Lesson 11 of 25 · 7 min

Why implied usually exceeds realised, and when it does not

It wins sixteen quarters out of twenty and still averages almost nothing, because the four losses are more than three times the size.

That implied volatility typically sits above subsequent realised volatility is one of the few reliable regularities in this subject. It has three causes, and none of them is a forecasting error.

Why the gap is usually positive:

Demand for downside protection is one-sided. Many participants want it and few want to provide it, so it clears above its expected payout.
The provider's loss has no ceiling while the receipt is fixed, and an exposure with that shape requires compensation beyond its average outcome.
An implied figure is an average over a horizon that includes the possibility of a jump. Most horizons contain no jump, so most of the time the average looks too high afterwards.

The exception arrives once volatility has already risen. Implied is an average forecast; realised measures the single path actually taken. When that path contains a cluster of the kind lesson 5 measured, realised overshoots whatever average was priced in advance, and it overshoots by a lot rather than a little.

Put illustrative numbers on twenty quarters. Suppose implied exceeded subsequent realised in sixteen of them, by an average of 3.4 points, and fell short in the other four, by an average of 11.6 points. The favourable side totals 16 × 3.4 = 54.4 points and the unfavourable side totals 4 × 11.6 = 46.4 points. Net across twenty quarters is 8.0 points, which averages to 0.4 points a quarter.

So the sentence implied usually exceeds realised is true as a frequency and nearly empty as an average. That is the same shape as the tail arithmetic in Track 4: a statement about how often is not a statement about how much. And the landing for a pledged portfolio is specific. The four exception quarters are precisely the quarters in which haircuts widen, thresholds are tested and protection is wanted. The regularity is reliable except in the periods it would matter.

Key terms

Frequency against average: The distinction between how often something happens and how much it amounts to. A relationship can hold four times in five and contribute nothing on average.
One-sided demand: A market in which most participants want the same side of a contract. It pushes the clearing price above the contract's expected payout.
Overshoot: Realised volatility exceeding what was implied, which happens when the path taken contains a cluster rather than an average spread of moves.

Worked example

Sixteen small wins against four large losses

An illustrative twenty-quarter tally of implied volatility minus subsequent realised volatility, in points. Invented figures, chosen to show the shape.

Quarters where implied exceeded realised: 16
Total from those quarters: +54.4 points
Quarters where it fell short: 4
Total from those quarters: −46.4 points
Net across twenty quarters: +8.0 points
Average per quarter: +0.4 points

Right eighty percent of the time, and worth four tenths of a point a quarter. Both facts come from the same twenty numbers.

Check yourself

Implied exceeded realised in 16 quarters by an average of 3.4 points and fell short in 4 by an average of 11.6 points. What was the average gap across all twenty?

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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.