What is volatility?

Volatility measures how much a value moves up and down over time. In finance it is usually the standard deviation of returns, which says how far a typical period's return lands from the average. It matters because two investments with the same average return can feel and perform very differently if one swings far more than the other.

How it works

A calm series stays close to its average and a volatile one jumps around it. To compute it, take the return each period, find the average, measure how far each return sits from that average, square those gaps, average them and take the square root. Volatility is often annualized: a monthly figure is multiplied by the square root of 12, assuming returns are independent from one period to the next.

Higher volatility means a wider range of outcomes, in both directions. It also quietly lowers long-run growth: a 50% loss followed by a 50% gain leaves you 25% down, not even. That is why volatility is treated as a cost of holding an asset, and why people ask for higher expected returns to hold riskier ones.

Example

Say asset A gains 2% each month, every month. Asset B alternates between +10% and −6%. Both average roughly 2% per month, but A has no volatility and B is highly volatile. Starting with 1,000, after two months A is worth 1,000 × 1.02 × 1.02 = 1,040.40, while B is worth 1,000 × 1.10 × 0.94 = 1,034. After a bad month B is at 940, which tests the owner's nerve and any borrowing limits. These are illustrative numbers.

How to model it in Machinations

Create a Pool for the asset's value and a Register that draws a random percentage change each step, for example within a range set by a Lever called volatility. A state connection applies the change to the Pool. Play many times at once and chart the Pool: low settings give a tight band, high settings fan the paths apart. Compare the final values to see how wide the spread becomes.