S&P 500 Price Change Frequency Distributions

This article presents the shape of the price change frequency distribution for the S&P 500 over approximately six decades on a daily basis, monthly basis and calendar year basis.

The degree of “normality” of S&P 500 price changes is high on a daily basis — it’s visually symmetrical. The average change of 0.03% is less than the median change of 0.05%.

The monthly distribution is not as visually smooth or symmetrical, but presents a “pretty” good bell shaped curve. The average change of 0.67% is less than the median change of 0.91%.

The calendar year distribution requires a bit of squinting and some imagination to see a bell shaped curve — making it “sort of” normal looking. The average change of 8.02% is less than the median of 9.76%.

The most extreme outliers, as measured by standard deviation, are at the daily level, then monthly and lastly calendar year.

click images to enlarge

Daily % Price Change Distribution

Monthly % Price Change Distribution

Calendar Year % Price Change Distribution

Directly relevant S&P 500 index funds are: SPY, IVV and VFINX.

While the “worst” has been worse than the “best” has been better, the negative outliers can be filtered out with stop loss orders. If persistent trailing stop loss orders are used to filter out the bad or poor, not just the worst; while letting the positive deviations run, the returns are increased.

We will reproduce these data sometime again over a shorter period. The daily data will look the same, as most likely will the monthly distribution. The annual data will vary substantially over different shorter periods.

For the data hungry, we hope this is helpful.

Disclosure: We own SPY in some managed accounts

Comments

[WACG:]

HA! The price change (or returns as the literature calls them) are, in general, NOT normally distributed. Only the the statistically unsophisticated determine whether a normal or Gaussian distribution is present by "just looking at a picture". In fact, the "picture" or histogram by itself reveals very little. Those that think that these "chi by eye" judgements of normality are sufficient will never comprehend important financial phenomena like "option smiles" or even Black-Scholes option pricing calculations. There are a virtual infinitude of non-normal distributions that "look like" a bell shape curve. Each one has different properties. By the way, "pretty good" is for religious judgements not mathematics.

Oct 23 09:09 AM

[searcher:]

Nonsense & phooey to any 'judgement' the precision afforded by mathematical modeling provides. Distributions are just that. Pretty good is damn good when you realize you cannot reify from distributions. Mathematical precision is not a guarantee of relevance. An idea of the distribution is really the best you can expect to be relevant to the market.

Oct 23 01:36 PM

[whipsaw:]

Interesting article. Rather than argue the degree to which the observed price history distribution approximates a Gaussian normal distribution (The article clearly does not state or imply the price distribution is normal), a more interesting question is how can one make use of this wealth of statistical information to improve trading odds? Eg, Set entry stops at 2 to 3-sigma when range bound, and exit stops @ 1-sigma when trend underway? Use limit orders if within 1-sigma of mean in direction of overall trend? What adjustments to make to take into consideration for 'fat tail' distribution oft noted in the academic literature or skewness on up days vs down days?

Oct 23 07:50 PM

[granger:]

good stuff as always

Oct 25 01:58 PM