The probability of a stock going up or down

"What is the probability of a stock's price going up vs going down at any given time?"

The answer depends on how you are looking at this:

(i) if you are looking purely at the very next second with no additional information, there are three ways the stock could go: up, down or flat (no change).

(ii) if you are looking at buying a stock at any given point in time but then holding it for a period of time, historical data starts to indicate that the odds favour up over down.

A while back I ran some stats on my domestic equities market (Australia). I found that 64% of industrial stocks (a broad category that excludes resources plays but includes most other sectors including tech and financials, achieved a positive return in the five years to May 20, 2018. The chart below sets out the distribution of returns.

36% of all stocks had a negative return while 31% at least doubled
But that is just one time period in time. Using US data, alpha architect ran a more detailed study that you can read here.

If you look at market returns rather than individual stock returns, famed academics Fama and French have written a paper, “Long-Horizon Returns” and they found the distribution of continuously compounded (CC) returns for US equities “are close to, but not quite normal for return horizons of ten years or more”. The table below, from that paper, shows CC returns have a positive mean over all periods from 1 month to 30 years.

Fama French - Moments of CC returns

And the next chart is also taken from that Fama and French paper, plotting out monthly US equity market returns.

Fama French - monthly market returns plotted by year

This answer was first published on Quora - you can find it here.

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