What volatility is, as a measurement rather than a mood

In ordinary conversation volatility means a market that feels unsettled. As a statistic it means something narrower and duller: the standard deviation of an asset's returns, computed over a stated window, expressed for a stated period. Almost everything in this track follows from taking the second definition seriously and refusing the first.

A volatility figure is not complete without three attachments. It needs a definition of the return being measured, a window length over which the returns were collected, and a period the answer is expressed for. Strip any of those away and the number stops being a measurement. Track 3 lesson 6 introduced the annualised figure as a pricing input; the point here is that the figure is an output of choices, and the choices are not visible in the number.

The clearest way to see the difference between measurement and mood is the dollar illusion. A share priced at $412.30 moves $8.15 in a session, and that reads as a large move. A share priced at $19.05 moves 37 cents, and that reads as nothing. In return terms the first is 8.15 divided by 412.30, or 1.9767 percent, and the second is 0.37 divided by 19.05, or 1.9423 percent. They are the same event. One of them made an impression because the number in front of the decimal point was bigger.

Volatility is also symmetric. It counts a rise and a fall of the same size identically, which Track 4 lesson 7 used to separate it from risk. The narrower point here is that it is not even a description of how the market feels, because the arithmetic has no term for feeling. It is a summary of a specific list of numbers.

A lender's collateral model cannot take a mood as an input. It takes a figure with a window attached, which means somebody chose the window — and that choice is where the surprises in this track live.