The variance risk premium, mechanically

The variance risk premium is the amount by which implied variance exceeds the variance the market expects to be realised. Insisting on variance rather than volatility in that sentence is not pedantry; it is the only way the figure adds up, for the reason lesson 9 established.

Take illustrative figures. Implied volatility is 24.8 percent, so implied variance is 0.061504, which is 615.04 variance points. The market's expectation of realised volatility is 20.3 percent, so expected realised variance is 0.041209, or 412.09 points. The premium is the difference: 202.95 variance points.

Now compare the two ways of describing the same premium. In volatility points it is 4.5 points on a 24.8 percent figure, which is 18.1 percent of the level and sounds like a modest wedge. In variance it is 202.95 points on 615.04, which is 33.0 percent of the implied figure. Same premium, two units, and the second is the one the exposure settles in. Note also that the square root of the premium itself is 14.25 percent, which is the volatility level a position would have to realise for the premium alone to be consumed.

What the premium compensates is a shape rather than a level. A party who takes the other side receives a fixed amount and carries an exposure whose loss has no ceiling, because variance has no ceiling. Most periods the premium is earned; occasionally it is lost several times over. Lesson 11 puts numbers on that frequency.

This lands on collateral as a cost rather than a mechanism. Protection against a decline in a pledged holding is available in the options market, and it is priced with this premium inside it. At an illustrative $250 per variance point, a year of it costs 202.95 × $250 = $50,737.50. So a market hedge and a lender's haircut are not substitutes: one is a buffer the lender withholds for nothing, and the other is a buffer that is rented at a price with a positive expected cost.