When stock prices fall

If a stock with a low standard deviation of returns falls by a small amount then in some ways that is equivalent to a much larger fall in a stock with a higher standard deviation of returns.

Why?

True, ipso facto, you lose less when anything falls less...

But that's not the point here....

What is interesting is that from a probabilistic point of view, a stock with a standard deviation of returns of (say) half that of another stock is falling the "equivalent" amount, again in a probabilistic sense, when it falls half as much as the second stock.

In other words, when you buy a stock, you're not just buying the return, you're also buying the risk.