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January 26th, 2012, 08:01 AM  #1 
Newbie Joined: Jan 2012 Posts: 4 Thanks: 0  Problem with evaluating S&P Return using Excel Hi, first poster here, but glad to have found a large community willing to help. I am currently finishing up my FSU finance program, interning at Merrill Lynch, and continually work on my own small Roth IRA. I am in the process of creating an Excel template that I can use over and over to measure volatility and beta of securities. What I did was compile a daily closing value of the S&P 500 (information from Yahoo! Finance) and list that information in a spreadsheet. A1;A3036 are the dates from Jan 3, 2000 to Jan 24, 2012. In the column B1:B3036 are the daily closing valuations of the index. In column C, I measured the amount of daily change from one day to the next. My problem is when I average the daily changes, I get a negative return, in which I know the S&P has returned somewhat of a positive return since 2000. Is Yahoo! Finance's information incorrect, or am I calculating incorrectly? If anyone would like to speak through email, I will gladly attach the spreadsheet and let you take a look. *Thanks in advance*, this has been bugging me for days now!!!! 
January 26th, 2012, 08:50 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,702 Thanks: 701  Re: Problem with evaluating S&P Return using Excel
daily closing value of the S&P 500: 1999 12 31 1469.25 2000 01 03 1455·22 2000 01 04 1399.42 2000 01 05 1402.11 2000 01 06 1403.45 ...... 2011 12 30 1257·60 2012 01 03 1277.06 2012 01 04 1277.30 2012 01 05 1281·06 2012 01 06 1277·81 If you want to see THEM ALL, go here: www.economagic.com/emcgi/data.exe/sp/daysp500c So of course you'll get a negative result! You said: "I get a negative return, in which I know the S&P has returned somewhat of a positive return since 2000." Not according to the data! 
January 26th, 2012, 09:04 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Problem with evaluating S&P Return using Excel
You need to take the geometric averages, not the arithmetic averages. So if you have a 50% loss followed by a 100% gain, followed by a 3% gain, you should average them as cuberoot((1  0.50)(1 + 1.00)(1 + 1.03)) = 1.009901... or about a 0.99% gain per day. (Arithmetic averages would make this seems like a 17.67% increase per day...) But this will make the average even lower. From 12/31/1999 to 01/06/2012 the value dropped about 13%, or 1.16% per year. Of course your choice of starting and ending dates can change things a lot, and I don't know if anything funny happened with the index in that time. 
January 26th, 2012, 11:34 AM  #4  
Newbie Joined: Jan 2012 Posts: 4 Thanks: 0  Re: Problem with evaluating S&P Return using Excel Quote:
I'm trying to figure out who is wrong: Yahoo! Finance data My calculations The supposed fact that the S&P has returned a "limited" but postivie return W/O DIVIDEND REINVESTMENT I have attached my template. GEOMEAN in the f(x) menu hasn't given me a numerical value it says error.. not sure why this is either. I need an excel/math whiz on this!!  
January 26th, 2012, 11:37 AM  #5  
Newbie Joined: Jan 2012 Posts: 4 Thanks: 0  Re: Problem with evaluating S&P Return using Excel Quote:
 
January 26th, 2012, 12:25 PM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,702 Thanks: 701  Re: Problem with evaluating S&P Return using Excel
opening Jan.3/00: 1469.25 closing Jan.24/12: 1314.65 Well, I see geometric mean as worthless...when working with numerous periods like 3036 in this case. 1469.25(1+i)^3036 = 1314.65 ; i = .00003662... The average of differences ,to me, is simply (endingbeginning) / periods: (1314.65  1469.25) / 3036 = .050922.... Simple example: 100 98....2 95....3 89....6 80....9 2369 = 20 ; 20 / 4 = 5 80  100 = 20; 20 / 4 = 5 
January 26th, 2012, 03:03 PM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Problem with evaluating S&P Return using Excel Quote:
Consider a savings account (bond, etc.) yielding a 3% return each year over a span of 30 years. The arithmetic mean gives an average return of 4.75%. How is that sensible? Even better, maybe you swich banks after 15 years to another offering the same rate. Withthe arithmetic mean you get an average return of 3.72%. Why did that change when you're making the exact same amount of money?  
January 26th, 2012, 04:17 PM  #8  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,702 Thanks: 701  Re: Problem with evaluating S&P Return using Excel Quote:
 
January 26th, 2012, 09:22 PM  #9  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Problem with evaluating S&P Return using Excel Quote:
 
January 26th, 2012, 10:10 PM  #10  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Problem with evaluating S&P Return using Excel Quote:
And yes, it would be without dividend reinvestment, because an index doesn't have dividends. But there are absolutely different ways you can define a return. I get stuff off Morningstar and while it might be interesting to know exactly how they calculate stuff, I've always been more concerned with things on a comparative basis, and they already have risk numbers on there. You're in finance and interning at Merrill Lynch and they've never taught you how to do this?  

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