/biz/ - Business & Finance

>>12326300
sound theory, and historical (accuracy foolish to assume it will always be true, but if a trend a few hundred (arguably thousand) years old is becoming false, then i got bigger problems to worry about than money)

assuming equal equity positions in all stocks consider two scenarios:
1. 100% of portfolio is stock XYZ
2. 50% of portfolio is stock XYZ, 50% is stock ZYX

in scenario 1, you need 100% of stock picks to be positive (increase in value by the time you sell)
possible outcomes are : 1/2 chance negative, 1/2 positive (ignoring positive or negative magnitudes (aka %change of stock's value))
in scenario 2, you only need 50% of picks to be true
you have three outcomes:1/4 chance you get two positive outcomes, so double gains (again ignoring magnitude of %change), 1/4 chance you get two negative, and 2*(1/4) chance you get one positive, one negative (no change compared to holding strait cash)
adding a third possibility, neutral (sideways), to each stocks movement over time, the total balance between positive and negative outcomes does not get unbalanced)

as you increase the number of stocks you hold (keeping an equal weight of each stock), your need to correctly guess if a stock will go up or down decreases as you add more stocks to hold
even as you strip away assumptions about magnitudes above, historical data shows that net positive is still the more likely outcome for a majority of stocks

based on historical movement, and because of the larger number of neutral outcomes as you pick more stocks, your probability of having a positive outcome tends to be higher than your possibility of having a total sum of negative outcomes

just look up random portfolios, google has plenty of examples, an I'm too lazy to type more

>>12326454
Brownian motion comes from fluid mechanics, so i guess differential equations
Bayes theory is babies first probabilities class though
and probability distributions pop up in many fields