Welcome back. In this lesson, we’re going to tell you all about volatility. Volatility is an important measure of risk, but what is risk? We’ve talked a little about it already, and you may have an intuitive idea for what it means. It’s basically uncertainty about the future and in particular, uncertainty about bad things happening, like losing all the money you’ve invested in something. In finance, risks can be thought of as uncertainty about future returns. Uncertainty, that sounds kind of hard to measure. How do you measure what you don’t know? Well, we can get started by thinking of the log return as a random variable that can assume different values with different probabilities. An important way of characterizing a probability distribution is with it’s expected or mean value. The mean is the average of many measurements of the random variable, and you already know that the standard deviation is a measure of the spread of a distribution. Volatility is simply the standard deviation of the probability distribution of log returns. It’s a measure of the spread of this particular distribution. It measures the dispersion of log returns around the expected log return. Volatility gives you a sense of the range of values log returns are likely to fall into. For example, say you measured log returns on investment for several years and found that they happen to be distributed more or less normally with a mean or expected log return of about