Cost of Equity and Asset Pricing

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cost of equity

From a reader on last night’s piece:

David, can you expand on this – ” I would revise the concept of the cost of capital to make it credit-centric.  All the efforts to calculate the cost of equity capital from equity market correlations are bogus.  They don’t make any economic sense.  In most cases, the cost of equity should not exceed the yield on an average CCC bond.”

All valuation classes teach the equity market correlation method so it would be interesting to hear your views.

Equity exists in many forms.  In securitizations, equity is the tranche that takes the first loss and controls the deal.  In a mutual insurer/bank/thrift, etc.,  the book equity is held by the dividend-receiving policyholders.  The real equity is held by management, who actually control the place, because the dividend-receiving policyholders will not vote them out.  In a credit tenant lease, there is the guy that owns the property, and typically he puts up a teensy amount of equity, because there is a “credit tenant,” one that has an investment grade rating, and the mortgage is secured by:

  • the property
  • the senior unsecured credit of the “credit tenant,” whose lease payments pay the mortgage, and go directly to the lender, and
  • the equity owner.

In practice, the first two offer real security, and the third is a joke, sort of.  The thing is, if commercial property values inflate, there is a *lot* of leverage the the CTL structure for the owner of the equity.  And, if things go badly, most equity owners own the property though a thinly capitalized subsidiary.  Can’t squeeze blood from a stone.  “Heads, I win. Tails, you lose.”

Then there are more normal examples, like public and private equity.  The ownership is clear, though control varies considerably, considering the stakes that control investors have.

Contingent Claims Theory

Leaving aside options on equity, the equity of an investment is the most volatile investment that funds the assets of an economic entity.  The equity of an entity controls the entity, and possesses a valuable option — the option to abandon it all, and hand the company over to the next most junior investor.

Option valuation can tell us a lot about about the cost of capital.  The put option inherent in any debt can be measured, giving the following observations:

  • The more of the company that is financed with debt, the greater the risk of owning the equity (the default option is near the money), and the higher the cost of equity is.
  • The more volatile the economic results of the company, the higher the probability of bankruptcy, and the higher the cost of equity will be.
  • The underlying volatility of a company’s assets radiates out through it liabilities, with liability volatility increasing as liability claims become more junior.

In essence, thinking like a securitization, where you have many, many levels of debt, and as debt gets more junior, its yield rises as its economic prospects become more volatile.  Equity is not debt, but it is the juniormost claim on the assets and cash flow of the firm, even while it has control, which includes the option to adjust the capital structure.  (Had to add that, because it is important, but not strictly relevant to my argument.)

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Holding the equity is holding control, with a complex option to adjust the capital structure, including the possibility of giving up control under bad conditions, or selling out under good conditions.  But now consider options on the equity — those options also imply a cost of equity capital:

  • The more volatile the at-the money option is, the higher the cost of equity.  (And the higher will be bond spreads…)
  • Another way to think about it is how expensive it is to set a floor under and equity investment.  Volatile companies have higher insurance premiums for their stocks.  That implies a higher cost of capital.
  • Using options, we can create pseudo-bonds, where we can lock in a certain range of returns.
  • A capital structure hedge fund can trade corporate debt and CDS [Credit Default Swaps] against equity options — they all price off of the volatility of corporate assets in the short run.
  • For any capital structure, the return on the assets can be modeled over a variety of credit scenarios.  Those returns can translate into returns for the various liability classes — e.g. trade claims, bank debt, senior unsecured debt, junior bonds, preferred stock, equity, and given the current prices for each class, the yields and yield spreads can be calculated, as well as the probability and severity of loss.


Cost of equity is a function of the overall volatility of the value of corporate assets, and the degree of leverage the firm employs.  This is how the cost of equity should be calculated.  Using a method like this, I believe the estimated cost of equity would be lower than what MPT models would produce, and the equity would display significant optionality, having very low returns under stress and very high returns under the best scenarios.

If we calculate the cost of equity like this, it will be an enhancement to DCF, and not require the bogus assumptions of MPT, because:

  • Risk is risk of monetary loss, not correlation to an index
  • Beta is not a stable parameter; correlation coefficients are not stable either.
  • This fits with the way that actuaries would price complex credit insurance policies, if they thought hard enough about it.
  • This fits with contingent claims theory, which legally describes the claim structures for competing classes of liabilities.

By David Merkel, CFA of Aleph Blog

This is my theory of asset/liability/equity pricing in broad. Comments are welcomed.

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