You will be able to calculate annualised volatility and explain why it treats gains and losses the same.
The risk score on Marcus's broker app puts his world equity ETF at 6 out of 7. A robo-advisor he tried once described his chosen portfolio as "moderately aggressive". Neither tells him what he actually wants to know: how much could this fall, how often, and could he stand it? Both labels come mostly from one number, volatility. It is the number every risk report starts with, so you need to know how it's built and where it stops being honest.
Volatility is the standard deviation of an asset's returns: a measure of how far each period's return tends to sit from the average. A fund that returns close to 1% every month has low volatility. One that swings between plus 6% and minus 8% has high volatility, even if its average is the same.
In a spreadsheet, put the monthly returns in a column and use STDEV, or STDEV.S in Excel. That gives you monthly volatility. Risk reports quote it as a yearly figure, and the conversion uses the square root of the number of periods in a year: multiply monthly volatility by the square root of 12, weekly by the square root of 52, daily by the square root of about 252 trading days.
Here's the example for the course. Over five years, the monthly returns of Marcus's world equity ETF have a standard deviation of 4.0%. These are made-up figures. Annualised, that's 4.0% times the square root of 12, about 13.9%.
The square root comes from an assumption that each period's return is independent of the last, so variances add up over time while standard deviations grow more slowly. It's close enough for most uses. When returns trend or reverse from month to month, the shortcut drifts, which is one reason two providers can quote different volatility for the same fund.
Lesson 1.1 noted that the gap between arithmetic and geometric average returns is roughly half the variance, which is volatility squared. That's the link: higher volatility costs you compounded return even when the average stays put.
Standard deviation measures distance from the average in both directions. A month of plus 9% counts as much against a fund as a month of minus 9%. An asset that occasionally jumps upward looks riskier than one that drifts gently, though no investor has ever lost sleep over a surprise gain.
This matters most for holdings with lopsided returns. A stock that sits flat for years and then doubles on a takeover will show high volatility. A strategy that earns small steady gains and then has one large loss can show low volatility right up to the loss. Lesson 2.3, Sharpe and Sortino ratios, and when each misleads, gives you a measure that only counts the bad side.
Standard deviation itself assumes nothing about shape. The trouble starts when people use it as the whole story, because then they are treating returns as a bell curve, where moves of more than three standard deviations almost never happen.
Markets don't behave that way. Large daily falls happen far more often than a bell curve would allow. On 19 October 1987, Black Monday, the Dow Jones Industrial Average fell about 22% in a single day, a move a bell curve fitted to the years before would treat as essentially impossible. March 2020 brought several daily falls in US shares that were each many standard deviations out. Analysts call this having fat tails, and lesson 2.6, Value at Risk, expected shortfall and fat tails, deals with it directly. For now, read any volatility figure as a description of normal months, not of the worst ones.
Volatility is measured from a window of history, and the window decides the answer. Five calm years produce a low figure, which then gets used to size positions just before conditions change.
Take Marcus's ETF again. Here are its made-up monthly returns in the worst year of the five: minus 4.8%, plus 1.9%, minus 2.6%, minus 7.9%, plus 0.4%, minus 6.8%, plus 5.9%, minus 3.7%, minus 8.6%, plus 4.9%, plus 6.2% and minus 1.5%. Compounded, the year lost about 16.7%. The monthly standard deviation of those twelve numbers is about 5.3%, which annualises to about 18.3%. The five-year figure said 13.9%. In the year that hurt, the fund behaved like a much riskier asset.
That's normal. Volatility clusters: calm months follow calm months and wild months follow wild ones. So a single volatility figure from a long, mostly calm window describes the typical year and badly misses the one that tests you. Risk desks look at several windows, including the worst year they can find, and so should you.
Volatility is still worth calculating. It's the input for the Sharpe ratio, for volatility-weighted position sizing in lesson 11.1, and for comparing funds that hold similar assets. Use it as a measure of the ordinary wobble, and pair it with the measures in the rest of this module for the parts it misses.
For the activity you'll need five years of month-end prices or total return index values for one holding. Your broker's chart export or the fund's website will usually have them, and you'll calculate the figure twice, once for the whole period and once for the worst year in it.
Calculate the annualised volatility of one holding from monthly returns over five years, then for its worst single year.
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