Merits of Volatility in a Portfolio

Here's a simple explanation of how volatility can work in an investor's favor to generate higher portfolio returns.

Prices in financial markets tend to move geometrically, not arithmetically. Certainly, at the extremes a stock's fall is limited to 100% but it can rise an unlimited amount. The basic geometrical "one-to-one mapping" of up moves to down moves is:

Probability of movement up X%
= probability of movement down [1 - 1/(1 + X/100)] x 100%

If we buy two stocks and one rises while the other falls an equal geometric amount, we end up with the following two-stock portfolio returns:

1% up move + 0.99% down move gives very close to 0% average move;
10% up move + 9.1% down move gives 0.45% average UP move;
30% up move + 23% down move gives 3.5% average UP move;
50% up move + 33% down move gives 8.3% average UP move;
100% up move + 50% down move gives 25% average UP move;
200% up move + 67% down move gives 67% average UP move;
500% up move + 83% down move gives 208% average UP move;
1000% up move + 91% down move gives 455% average UP move;
etc.

Observe how volatility is an investor's friend. For example, it is better to buy two volatile stocks and see one rise 100% while the other falls 50%, producing an average portfolio return of 25%; than to buy two less volatile stocks, see one rise 10% and the other fall 9.1% and end up with an average portfolio return of a measly 0.45%. At the ten-bagger extreme, with one stock rising 1000% and the other falling 91%, the advantage of high volatility becomes strikingly clear--no one would complain about a portfolio return of 455%!

For this reason, I prefer to hold volatile stocks rather than less volatile ones, believing that over time the volatility will work in my favor on a portfolio basis.