Lesson 8 of 25 · 7 min
Realised against implied, and what the gap is
The usual comparison puts a forecast beside a history, which is why the gap so often points the wrong way.
Track 3 lesson 9 established that implied volatility is an inverted price rather than a measurement. This lesson is about the arithmetic of comparing it with an actual measurement, and the comparison almost everyone makes is set up wrong.
Take illustrative figures. Options expiring in thirty days imply 27.4 percent. Realised volatility over the trailing thirty sessions is 19.6 percent. The gap is 7.8 points, and the natural reading is that options are expensive relative to how the asset has been behaving.
The two numbers do not cover the same time. The implied figure describes the thirty days ahead; the realised figure describes the thirty days behind. Suppose the next thirty sessions come in at 31.2 percent realised. Against the period it was actually a forecast of, the implied figure was 3.8 points too low.
So the same 27.4 percent was simultaneously 7.8 points rich against the past and 3.8 points cheap against the future. Nothing about the number changed; the comparison changed. Any statement about implied volatility being high or low is a statement about which window it was set against, which makes it the same kind of claim as lesson 4's.
The landing matters for a pledged portfolio, because the three figures do not enter the same places. A lender's collateral model takes trailing realised volatility, so in this episode the lender's input was 19.6 percent while the options market was pricing 27.4 percent and the world went on to deliver 31.2 percent. With a 3.5 coverage multiple and a 22-session exit, those three inputs produce haircuts of 20.27 percent, 28.34 percent and 32.27 percent. The buffer in force during the episode was the smallest of the three.
Key terms
- Horizon matching
- Comparing two volatility figures that describe the same span of time. Implied against trailing realised fails this, because one looks forward and one looks back.
- Trailing realised volatility
- Volatility computed from the most recent completed window. The figure a collateral model generally consumes, and the only one of the three that is knowable today.
- Subsequent realised volatility
- What the asset actually went on to do over the period an implied figure was quoted for. The only fair benchmark for that figure, and unavailable when it matters.
Worked example
One implied figure, two verdicts, three haircuts
Illustrative figures for one episode. Coverage multiple 3.5, assumed exit 22 sessions, so each haircut is 3.5 × volatility ÷ 15.8745 × 4.6904.
- Trailing 30-session realised
- 19.6%
- 30-day implied
- 27.4%
- Subsequent 30-session realised
- 31.2%
- Implied against trailing
- +7.8 points
- Implied against subsequent
- −3.8 points
- Spread between the largest and smallest haircut
- 12.00 points
Haircut 20.27%.
Haircut 28.34%.
Haircut 32.27%.
Reads as expensive.
Was in fact too low.
The lender's input was the lowest of three available numbers, and it was the only one available at the time. That is a structural feature, not an error.
Check yourself
Implied volatility is 27.4 percent, trailing realised is 19.6 percent, and the subsequent period realises 31.2 percent. Was implied high or low?
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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.