Stock Market Valuation, Earnings Yield Divergence Solved - A Required Yield Theory Mechanism

Includes: SPY
by: Julian Van Erlach

Stocks have earnings and pay dividends and Treasuries pay interest which can be translated into a yield to maturity. Academics and professional investors use various metrics to assess the valuation of stocks: the P/E ratio (inverted as the E/P or earnings yield), the dividend yield, dividend discount model, and the relationship of the forward E/P to the long Treasury yield (the “Fed Model”) to name some of the most popular.

I will review the weaknesses of current stock market valuation finance theory and offer an alternative theory that both resolves them and produces the most accurate empirical result of any public domain model. The Required Yield Theory model shows that both stocks and bonds are correctly priced as a function of expected very low intermediate to long term real GDP growth. The earnings yield vs. Treasury yield divergence is caused by the capital market requirement that that the after-tax shortfall in expected EPS growth (capital gains) in relation to normal long term real GDP growth be compensated by the after-tax dividend yield.

The Failure of Modern Finance Theory

Listening to academics, stock market valuation gets curiouser and curiouser:

  • The pesky equity premium : Ibbotson and Chen, Jeremy Siegel and others posit that in the long run, the Stock Market has a risk-based real return premium over long Treasuries of a compounded 3-5%. Compound that and you go parabolic compared to GDP growth and thus GDP itself. Just how “risk” is a source of return, as opposed to growth say, is an unaddressed mystery in Finance.
  • After-Tax Return: do you care about what you get to keep to reinvest after taxes? So where’s the after-tax return in CAPM, etc.?
  • Why should the earnings yield (E/P) be anchored to the long Treasury Yield? Is there a macro determinant of both?
  • Why did the E/P and the long bond yield “decouple” after two decades of correlation and co-valuation? Why were they coupled in the first place since ANY risk premium in the stock E/P would cause it to be greater than the long bond yield. In the theoretical special case where the long term earnings growth rate would exactly equal the “risk premium”, the two would cancel and the yield would equal the long bond yield. But then investors wouldn’t want to hold bonds if they could always get this extra real return from stocks. Furthermore, why investors would price stocks differently from bonds would be inexplicable. RYT states that all assets are prices in relation to a constant: real, long term per capita productivity growth.
  • Is risk just relative volatility (beta) (and if so, how do you get a higher return, long term, just from higher relative volatility?)
  • Despite the theoretical and empirical failures, the Fed is targeting “bubbles” in assets that it admits it can’t price with tools whose effects it therefore can’t predict. Not a promising recipe.

The Required Yield Model provides the following SP500 valuation model spanning 1978-11/18/2011 with an absolute variance of < 11.4% to actual prices – which far out-performs the “Fed Model” relationship and fully explains the Earnings Yield – Long Bond Yield Divergence. The explanatory power of the model is near perfect if one removes the .COM pricing bubble period. But then, a bubble should be clearly identified as one as it is here. This model also holds for the first 80 years of the last century; explaining high dividend yields due to high marginal capital gains rates and/or low EPS growth.

(Click to enlarge)

In a previous SA article I showed how Required Yield Theory correctly values gold and provided a link that demonstrates the supporting and fully consistent novel solution to Gibson's Paradox. The current stock pricing model uses the same theory and is based on a paper published by the NYU Graduate Business School’s Salomon Center that I co-authored on stock market valuation and Treasury yield determination. A key enhancement is that I have theoretically and empirically removed any role for a risk premium (a version of which is used in the paper in a very novel way but which I now see as incorrect and unnecessary).

Data Elements

  • SP500 forward operating top down and bottom up earnings estimates
  • Dividends and estimated dividends (no estimate for dividends is provided; the author calculates one)
  • Effective marginal capital gains, income, deferred tax rates
  • Treasury yields across the term spectrum
  • TIPS yields
  • Blue Chip Inflation Rate Forecast; TIPS-Treasuries implied expected inflation

The Theory and Solutions to the Problems in Modern Finance

The Equity (Risk) Premium: there isn’t any, can’t be, and never was. Nor does the use of one add the least bit of explanatory power to the model shown. Here’s why. The academic research (e.g. 1926-1990; Jeremy Siegel) does indeed show that an investor who reinvested dividends without taxation into stocks would have earned a real compounded return over reinvesting tax-free interest on long bonds of 3-4%. This excess real equity return has been termed the “equity premium” and academics believe stems from the higher risk (relative volatility of stock returns vs. bond returns).

Before ascribing this performance to the entire stock market, one has to differentiate the dynamics driving investor vs. market returns and relate these to GDP. GDP growth is comprised of population growth, per capita real productivity growth and inflation. Population grows about 1%, and productivity long term about 2%; which gives the historically accepted real total GDP growth rate of about 3%. The total real stock market returns academics are talking about are far in excess of real GDP growth and imply that if this thinking is applied to the market as a whole, market valuation increased exponentially in relation to GDP which is counterfactual and ridiculous. So what is going on?

Shares are issued at a long term rate that approximates population growth, resulting in a constant number of shares per capita and enabling long term EPS growth of GDP per capita, which includes both real per capita productivity growth and inflation. Per share capital gains long term are delimited by EPS growth and are taxed (valuation cannot indefinitely shrink or rise for reasons shown later). Thus, after tax, real returns must be less than real per capita productivity growth. Enter dividends. Dividends and the dividend yield exist to precisely offset, after tax, capital gain taxes so that real sustainable after tax returns to capital equal long term real per capita productivity growth. Wages also increase at this rate in the long term. The return to capital and labor must equal for capital comes from labor savings. For a share to both return this amount and be affordable, its real price must also increase at this rate; which it does historically.

The equity premium arose during a period when: a) corporate tax rates fell dramatically, thus increasing retained earnings and thus EPS growth; b) the personal marginal tax rate on both capital gains and dividends fell dramatically, thus increasing valuation and deferred taxation pension plans emerged (The Revenue Act of 1978: IRC 401(k)): also increasing valuation by reducing the effective tax rate; c) tax advantaged corporate leverage as a share of total capital more than doubled, thus adding to earnings and EPS growth; d) US companies increased their share of sales and earnings from abroad, thus increasing EPS growth (SP500 has about 1/3 of revenue and nearly 50% of earnings from outside the US); and e) the quasi US gold standard until the late 1970’s imposed a Gibson’s Paradox effect on the Treasury yield making it incomparable directly to the E/P. None of these key factors are sustainable, and fully account for the observed equity premium. Academic treatments of the equity premium fail to mention or account for these crucial factors.

Even so, the premium only emerges at the investor, not market level. The stock market as whole most certainly did not exhibit anywhere near the stated premium but rather returned slightly more than GDP growth due to the above factors. Furthermore, the share issuance rate was far lower than the dividend yield which at the market level, made it impossible to reinvest all dividends. Rather, the premium accrued only to an investor who faced no taxes and was able to invest all dividends, thus increasing his share of the total market. In this working paper from U. Albany, we detail this issues and a summary of an analysis of the compound total return of the stock market and issued dividends from the Federal Reserve Flow of Funds reports since their inception, which fully support this contention.

There is no inherent, sustainable equity premium. Rather, the long bond yield has been shown in my referenced working and published papers to be such that on average, after tax and inflation, it yields precisely 2% which is real long term per capita productivity growth and also the sustainable after-tax real return per share, of the stock market, after dividend reinvestment which as I have noted offsets capital gains taxes per share. Thus, the E/P and long bond yields should equate unless other factors are present that affect asset-specific returns. The establishment of deferred tax retirement accounts in 1978 effectively equalized tax rates for stock and bond investors which brought yields closer. The full elimination of the US gold standard caused the Gibson’s Paradox bond yield effect to disappear, which also brought yields of stocks and bond closer.

Real Stock Earnings, Nominal Bond Interest and Taxation: any payout of any kind by a fiat asset is always nominal. Its valuation is subject to assessment of taxation of every cash flow so that a real, required yield after taxes is attained in relation to long term real per capita productivity growth of about 2%, which is an empirical constant. I won’t belabor the proof of this assertion here which is amply articulated in the referenced papers and incorporated in the extremely successful valuation model shown above. Both the long bond yield and the stock market E/P are determined by this macro requirement which assures the return on capital and is arbitraged continuously across asset classes globally. Stock market E/P is not set in relation to the long bond yield, but rather both are determined by macroeconomic absolutes. The highest bidder in this context is the long term investor who also divests over a long time horizon (pension fund on behalf of clients) because average return risk in relation to GDP growth is minimized and the effective tax rate is the lowest.

Why the E/P Decoupled from the Long Bond Yield: The low real after-tax long bond yield is blatantly saying that the capital markets believe that real, longer term per capita productivity growth will be severely impaired. (I will address the reasons why QE is responsible for this as well as for the high rate of unemployment in a future article) Since capital gains are determined by EPS growth in the longer term, not valuation, and in order to satisfy the Required Yield must grow at a real 2% after tax, the market is saying prospects for this are poor as evidenced by the very low long bond yield. The other prospect for stock market return is dividends. When, as in the period of the US Great Depression, EPS growth was absent or negligible, the dividend yield (rises) must make up the shortfall in return to attain the Required Yield. Thus, due to poor expected EPS growth, the market is valuing stocks so as to make up the shortfall in needed capital gains through a proportionately higher dividend yield adjusted for relative marginal taxation effects; thus raising the E/P. While a bond’s yield is its return, stock market E/P is not a return. It embodies the market’s expectations for EPS growth (capital gains which is a return) as well as balances the required dividend yield which compensates for capital gains taxation and below-normal expected long term capital gains stemming from EPS growth.


Equity valuation is driven by a principle: the requirement that capital earn an expected, after-tax real return in relation to long term real per capita productivity growth. The long bond yield is determined by the same principle. Furthermore, my referenced SA article on gold valuation shows that a Troy Oz. of gold, long term, must and does obtain exactly this same return and is priced according to the same Required Yield principle.

Current valuation of stocks, bonds is appropriate and driven by extremely low expected longer term real per capita productivity growth.

Consistently generating above-market returns is predicated on understanding both how assets are priced and in what direction expectations regarding the variables that determine valuation are likely to move. Investors who believe that growth will normalize should invest in stocks wherein both earnings growth and upward valuation of earnings would drive explosive returns if market expectations reach the same conclusion. Likewise, bonds should be sold or shorted as yields would rise due to increased expectations for real growth. Investors expecting a further slowdown would see stock market valuations decline further, coupled with possible downward revisions to EPS expectations and even dividends in a more severe downturn which would compound valuation declines. For the same reasons, bond prices would rise as real yields fall.

What is novel here is that valuation itself is a function of growth in relation to the noted productivity constant of about 2%.

Intellectual Property Notice

Required Yield Theory ™ and RYT ™ are trademarks. Required Yield Theory is patented in the U.S. under two patents (US #7,725,374, and allowed Serial No. 12/766,956); is also patent pending under several applications; and patent-pending in the EU and other political jurisdictions. Public domain formulas may not be used in computer applications without license from the author. Asset managers wishing to learn about the applications for gold, stock, bond and oil valuation may contact the author through . Formulae and data will be provided under NDA for evaluation.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.