What volatility measures
Volatility describes how much an investment’s returns vary from one period to the next. An investment whose price barely changes from week to week has low volatility; one that jumps up and down sharply has high volatility.
It is usually measured with a statistic called standard deviation, which summarises the size of those moves in one number. A larger standard deviation means the returns were more spread out, and the ride was rougher.
Why volatility is treated as risk
Volatility is not the only kind of risk, but it stands in for something real: uncertainty about where you will end up, and the discomfort of holding an investment that can fall a long way before it recovers. Sharp moves also raise the chance that an investor sells at the worst moment, locking in a loss they would have avoided by holding on.
Because it can be measured directly from past prices, volatility is the building block for other measures. The Sharpe ratio, for example, divides return by volatility to judge whether the return was worth the risk.
An example
Two investments can finish a month with the same total return while getting there very differently. One drifts upward steadily. The other rises and falls sharply day to day before landing at the same place.
They earned the same return, but the second carried more volatility, and most investors would not experience the two as equally comfortable to hold. The end point was identical; the path was not.
How volatility grows with time
Volatility depends on the period you measure it over. Daily moves are small; the same investment measured monthly or yearly shows larger swings, because the moves accumulate. As a rule of thumb, volatility grows with the square root of time, so an annual figure is roughly the daily figure multiplied by about sixteen (the square root of the number of trading days in a year).
This is why a return or a risk figure only means something when you know the period it covers. The course keeps that unit attached to every number it shows.