MSF Bootcamp Statistics Data Project - Stats Project” - Statistics Assessment Answer

MSF Bootcamp Statistics Data Project - Statistics Assessment Answer

Assessment Task:

Instructions
At the course web site in the “my grades” section in the left?hand?side menu, find the item “Stats Project Asset #” and make note of your asset. Now find the “Stats Data” spreadsheet in course documents (math/stats section). Copy all information provided for your asset, and also the monthly returns on the Russell 2000, into a new spreadsheet. Note that the returns you see for your asset assume any dividends were paid at the end of a month and that they were immediately reinvested. You will thus not need to worry about any complications due to dividends in this project. Save this new spreadsheet on your computer. Specifically, here is what you need to copy:
1. Monthly returns for the Russell 2000
2. Monthly returns for your asset
3. The values highlighted in orange for your asset: Hypothesized mean, Test value 1, and Test value 2

You will perform the calculations numbered below, and once you have all answers, type them into the appropriate place in the assignment “Stats Project” that you will find in the assignments section of the course web site. Make sure you pay close attention to the format you are to use when you type in answers (instructions are provided in the assignment).
Organize your spreadsheet so that all calculations and work are easy to find…label everything carefully. Your spreadsheet should not just contain numbers….it should contain all calculations and make it easy to see how the calculations are made by retaining the formulas. See the file “Example spreadsheet” for a simple illustration for how you should build your spreadsheet.
When you build a formula to perform a calculation, keep the formula (instead of replacing it with the answer number). Save your spreadsheet with the name that indicates your last and first name, in the format of Lastname.firstname (and of course the extension that indicates the file is an excel file). For example, Smith. Tom or Xu.Yao. Upload your spreadsheet in the assignment “Submit data project spreadsheet here.”

You are to do the work on your project on your own.
Everything is due by 1 pm on Monday, August 19:
1. Properly named spreadsheet file submitted to the “Submit data project spreadsheet here” assignment in the “course site’s math/stats area in the “Assignments” section in the Math/Stats assignment section.
2. All final answers entered and submitted in the “Stats Project” assignment in the course site’s math/stats area in the “Assignments” section. There is no “hard copy” of anything (something printed) you need to submit.

Calculations (PLEASE READ CAREFULLY)
1. What is the number of your asset (1?50)? For the remaining questions: Unless otherwise instructed or you are asked a qualitative
question (e.., “Yes or no?”), express all answers in your spreadsheet the format of 0.12345 (not 12.345%, not 0.1235, not 0.123456, etc.). In excel, this is a simple matter of formatting your final answers properly. Likewise, this is how you will type in your answers into the Data Project Answers assignment you will eventually find posted in the Assignments section (math/stats) of the course web site.
2. What is your asset’s arithmetic average monthly return?
3. What is your asset’s annualized time?weighted return (i.e., CAGR)? Hint: you have 60 monthly returns….one way to compound them is to create a new column in which you add 1 to each return, and then in your calculation cell make use of the =Product() function in excel. Note this will show you how $1 would have grown but this is only the first step in calculating the time?weighted return (it is not the final answer). Also, remember you are asked for the annualized return, not the monthly return.

4. Suppose you opened a new account and invested $10,000 in your asset in the beginning of 2014, that on June 30, 2016 you invested an additional $5,000, and that on January 31, 2017, you withdrew $2,000. If there were no other cash flows coming into or out of the account, what was the dollar balance at the end of 2018 (yes, do include the effect of the return earned during December 2018)?
5. Given the information in #4, what is the dollar?weighted annualized return in your account? Please note you cannot only use the beginning investment and ending account value to calculate this (that is not how the dollar?weighted return is calculated when we have interim cash flows in or out of the account!).
6. Suppose you wish to use the 60 prior monthly returns (of the stock itself, not considering your personal investments and withdrawals) to estimate your asset’s monthly standard deviation. What is your estimate of the monthly standard deviation?
7. What is your estimate of the annual standard deviation? (Note: this is not in your notes but to annualize a standard deviation calculated from monthly returns, you multiply the monthly standard deviation by the square root of 12, which is SQRT(12) in excel).

8. Using the =COVAR() function, what is the “population” covariance between your asset’s monthly returns and those of the Russell 2000?

9. Construct a formula that calculate the correlation by dividing the answer to #8 by the (monthly) population standard deviation of your asset’s monthly returns and also the (monthly) population standard deviation of the Russell 2000’s monthly returns. What is the correlation you have calculated?
10. Now use the =CORREL() function to calculate the correlation. What is the correlation the formula gives? (For your own knowledge….is this the same answer as for #9? What if you had calculated each standard deviation using the sample standard deviation instead of the population?)
11. Suppose you form a portfolio in which you invest 25% in your asset 75% in XYZ stock. If the monthly standard deviation of XYZ is 0.04200 and the correlation between your asset and XYZ is 0.60, what is the monthly standard deviation of the portfolio? In this calculation, use the sample monthly standard deviation of your asset (you calculated it in #6). Note the answer is NOT = (0.25)(SD of your asset) + (0.75)(SD of XYZ). See your class notes.

Using the sample monthly standard deviation of your asset from #6 and the number of monthly returns you are working with, according to the Central Limit Theorem, what is your estimate of the standard deviation of arithmetic average monthly return you calculated in #2?
13. Suppose you believe the true mean of your asset’s monthly stock returns = Hypothesized mean (This is specific to your particular asset and is provided in the Stats
Data spreadsheet). Using that value, your answers to #2 and #12, and the =NORMDIST() function in excel, perform a “two?tailed test” of H0: μ = Hypothesized mean vs. Ha: μ ≠ Hypothesized mean. (Hint: a similar test is shown in your class notes). What is the pvalue?
14. If your desired significance level is 5%, should you reject H0: μ = Hypothesized mean in favor of Ha: μ ≠ Hypothesized mean?

15. Using the NORMDIST function and your answers to #2 and #12 to characterize the distribution of your asset’s arithmetic average monthly return (i.e., assuming #2 and #12 are the true mean and standard deviation), what is the probability that we would observe an arithmetic mean monthly return between Test value 1 and Test value 2?
(These test values are specific to your asset and provided in the Stats Data spreadsheet).
16. Estimate a linear regression of your asset’s monthly returns against the monthly returns of the Russell 2000 (i.e., find the “best fit” line Y = α + βX where Y = your asset’s monthly return and X = the Russell 2000’s monthly return). Non?apple users: Regression is in the “Data Analysis” section that will appear to the far right under the “Data” tab assuming you have installed the add?in “Analysis ToolPak” (we discussed how to do this in class but google how to install an add?in in excel if needed). If you have Excel 2016 for Mac, look under “Tools” for “Excel add?ins” (Analysis ToolPak is not available on older versions of Excel for the Mac…email me for help if you have an older version). What is α?
17. What is β?
18. Is β ≠ 0 at the 5% significance level (yes or no)? You will use the “p?value” you see in the regression output) for this.
19. What is the R2 value of the regression?
20. What is the square of the correlation between your asset and the Russell 2000 (your answer to 9)?
21. What do you notice about #19 and #20? (Write a short statement)
22. Divide the covariance between the returns of your asset and the Russell 2000 (calculated in #8) by the population variance of the returns of the Russell 2000 (which
you have not yet calculated). What is the result of dividing this covariance by this variance?
23. Compare the answer to #22 to the answers of the regression questions above…what do you notice? (Write a short statement).

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