De-equitisation is the substitution of debt for equity, especially at the level of markets. At the company level de-equitisation occurs through share buy-backs, acquisitions for cash, and similar transactions.
Despite Modigliani-Miller, capital structure does matter enough to persuade persuade companies to adjust in response to changing conditions. The changes that trigger de-equitisation (or its opposite, re-equitisation) reflect changes in the cost of debt and equity.
The motive for adjusting capital structure is usually to lower the cost of capital (i.e. the WACC). One would therefore assume that de-equitisation would occur when debt is cheap and re-equitisation when equity is cheap — note that this is from the point of the issuer, so cheap means high share prices for equity and low yields for debt.
This means that de-equitisation and re-equitisation can be indicators of the relative valuations of debt and equity, Most commonly, debt-funded share buybacks are interpreted as indicating that equities are under-valued. This may apply at both the company and market levels.
However, it would be more accurate to say that what is indicated is the view of the management on whether debt or equity is cheaper. The cost of equity depends on expected returns, and in assessing this managers can make the same mistakes as investors, despite having more information.
One example of wide-spread management mistakes lies in the volume popularity of buy-backs during the dotcom boom. Both shareholders and management shared over-optimistic predictions of growth, encouraging them to wrongly assess equities as cheap.
The cost of both debt and equity is affected by perceptions of risk. It is easy to see that de-equitisation in 2007 and 2008 was caused a need to strengthen balance sheets as investors shied away from debt. While this makes both equities and debt less volatile, the larger amount of debt held meant the market as a whole was still exposed to the same total risk — a moments contemplation of the Modigliani-Miller argument will show that this must be so.
A less fundamental cause of changes in the relative costs of debt and equity is taxation. Buy-backs are also sometimes used as a tax-efficient method of returning money to shareholders, that would otherwise be paid as dividends, but this should not have more than a limited effect on de-equitisation because it is a means of making a payment to shareholders, not a reason for making a larger payment, to shareholders.