Thursday, July 10, 2014

Risk & Valuations, Part 8: Beta has its own alpha.

Think of any investment valuation as a sum of discounted cash flows of the form a sum:

x = cash flow in time, t
y = interest rate

Over time, short term bills, which have very little exposure to changes in rates and no exposure to cash flow volatility, have tended to have a small positive return.  Longer term fixed rate bonds have a maturity beta.  They tend to earn more because of their exposure to interest rate volatility.  But, cash flow remains stable.

The equity premium comes from exposure to Cash Flow fluctuations.  The CAPM model, in its simplest form, is summarized by this equation:

It is an estimate of the required return of a given equity.  Theoretically, if we have two firms with exactly the same operational expectations, but different levels of leverage.  Investors could mimic the investment of the most leveraged firm by leveraging their own portfolio and investing in the least leveraged firm.  So, there should be a tendency for arbitrage investing to push equities toward prices that reflect their relative market-related volatility.

Some research has found an anomaly where low beta stocks seem to outperform high beta stocks, at least on a risk adjusted basis. In other words, returns may not correspond to beta on a full 1:1 basis.  I think there are several issues at play here.  Equity premiums are hard to pin down.  I think some of this anomaly tends to go away when long duration risk free rates are used, instead of short term rates.  There have been long periods with high equity premiums and long periods with negligible equity premiums, depending on how you measure bond returns.

But, I would like to propose a theoretical explanation for at least part of any anomaly that might exist.  Going back to Part 6 of this series, I want to reintroduce the idea that there is a sort of regime shift that happens when we move from a context of uncertainty to a context of certainty.  In a context based on nominal certainty, functions can be optimized to a very high degree.

I don't know if this is too obvious to require an example.  But think of a calendar.  If you have a job that requires you to be on call, your entire schedule must be tentative.  If you have a job with broad deadlines and the ability to be flexible, then planning that 2 week long trip to Seattle is a lot easier to do.  Household income has the same effect.  The budget process for a household with salaried professionals can be much more precise than the budget for a household with a sole proprietor's income.  As long as the context is stable, this certainty allows for much more rational and optimal behavior.  The certainty itself provides value.

So, moving from bonds to equities moves us from a context where there is exposure to just one variable (interest rates) to a context where there is exposure to two variables (interest rates and cash flow).  In both bonds and stocks we can see a discrete payout for this added exposure above and beyond the proportional level of the exposure.

So, even adjusted for inflation, short term bonds, over time, have provided a premium over cash, plus they have provided a maturity premium that relates to their exposure to interest rate changes.  In other words, bond returns have an alpha and a maturity beta.

I want to suggest that equity also has an alpha and a beta.  So, properly rendered, CAPM should have a third variable, which is the Equity Alpha.  This is the added return one earns simply for stepping into the world of unknown cash flows and unsecured existential risk.  This premium would apply equally to all equities.  In addition to this premium, then, equities would also have an Equity Premium beta, which would relate to their proportional market risk.

In the hypothetical world of identical equities that can be arbitraged, this alpha would seem to be bid away.  But, in the actual world of investing, it is not difficult to imagine a discrete set of risks that come from life as a stand-alone firm, that would exist in a constant form, somewhat unrelated to temporary fluctuations in market values.  So, before adding factors to the CAPM model, I think that to be properly specified, it might need to look like this:

The expected return on an equity would consist of the alpha return on discount rate risk (short term risk free rates), plus the return on maturity risk (risk free duration premium), plus the equity alpha (cash flow risk), plus the equity beta (proportional volatility risk).
None of this is particularly complicated.  But, it does provide a method for accounting for risks that aren't proportional.  In addition to discrete, firm-based issues, a low equity beta increases an equity's proportional reaction to changes in other variables, such as real rates, growth expectations, and changes in beta.  Many types of risks might be accumulated within the Equity Alpha.

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