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• S&p 500 Historical Data Monthly

I found the raw data here and wondered what conclusions I could draw from it.

I could not discern from that site if the 'annual return' is 'price return', 'dividend return', or 'total return'.

Here are the raw data sorted by year:

The interval between 1928 and 2015 represents 88 calendar years.

Of those 88 years, the S&P 500 went up in 64 years (72.7273%) and went down in 24 years (27.2727%).

The ratio of up years to down years was 64 / 88 or 2.66667, which means the S&P 500 went down once every (approximately) 4 years on average.

Here are the raw data sorted by return:

The worst return was -43.84% in 1931.

The best return was 52.56% in 1954.

Here are the raw data sorted by the frequency of similar returns:

number of losses >= -44% and < -43% is 1

number of losses >= -37% and < -36% is 1

number of losses >= -36% and < -35% is 1

number of losses >= -26% and < -25% is 2

number of losses >= -22% and < -21% is 1

number of losses >= -15% and < -14% is 1

number of losses >= -13% and < -12% is 1

number of losses >= -12% and < -11% is 1

number of losses >= -11% and < -10% is 2

number of losses >= -10% and < -9% is 2

number of losses >= -9% and < -8% is 5 At&t apn carrier settings.

number of losses >= -7% and < -6% is 1

number of losses >= -5% and < -4% is 1

number of losses >= -4% and < -3% is 1

number of losses >= -2% and < -1% is 3

number of gains >= 0% and < 1% is 1

number of gains >= 1% and < 2% is 2

number of gains >= 2% and < 3% is 1

number of gains >= 3% and < 4% is 1

number of gains >= 4% and < 5% is 1

number of gains >= 5% and < 6% is 4

number of gains >= 6% and < 7% is 2

number of gains >= 7% and < 8% is 2

number of gains >= 9% and < 10% is 1

number of gains >= 10% and < 11% is 2

number of gains >= 12% and < 13% is 2

number of gains >= 13% and < 14% is 1

number of gains >= 14% and < 15% is 2

number of gains >= 15% and < 16% is 2

number of gains >= 16% and < 17% is 2

number of gains >= 18% and < 19% is 5

number of gains >= 19% and < 20% is 2

number of gains >= 20% and < 21% is 2

number of gains >= 22% and < 23% is 3

number of gains >= 23% and < 24% is 3

number of gains >= 25% and < 26% is 2

number of gains >= 26% and < 27% is 1

number of gains >= 28% and < 29% is 2

number of gains >= 29% and < 30% is 1

number of gains >= 30% and < 31% is 2

number of gains >= 31% and < 32% is 4

number of gains >= 32% and < 33% is 2

number of gains >= 33% and < 34% is 1

number of gains >= 35% and < 36% is 1

number of gains >= 37% and < 38% is 2

number of gains >= 43% and < 44% is 2

number of gains >= 46% and < 47% is 1

number of gains >= 49% and < 50% is 1

number of gains >= 52% and < 53% is 1

Ups and Downs

After a down year, the following year was a down year 8 times out of 24 (33.33%), and was an up year 16 times out of 24 (66.67%).

After an up year, the following year was a down year 16 times out of 63 (25%), and was an up year 47 times out of 63 (75%).

Streaks

Here are the streaks of consecutive down years:

streak starting in 1973 for 2 consecutive years

streak starting in 1939 for 3 consecutive years

streak starting in 2000 for 3 consecutive years

streak starting in 1929 for 4 consecutive years

Here are the streaks of consecutive up years:

streak starting in 1935 for 2 consecutive years

streak starting in 1967 for 2 consecutive years

streak starting in 1975 for 2 consecutive years

streak starting in 1954 for 3 consecutive years

streak starting in 1978 for 3 consecutive years

streak starting in 1963 for 3 consecutive years

streak starting in 1970 for 3 consecutive years

streak starting in 1942 for 4 consecutive years

streak starting in 1958 for 4 consecutive years

streak starting in 2003 for 5 consecutive years

streak starting in 1947 for 6 consecutive years

streak starting in 2009 for 7 consecutive years

streak starting in 1982 for 8 consecutive years

streak starting in 1991 for 9 consecutive years

Streaks of up years tend to be longer, and occur more frequently, than streaks of down years.

Mean, Standard Deviation, and Compound Annual Growth Rate [CAGR]

The mean return was 11.4122%. This is the simple arithmetic average of all of the returns.

The interpretation of 'average' is not as easy as it looks. Perhaps you've heard the quote from William Kruskal's article, 'Statistics, Moliere, and Henry Adams', American Scientist 55 (1967), p. 416 to 428: 'A man standing with one foot in a bucket of boiling water and the other in a bucket of freezing water would be a ridiculous fool to summarize his experience by saying, 'On the average, I feel fine.'

Suppose you begin with $100. During the first year, you experience a return of +50%, and end up with $150. During the second year, you experience a return of -50%, and end up with $75. It is indeed nonsensical to claim that your 'average' return was 0.

Standard deviation 'is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A standard deviation close to 0 indicates that the data points tend to be very close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.'

The standard deviation of S&P 500 returns was 19.7028%.

This means that 68% of the time the S&P 500 return was between the mean +/- one standard deviation (i.e. -8.2906 and 31.115), 95% of the time the S&P 500 return was between the mean +/- two standard deviations (i.e. -27.9934 and 50.8178), and 99.7% of the time the S&P 500 return was between the mean +/- three standard deviations (i.e. -36.284 and 81.9328).

To help you visualize what this means, there is a good diagram here.

The compound annual growth rate [CAGR] answers the question, 'What constant rate of return would take you from the starting value to the ending value over the time interval?'. If you bought $1 worth of S&P 500 at the beginning of 1928, you would end up with $2,940.88 at the end of 2015. The CAGR of S&P 500 returns was 9.5%.

Conclusions

S&p 500 Historical Data Monthly

What conclusions can be drawn from these data?

I hesitate to make guesses, estimates, or predictions of future returns based on the history of past returns, because as all investors hear at least once per day, 'past performance is no guarantee of future results'.

One must be careful to avoid the Gambler's Fallacy - 'the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future (presumably as a means of balancing nature).'

2015 was the 7th year in a streak of up years. What does that say about 2016? Sadly, very little of statistical significance.

I wish good luck to all investors.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.