Lesson 15 of 25 · 7 min

Why an equity skew exists at all

A company's shares get more volatile as they fall for a reason involving no fear, no trading and no revision of anything.

Track 3 lesson 10 explained the equity skew by saying declines are faster and more correlated than advances. That is a description of the pattern rather than a cause of it. At least part of the cause is arithmetic, and it can be computed.

The mechanism is the leverage effect, and it follows from what a share is. A company's assets have some volatility. Its equity is the residual after debt, so the equity's volatility is the asset volatility scaled up by the ratio of assets to equity. Illustratively: assets of 1,000, debt of 400, equity of 600, and an asset volatility of 18 percent. Equity volatility is 18 × 1,000 ÷ 600 = 30 percent.

Now let the assets fall 12 percent, to 880. The debt is a fixed claim and does not move, so the equity is 880 − 400 = 480, which is a 20 percent fall. The ratio is now 880 ÷ 480 = 1.8333, so equity volatility is 18 × 1.8333 = 33 percent. Nothing about the business changed. Nobody revised a forecast. Equity volatility rose three points because the denominator shrank.

The effect accelerates. A 25 percent asset fall leaves equity at 350, a ratio of 2.1429 and an equity volatility of 38.57 percent. A 40 percent fall leaves a ratio of 3.0 and 54 percent. So volatility is a convex function of the decline, which is the same thing as saying the market is right to charge more for downside strikes than a single-volatility model would.

Two other mechanisms sit alongside it — correlations rise in declines, which Track 7 covered, and the one-sided demand for protection from lesson 11. But the leverage effect is the one that lands hardest on a pledged portfolio, because it means the two inputs to lending value move together from a single cause. Market value falls, and the volatility that sets the haircut rises. Running the collateral model at 30 percent gives a 28.06 percent haircut; at 33 percent it gives 30.87 percent. The shrinking base is multiplied by a widening discount.

Key terms

Leverage effect: The rise in a company's equity volatility as its share price falls, caused by the fixed debt claim becoming a larger share of the capital structure.
Asset volatility: The volatility of a company's whole asset base, before the debt claim is subtracted. Usually lower than its equity volatility and far more stable.
Residual claim: What equity is: whatever remains after fixed claims are met. A small change in a large base becomes a large change in a small residual.

Worked example

Equity volatility rising with nothing changing

An illustrative company: assets 1,000, debt 400, equity 600, asset volatility 18 percent. Debt is unchanged throughout.

At the start: Equity volatility 30.00%
Assets fall 12%, to 880: Equity 480
New ratio of assets to equity: 1.8333
New equity volatility: 33.00%
If assets fall 25% instead: Equity volatility 38.57%
Haircut at 30% against 33%: 28.06% against 30.87%

A 20 percent fall in the shares raised their volatility by three points and widened the haircut by 2.81 points. Neither was a decision.

Check yourself

A company has assets of 1,000, debt of 400 and asset volatility of 18 percent. The assets fall 12 percent. What happens to the equity's volatility, and why?

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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.