Homework 1 – BenchmarksIt is imperative to have a good set of benchmarks for comparative analysis. Your assignment is to obtain annual returns, based on a January 1 investment date with holding period of 1 year. You should be aware of the distinction of closing the position on 12/31/xxxx vs. an exact 1-year closing date of 1/1/xxxx+1. Of course, these would be LTDOY and FTDOY instead of the end of the calendar year.You must also calculate all decade-CAGR’s and an N-year CAGR using these data. Specifcy N. Feel free to calculate and report the average returns but we must have CAGR’s.If possible, you should find benchmark annual returns for DJIA, SP500, NYSE/AMEX, NYSE/AMEX/NASDAQ, RUT3000, RUT2000, etc. You muse obtain returns for level data (no dividends) as well as dividends included (this is called Total Return). You should also try and get benchmark return data for Market-Weighted as well as Equal-weighted.You must include a summary of what these indexes are, and their methodology. These are all available from the appropriate index website. You must summarize IN YOUR WORDS.Some of the returns will be harder to get than others. Note that dividends-included (total) returns for the Dow and S&P are readily available from their applicable websites. You’ll have to register for a login which takes and hour or so, plan accordingly. Both and 482 and 682 students should obtain data going back to 1925 (for returns beginning 1926).We have put some returns in the Canvas Resources – Projects directory to help you calibrate your benchmarks. Also see the good examples in Resources/Projects/Gallery of Great Ones. You must go through the end of last year (12/31/xx in most cases), and you should have an YTD for this year as well so you can see what a 9-month return looks like. We are almost 100% sure these are right, but let us know if they are not.Stat 682In addition, Stat 682 students must derive the following:(a) Suppose that an N-year CAGR is calculated giving r*, and suppose that the following year we have a loss of 40%. What effect does this have on the (N+1)-year CAGR? I.e., what is the difference in percent as a function of N, r* and r_(n+1)? This would be an actual difference, not a ratio.(b) Let N=57 years and r* be 10%. What is the difference in CAGR?(c) Derive an expression for the difference in terminal value over N+1 years for a general difference in CAGR. Use a starting portfolio value of $1.00. For example, the terminal value of 58 years at 10% CAGR is $251.64, but for a CAGR of 8.86% the terminal value is $137.26, giving a difference of $114.38.NOTE – Please take note of these and above instructions; credit will be deducted for not following instructions.a. DO NOT REPORT GROSS RETURNS, nor use too many digits. Think how a professional money manager would report these data. OTOH, if you choose not to report percents (1.2%), then you must use 3 digits if left as decimal (.012, not .01)b. Please check your numbers to ensure they make sense.c. Points will be deducted if you do not calculate and report CAGR.d. You MUST include N-year returns. If an index had not been published over the entire DOW/SPX/NYSE/AMEX timeframe, make note of it.
