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Plan for Unit 1, Risk and Return
Complete Part One of class project

In this class we will complete a project over the whole semester which will create a portfolio of industrials sector ETFs for the industries represented in the GMU Student Managed Investment Fund (SMIF, https://www.smfund.gmu.edu/), perform tasks to achieve optimal allocation across these sectors, and then select the best individual securities within the sectors. Finally we will compare the performance of our actively managed portfolio with the performance of the SMIF, and with the passive benchmark SPY (S&P500 ETF).

Part One

(learning Bloomberg and working with financial data)

  1. Obtain an individual login from Bloomberg, following the instructions in this document: obtain_bb_login.html
  2. Be able to explain what an ETF is. (20min)
  3. Go to PORT in Bloomberg and select the SMIF portfolio. Look up the holdings of the portfolio. If you do not have access to Bloomberg please visit http://smfund.gmu.edu and review the portfolio holdings. (40min)
    1. How many industry sectors does the SMIF have?(20 min)
    2. Which companies are in each sector?(20min)
  4. Research on your own what a price-weighted index is, and what a value-weighted index is. What is the difference between the two? (50 min)
  5. Collect data for the sector ETFs of the SMIF. Specifically you will obtain the total return index for the following ETFs:
    NumberTickerName
    1 XLB Materials (not used, not currently in SMIF)
    2 XLE Energy (not used, using utilities instead)
    3 XLF Financials
    4 XLI Industrials
    5 XLK Technology
    6 XLP Consumer Staples
    7 XTL Telecommunications
    8 XLV Healthcare
    9 XLY Consumer Discretionary
    10 VPU Utilities (added 26 Aug 2019)
    11 VNQ Real Estate (added 26 Aug 2019)
    To obtain the data, you can use either the GP function in Bloomberg or the Bloomberg add-on in excel. Obtain the indexes at the monthly frequency, starting on December 31, 2009 and ending on December 31 2019. If you do not have access to Bloomberg, visit http://finance.yahoo.com. Type the ticker of the ETF in the search button and then click on 'Historical Data'. (60min)
  6. Calculate the monthly holding period returns from the total return indexes. You will have return series for 120 months, from January 2010 to December 2019. (20min)
  7. What is the holding period return for each ETF for the entire investment period?(10 min)
  8. Compute the arithmetic mean monthly return for the nine sector ETFs. What is the meaning of the arithmetic mean? (20 min)
  9. Compute the geometric mean monthly return for the nine sector ETFs. What is the meaning of the geometric mean, and how does it differ from the means in the descriptive statistics table? (20 min)
  10. Focus on the values of the total return index over the 12 months of 2016. What is the average monthly return for that year? What is the annualized return? What is the APR (Annual Percentage Rate)? What is the EAR (effective annual rate). Suppose you were only given the value of the total return index on the XLF ETF in December 2015. Suppose that this index value is your initial wealth. Using one of the above rates, would you be able to estimate the value of your wealth at the end of December 2016? Which rate would you use (APR, EAR, monthly rate, etc)? (30min)
  11. Prepare a report describing the data on the nine industry sectors (120min)
    1. Plot the time series of the returns (individually on separate plots).(20min)
    2. Prepare a histogram plot for each industry sector ETF.(20min) You can watch this YouTube video on how to draw a histogram in Google sheets: https://www.youtube.com/watch?v=O1WEJdxtxDc
    3. What do the histograms show? Do these return series appear to be normally distributed (i.e. from a normal distribution)? How can you describe what a normal distribution is? What are the most important properties of the normal distribution? (20min)
    4. Prepare a table of descriptive statistics for the nine industries. The table should include means, standard deviations, skewness and kurtosis coefficients, medians, 5, 10, 25, 75, 90, and 95 percentile returns, minimum and maximum values. (20min)
    5. What does each of these descriptive statistics tell us?(20min)
    6. Describe the industries based on these statistics, i.e. which has the highest/lowest average return (note: this is different from finding the minimum return within an industry or across industries), the highest/lowest risk, do industries appear to be normally distributed?(20min)
  12. What is the risk-free rate. What instrument would you use (e.g. Treasury bill) and at what maturity to represent the risk-free rate. Download the data for the chosen instrument from Bloomberg next to the industry ETF series. (20min)
  13. On an new graph plot the nine industry ETFs in risk-return space (return on the y-axis, risk on the x-axis). Identify the risk-free rate on the graph as well. Can you tell which of the portfolios has the highest Sharpe ratio? The lowest? (30 min)
  14. Compute the Sharpe ratios for the industry ETFs. Explain how you did that. Describe your results.(30min)
  15. Based on the descriptive statistics in 9d, compute VAR for each of the nine industry portfolios. Compare the VAR measures and describe what they mean. What is the main assumption you are making when computing VAR? (50min)
  16. Based on the descriptive statistics in 9d, compute The Expected Shortfall (ES) for each of the nine industry portfolios. Compare the ES measures and describe what they mean. (50min)
  17. How many three-sigma events are there in each of the nine industry portfolios? Describe these for each portfolios? How many such events would be expected if the returns are normally distributed?
    18. (40min)