What is volatility

"Tiddy Ogg" wrote

This would mean that "the market as a whole" could never be volatile. Is this true?

Volatility is a measure of the amount of fluctuation in the stock - a measure of its randomness if you like. You could measure it relative to the market or absolutely depends on what you define.

However, the relative measure on stocks is known as its "beta" which is the standard deviation of the covariance of a stock price movement relative to the market benchmark.

Volatility more customarily refers to options pricing, where the term is commonly used, is the standard deviation of a stock price movement i.e. the randomness of the drift over a measured time period.

The market has a beta of 1 i.e. no relative movement (its definitional) but it does have a volatility.

The financial economics answer is that volatility is the same as modified duration and discounted mean term. It is measured as % change in price / % points change in yield, e.g. a price change from 100 to 110 when the yield falls from 5% to 4% implies a volatility of (110 - 100) / (5% - 4%) = 10.

As you can guess this only applies to bonds. I haven't seen a mathematical definition for equities but I am sure someone can enlighten us all.