. c. What range of returns would you expect to see 99 percent of the time? Note: Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and…
Suppose the average return on Asset A is 6.6 percent and the standard deviation is 8.6 percent and the average return and standard deviation on Asset B are 3.8 percent and 3.2 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 11 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on Asset B will be greater than 11 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. In a particular year, the return on Asset A was −4.25 percent. How likely is it that such a low return will recur at some point in the future? (Do…
Over the past 4 years an investment returned 0.1, -0.12, -0.08, and 0.13. What is the standard deviation of returns? (Note: input raw results with four decimal digits, NOT percentage results. For example, input 0.0102 NOT 1.02%)
Show your work (use of formula, etc.) in solving the problem. Provide your answer/solution in the answer space provided below. Answer the question: Given the following historical returns, calculate the average return and the standard deviation: Year Return 1 14% 2 10% 3 15% 4 11%
Given the following historical returns, calculate the average return and the standard deviation: Year Return 1 14% 2 10% 3 15% 4 11%
Consider the following time series: a. Construct a time series plot. What type of pattern exists in the data? Is there an indication of a seasonal pattern? b. Use a multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise. c. Compute the quarterly forecasts for next year.
Consider the following time series data: Construct a time series plot. What type of pattern exists in the data? Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2. 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise. Compute the quarterly forecasts for next year based on the model you developed in part (b). Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for quarter 1 in year 1, t = 2 for quarter 2 in year 1, … t = 12 for quarter 4 in year 3. Compute the quarterly forecasts for next year based on the model you developed in part (d). Is the model you developed in part (b) or the model you developed in part (d) more effective? Justify your answer.