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URL:  http://boards.fool.com/distributions-of-sp500-returns-30615891.aspx

Subject:  Distributions of S&P500 returns Date:  3/31/2013  5:34 PM
Author:  Rayvt Number:  71605 of 78166

[Spun off from the 7702 thread.]

Whenever the topic of annual floors and caps comes up, the question arises of: What do the returns look like? How many times is the annual return of the S&P500 below the XX% floor, and how many times is it above the YY% cap?

I computed the rolling 12-month returns of the S&P500 index (excluding dividends) beginning Jan 1975 and ending Dec 2012. That's 37 years, and 456 rolling annual periods.

The worst 12-month loss was -45%.
The best 12-month gain was +53%.

Here's the table of the distribution of the returns. (Explanations following.)
Gain	Cnt	Pct	Cum pct	Weighted	Floor/Cap
-45% 7 1.5% 1.5% -0.6140
-35% 1 0.2% 1.8% -0.0713
-30% 5 1.1% 2.9% -0.3015
-25% 11 2.4% 5.3% -0.5428
-20% 14 3.1% 8.3% -0.5373
-15% 14 3.1% 11.4% -0.4145
-12% 10 2.2% 13.6% -0.2412
-10% 7 1.5% 15.1% -0.1458
-9% 4 0.9% 16.0% -0.0746 ** These are eliminated **
-8% 6 1.3% 17.3% -0.0987
-7% 5 1.1% 18.4% -0.0713
-6% 4 0.9% 19.3% -0.0482
-5% 6 1.3% 20.6% -0.0592
-4% 3 0.7% 21.3% -0.0230
-3% 5 1.1% 22.4% -0.0274
-2% 8 1.8% 24.1% -0.0263
-1% 3 0.7% 24.8% -0.0033
0% 7 1.5% 26.3% 0.0077 0.0077
1% 9 2.0% 28.3% 0.0296 0.0296
2% 9 2.0% 30.3% 0.0493 0.0493
3% 8 1.8% 32.0% 0.0614 0.0614
4% 12 2.6% 34.6% 0.1184 0.1184
5% 9 2.0% 36.6% 0.1086 0.1086
6% 19 4.2% 40.8% 0.2708 0.2708
7% 15 3.3% 44.1% 0.2467 0.2467
8% 8 1.8% 45.8% 0.1491 0.1491
9% 16 3.5% 49.3% 0.3333 0.3333
10% 13 2.9% 52.2% 0.2993 0.2993
11% 12 2.6% 54.8% 0.3026 0.3026
12% 47 10.3% 65.1% 1.3914 5.4211
15% 42 9.2% 74.3% 1.6118
20% 39 8.6% 82.9% 1.9243
25% 34 7.5% 90.4% 2.0504 ** These all become 12% **
30% 25 5.5% 95.8% 1.7818
35% 11 2.4% 98.2% 0.9046
40% 8 1.8% 100.0% 0.8158
53% 100.0%
Total 456 9.8421 7.3980

# periods with returns...
< 0% 113
>= 0% 343
>= 12% 206


Each row represents one bucket of periodic returns.
"Gain" is the annual gain.
"Cnt" is the number of periods with a return in that bucket. For example, 7 periods had a gain of 0% to 1%. That's the 0% bucket.
"Pct" and "Cum pct" is the percentage of that cnt of periods.

The next question is: How much does each bucket contribute to your overall gain/loss?
"Weighted" is the average gain of the bucket multiplied by the Pct.
For example, 7 periods were in the 0% bucket, which has average gain of 0.5%, and that happens 1.5% of the time. That bucket help you only a little bit.
Another bucket had 7 periods, that's the -10% bucket, with an average loss of -9.5%.
The -10% bucket hurts a lot more than the 0% bucket helps.
Basically, a big Weighted value is a big contribution to the overall gain, and a negative weighted value is harmful to the overall gain.

The total row is the sum of all those individual weights, which is 9.8421.

"Floor/cap" column:
Obviously, if you get rid of negative values, the total will be higher, which means that the overall gain will be higher. Setting a floor of 0% does just that.

But they also impose a cap -- in this example 12% cap. Everything above 12% is capped to 12%. The floor/cap column is the weighted values is all the b