Problem with evaluating S&P Return using Excel

[DynamiCAM]

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!!!!

[Denis]

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!

[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.

[DynamiCAM]

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!!

[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.

[Denis]

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

[CRGreathouse]

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?

[Denis]

> 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

[Erimess]

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.)

[Erimess]

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?

[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?

I also calculated Jan 00' to Dec 31 2009' FYI. And no, they don't teach us pre-made tools created by companies for "investors" to aimlessly point and click and blindly assume correctiveness. I've been taught to think and do my own work which provides me a true understanding. That being said thanks for the condescending help you offered.

[Denis]

I've been taught to think and do my own work which provides me a true understanding.

Agree....well put

[Erimess]

I also calculated Jan 00' to Dec 31 2009' FYI. And no, they don't teach us pre-made tools created by companies for "investors" to aimlessly point and click and blindly assume correctiveness. I've been taught to think and do my own work which provides me a true understanding. That being said thanks for the condescending help you offered.

I wasn't in any way attempting to be condescending. I was just talking simple facts. If you're going to talk about 12 year returns not being what you expected for "a decade," you have to expect someone to point that out.

And I was also not talking about pre-made tools created for people to just point and click blindly. Far from it, and you're assuming. I didn't ask if they pointed you to some tools online that you could use. I'm very much against tools as a method of "learning" how to do something, but rather the understanding behind it. You can ask anyone here exactly how much I hate memorizing processes and using pre-fab stuff.

I was talking about actually learning how it's done, the math behind it, the concepts behind it, etc. I said "how it's done" not "what tools exist." If you're in finance, you should be taught this. "Average return" can be defined in different ways, and you can't figure out how it's done if you're not understanding the meaning behind it. That is what I'm talking about in terms of being "taught this stuff," not some silly tool. Yes, I mentioned Morningstar - I also said that's where I go - there's already tons of stuff out there for the non-finance majors like me. I wasn't implying you should go there - if you're going to do finance, I would highly suggest you learn the stuff, not go to Morningstar.

You weren't getting the returns you expected to get - I was tossing my two cents in about some reasoning behind it. Did you even pay any attention to what I was saying?