Lesson 14 of 25 · 7 min

Recency, and the volatility you last lived through

The same 19.8 percent of headroom is four ordinary months in one regime and one and a half in another.

Recency is the overweighting of the most recent stretch of experience when estimating what is normal. It is efficient in most of life, because conditions persist. It fails on volatility, because volatility is the one quantity that clusters and then changes regime.

The failure is quantifiable, because headroom and volatility are both percentages of the same thing and can be put in the same unit. A monthly figure is derived from an annualised one by dividing by the square root of twelve, since deviations scale with the square root of time rather than with time.

monthly deviation = annualised volatility ÷ √12

annualised volatility: The typical size of a price move over a year, stated as a percentage.
√12: The square root of the number of months in a year, about 3.464. Deviations grow with the root of time, not with time.
monthly deviation: The typical size of a one-month move implied by the annual figure.

Suppose the trailing twelve months delivered 16.4 percent annualised volatility and a longer window contains a stretch at 47.2 percent. Both are illustrative. The calm regime implies 16.4 ÷ 3.464 = 4.73 percent a month; the other implies 47.2 ÷ 3.464 = 13.63 percent. Headroom of 19.8 percent is therefore 19.8 ÷ 4.73 = 4.18 monthly deviations in the first case and 19.8 ÷ 13.63 = 1.45 in the second.

Nothing about the account differs between those two sentences. The headroom is 19.8 percent in both. What differs is the yardstick, and the yardstick in use is generally the last twelve months, because that is the period the borrower has actually experienced. A cushion described as comfortably more than four normal months is the same cushion as one described as a month and a half.

Key terms

Recency: Treating the most recent period as representative of the whole distribution, because it is the part that has been lived through.
Realised volatility: How much a price actually moved over a past window, annualised. A measurement, and one that changes substantially between windows.
Square-root-of-time scaling: The rule that a deviation over a shorter period is the annual figure divided by the square root of the number of such periods in a year.

Worked example

One cushion, two yardsticks

Headroom 19.8%. Trailing twelve-month volatility 16.4% annualised; an earlier stretch ran at 47.2%. Both illustrative.

Monthly deviation in the calm regime: 4.73%
Monthly deviation in the other regime: 13.63%
Headroom in calm-regime months: 4.18
Headroom in other-regime months: 1.45
Ratio between the two descriptions: 2.88 times

The account did not change between these rows. The only thing that changed is which twelve months are being used as the definition of normal.

Check yourself

Headroom is 19.8 percent. Trailing volatility is 16.4 percent annualised, but an earlier period ran at 47.2 percent. How many monthly deviations of cushion is that, on each measure?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.