Tuesday, July 8, 2014

Risk & Valuations, Part 7: A Risk-Based Theory of the Firm

If we view an economy as a market divided between risk buyers and risk sellers, then labor and bond holders form a class of fixed income stakeholders.  Does some of the equity premium come from the local certainty that equity holders sell to the labor class?  Can we consider a theory of the firm that consists of risk-trading?

If we look at just the traditional capital structure of a firm, capital is divided between creditors and equity ownership.  Creditors receive a return that is some combination of the risk free rate of return on capital and a credit premium related to the risk of the specific firm.  Equity holders receive a return that consists of that fixed return premium plus an equity premium, which is composed itself of a market equity premium and a multiple based partly on the amount of financial leverage equity employs.  The most basic form of this idea for the whole market, from the Capital Asset Pricing Model, is this:

The return to equity in the market is a function of the risk free rate of return on capital and the premium demanded for taking the residual risk.

What if we applied this idea to labor, also.  In a fixed wage labor contract, there is a gross value of the contract that simply entails the value of the work being performed by the laborer.  But, embedded in the contract is a risk discount.  The employer promises to pay a relatively fixed amount to the laborer, so we can think of the labor contract as including a sort of swap, where the firm takes a floating payout, based on the results of operations, and the laborer takes a fixed payout.  This results in a premium paid to the firm that is a product of the volatility of operational returns and a market risk premium taken as payment for exposure to that volatility.

In other words, the laborer contract includes a rate swap.  Under the contract, the laborer owns a bonds payout and the firm takes an equity payout, complete with a risk premium that is taken as a discount from the gross value of the labor.

What if, instead of dividing the firm into debt and equity, we divide it into (1) labor and debt, together, and (2) equity, but we still apply this same model of risk premiums?  Now, we can arrive at an intrinsic value for the firm derived as such:

I will deal with this now simply on the theoretical level.  The numerical cost and level of the labor "security" is a problem I haven't worked out.  The simple regression below of Compensation to interest rates and the equity risk premium would suggest that the value of the security embedded in labor contracts increases labor compensation by about 1% for each 1% decrease in the Equity Risk Premium (ERP), although, to the extent that this relationship is legitimate, it might be stronger than that.  The jumps in compensation in the last 15 years represented disequilibria, so equilibrium compensation levels are probably closer to the lower levels seen during the recoveries.  Of course, at the firm level, this would vary by job and by firm, depending on the conditions of each labor agreement.

I wonder if this model could provide a better indication of true risk represented by a firm's equity, and of the trade-offs between labor and capital in the firm's business model.  An fully unlevered Equity Risk Premium could be calculated, reflecting the premium that would exist before equity trades risk with labor or debt holders.  Changes in operations and capital allocation could be analyzed to see how they affect that value, which would represent a sort of risk-adjusted value of the equity.

I'll also note here that this presents another way to view the effect of taxation and changing premiums on equity returns.  Just as this creates a tendency for more debt financing as base interest rates increase and equity premiums decrease (see parts 1 through 5), the usage of labor and the premium paid to labor might change with risk premiums.  As with debt, we might expect labor compensation to rise when interest rates rise and equity premiums fall.  This matches historical data!
Rates at right scale, ratios at left scale

Now, it would be difficult to establish a numerical statistical relationship here that is significant, but this is the relationship we would expect to see if we are looking at compensation through a risk-trading lens.  The current, relatively low level of compensation could be, in part, a product of low interest rates (both inflation and real) and high equity premiums.  The risk trade with compensation is mostly related to firm profit volatility.  Over time, compensation growth rates in a firm can be affected by inflation and real economic growth - wages aren't entirely fixed over time like a fixed rate bond - so it might be conceived as a sort of inflation protected, semi-floating rate security.  So, its exposure would probably be mostly related to the Equity Risk Premium (ERP), and less to the interest rate.  In fact, this is what a simple regression suggests.

At this point, this is nothing more than an indication that the data could fit the theory, because this is not a robust regression, but here is a comparison of actual compensation as a proportion of GDI and a a model of predicted Compensation, using interest rates and UERP.  Note that the actual Compensation figure tends to follow the predicted figure, with wide swings through business cycles.  Note, when actual Compensation is above the model, this is generally during downturns when unemployment is high.

We could view unemployment through this lens.  During a downturn, when there is a shock to equity values, firms become "overleveraged" with labor.  The ratio of labor value to Enterprise Value becomes too high, and firms must re-establish the labor equilibrium either through revenue growth, lower equity premiums, or higher risk free interest rates.  However, whereas with debt, firms cannot easily default; with labor, at some level of crisis, firms can "deleverage" through unemployment.

Here is a comparison of compensation, equity, and debt, over time.  Remembering the previous posts in the series, we can roughly summarize the decades:

Higher interest rates (RFR) & ERP going into the 1970s corresponds to above trend debt, below trend equity, and on trend compensation.

ERP drops going into the 1980s, which raises debt, equity, and compensation.

RFR drops going into the 1990s, which lowers debt, raises equity, and moderates compensation.

RFR drops and ERP rises going into the 2000s, which lowers debt and compensation dramatically and moderates equity values.

But, beyond these apparent relationships, when we look at compensation this way, we see that two issues with recessions: (1) the sticky wage problem and (2) the Fisher debt deflation problem are the same problem.  And the problem is essentially a cultural one.  Modern financial systems have created an economy that is tremendously efficient at trading risk.  The human demand for certainty and the local optimization that certainty allows met the modern financial system, and together they created an economy where very large subsets of the economy are not prepared to accept fluctuating financial returns during periods of manageable economic volatility.  That means that almost all of the force of volatility falls on the small group of equity holders.  And we can see this in the graph above.  Debt and labor move along in relatively straight trends, while equity bounds up and down with the business cycle.

This is well enough, as it goes.  But the problem is that unemployment and deleveraging dislocations aren't unavoidable outcomes of occasional economic fluctuations.  They are products of equity holders being pushed so far out of equilibrium value that suboptimal corporate structural changes must be instituted to regain equilibrium.  Unemployment is, to an extent, a regime specific problem.

This is one reason why policies that encourage ownership of equity are so important.  The more that economic actors can be incentivized into the residual ownership group - the group that absorbs some of the pain - the more removed the economy becomes from this regime of disequilibria.

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