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Calculating S&P Rates of Returns

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fast
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Calculating S&P Rates of Returns  Reply with quote  

In 1989, my earnings for the year was $837.00, and if I would have invested 15% of that, then I would have invested $125.55. If I invested that in the very beginning of 1990 in a mutual fund that successfully mimicked the results of the S&P 500 index, then by the end of 1990, my investment would have changed to $121.66 since the S&P 500 had a negative rate of return: (-3.10%). After two years, my investment would have grown to $158.73 since the rate of return for the infamous S&P benchmark for 1991 was 30.47%.

From 1990 to 2011, the historical rates of returns in percentages were -3.10, 30.47, 7.62, 10.08, 1.32, 37.58, 22.96, 33.36, 28.58, 21.04, -9.10, -11.89, -22.10, 28.69, 10.88, 4.91, 15.79, 5.49, -37.00, 26.46, 15.06, and 2.05.

If my math is correct, then my $125.55 invested on the early morning of January 1st, 1990 would have grown to $713.92 by the late night of December 31st, 2011.

In fact, I created a spreadsheet that listed my earnings for every year Iíve worked in hopes of calculating what I call my magic numberóthe amount I should have in retirement had I invested 15% of my earnings beginning in the year following the year I earned it.

But, I donít trust my math, even though I used a spreadsheet. I went to that site another poster turned me on to (www.politicalcalculations.blogspot.com) and tried to verify the accuracy of my own figures, but they didnít match up. Iím not sure if itís because the site uses averages or if my math is just that weak.
Post Sun Feb 19, 2012 5:04 am
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coaster
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I took your numbers, did the spreadsheet, and came up with the same result you did: $713.92.

I couldn't verify that the numbers used as input are correct, though, as the S&P website isn't responding right now.

Keep in mind that when returns are mentioned, they're usually in the context of average annualized compounded which is going to produce a lower number than a simple average.

~Tim~
Post Sun Feb 19, 2012 6:13 am
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fast
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quote:
Originally posted by coaster
I took your numbers, did the spreadsheet, and came up with the same result you did: $713.92.

I couldn't verify that the numbers used as input are correct, though, as the S&P website isn't responding right now.

Keep in mind that when returns are mentioned, they're usually in the context of average annualized compounded which is going to produce a lower number than a simple average.


Oh goodness gracious wow, thank you very much.

I'm confused though, which for me, is par for the course, but since my math is correct and therefore I would indeed have had $713.92 by the end of 2011, and since returns are usually announced as average annualized compounded which yield a lower number, why on Earth would I use average annualized compounded figures if they're gonna result in skewed and incorrect figures?

I bet that's a dumb question. I can just feel it. Embarassed

By the way, what is that site? I'd like to have a reliable go-to place for checking the numbers.
Post Sun Feb 19, 2012 1:53 pm
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oldguy
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On the SP500 Website, I put in 1990.01 to 2011.12 and got 8.34%/yr. For 22 yrs that comes to $731.43. (1.0834^22 * 125.55). That would be compounded annually.

If you use continuous compounding (remember those S&L's in the 1980's that advertised daily compounding?) it would be e^(.0834*22) = $786.28 (The Rule of 72)

And when I do the excel spreadsheet I get what you get, ie $713.91. That would be 8.22%/yr, rather than the 8.34%/yr from the website.

I don't know where the difference is. Maybe someone will jump in - the author of the SP500 website came online and commented on something a few years ago.
Post Mon Feb 20, 2012 12:15 am
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fast
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quote:
Originally posted by oldguy
On the SP500 Website, I put in 1990.01 to 2011.12 and got 8.34%/yr. For 22 yrs that comes to $731.43. (1.0834^22 * 125.55). That would be compounded annually.

If you use continuous compounding (remember those S&L's in the 1980's that advertised daily compounding?) it would be e^(.0834*22) = $786.28 (The Rule of 72)

And when I do the excel spreadsheet I get what you get, ie $713.91. That would be 8.22%/yr, rather than the 8.34%/yr from the website.

I don't know where the difference is. Maybe someone will jump in - the author of the SP500 website came online and commented on something a few years ago.
Maybe it has to do with the number of places after the decimal. Where is the authoritative place for finding the numbers I did manage to come up with?

ETA: it might (just might) have something to do with the dates I'm putting in. If I put in the same month and year for beginning and ending date (for example, 2011.12), then I don't get a rate of return, but if I want to know the return for a given year, what am I to do (?), put in the first month and last month?; that would only be 11 months since we can't count the first month, right? If I put in December 1989 to December 2011, then the numbers are even closer, but then the problem is that it's giving me the average for the beginning month and not the end.

See what happens when I start over-thinking things? What should be simple and straightforward gets all complicated. I really oughta stop that.


Last edited by fast on Mon Feb 20, 2012 12:54 am; edited 1 time in total
Post Mon Feb 20, 2012 12:43 am
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coaster
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quote:
Originally posted by fast
I'd like to have a reliable go-to place for checking the numbers.

Be cautious about numbers. They aren't always what they seem to be. For example, the formula that produces the number for what's reported as the S&P 500 Index is periodically adjusted and companies in the index are dropped and replacements added. Is that number you see the actual S&P 500 index number reported on that date, or has the historical data been back-adjusted to reflect the current formula and mix of companies in the index?

I think historical data is useful for comparing relative changes; it's tricky for comparing absolutes. Just accept that all numbers are skewed; some intentionally for some purpose; if you understand that and know what the skew is, it's not a problem.

(Might explain the difference noted above)

~Tim~
Post Mon Feb 20, 2012 12:54 am
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coaster
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I think that in the context of making retirement plans, it's best to make a range of projections; make your assumptions for worst-case scenarios on the one tail of the curve and your assumptions for best-case scenarios on the other tail of the curve, and then go with your comfort level.

As they say: nobody knows what the future will bring.

And they also say: the best guide to the future is the past.

Laughing Laughing Laughing

~Tim~
Post Mon Feb 20, 2012 1:02 am
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fast
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quote:
Originally posted by coaster
Is that number you see the actual S&P 500 index number reported on that date, or has the historical data been back-adjusted to reflect the current formula and mix of companies in the index?


The footnote says, "Total returns including reinvested dividends, in percent. In other words, these are the changes in the total return version of the index."

At least the difference isn't significant over that amount of time.
Post Mon Feb 20, 2012 1:03 am
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coaster
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... and that brings up another "gotcha" .... TOTAL RETURN!! Shocked

... which includes reinvested dividends ... and are you reinvesting yours???? Twisted Evil

... which brings to mind a quote old Sam Clemens made famous, though he didn't author it:

"there are lies, damned lies, and there are STATISTICS" ....

(and naturally)

HISTORICAL RATES of RETURN are STATISTICS!!! Laughing

Numbers don't lie; after all, numbers are numbers and 1 + 1 is always 2 (at least in this universe and at sub-light-speed); though you can make of those numbers pretty much whatever you want.

So, I don't make too much of historical data; what's more to the point is whether my net worth is growing in excess of the rate of inflation (the real rate, not the hokey government numbers)

~Tim~
Post Mon Feb 20, 2012 7:20 am
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