My Math Forum Problem with evaluating S&P Return using Excel

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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 e-mail, 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/em-cgi/data.exe/sp/day-sp500c 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
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Re: Problem with evaluating S&P Return using Excel

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 Originally Posted by CRGreathouse 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.
I was thinking Geometric as well. However, as you said, this would cause my "return" to be even lower. I know for a fact that I've heard in the last decade the S&P has returned around 0.4%-1%, and this number is w/o dividend reinvestment.

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
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Re: Problem with evaluating S&P Return using Excel

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 Originally Posted by DynamiCAM 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!!
My file is 15kb too big to attatch. But anyone who would like to see my spreadsheet I will email it. If I can get this correct this will be a valuable tool for anyone to use to determine any securities risk with it's historical price information. I will gladly share it when completed.

 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 (ending-beginning) / periods: (1314.65 - 1469.25) / 3036 = -.050922.... Simple example: 100 98....-2 95....-3 89....-6 80....-9 -2-3-6-9 = -20 ; -20 / 4 = -5 80 - 100 = -20; -20 / 4 = -5
January 26th, 2012, 03:03 PM   #7
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Re: Problem with evaluating S&P Return using Excel

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 Originally Posted by Denis Well, I see geometric mean as worthless...when working with numerous periods like 3036 in this case.
You'll get poor results, then. The geometric mean is the only sensible way to deal with increases of this type.

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
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Re: Problem with evaluating S&P Return using Excel

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 Originally Posted by CRGreathouse > You'll get poor results, then. The geometric mean is the only sensible way to deal with increases of this type. Agree, CR; but the OP "seems" to be inquiring about the effectiveness of averaging daily changes. > 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? Agree, sure not indicative of much; but the annual income remains $30 per$1000, of course. > 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? Well, ok, but no need to switch banks for that; you can just switch account numbers in the same bank

January 26th, 2012, 09:22 PM   #9
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Re: Problem with evaluating S&P Return using Excel

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 Originally Posted by CRGreathouse 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.
Only 2 big crashes. (Following periods that were getting hot.)

January 26th, 2012, 10:10 PM   #10
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Re: Problem with evaluating S&P Return using Excel

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 Originally Posted by DynamiCAM I was thinking Geometric as well. However, as you said, this would cause my "return" to be even lower. I know for a fact that I've heard in the last decade the S&P has returned around 0.4%-1%, and this number is w/o dividend reinvestment.
But your time period isn't "the last decade." Change time periods even slightly, depending on what's been going on, can have drastic changes in the returns. The market was pretty hot the last of the 90's and peaked around beginning of 2000. It was up to 1400 something, and then went down under 900 in the post-911 crash. Comparing the last decade is starting in the middle of that big crash when the thing was lower, and yeah, we're back down to about that point with little return. But if you compare today to 1999, you're hitting when it was near the peak and there's going to be a loss.

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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