Why There Is No Inherent Equity Premium: The Total Market Return vs. the Per Share Return

Julian Van Erlach

Nexxus Wealth Technologies, Inc.

November 30, 2015


The Equity (return) Premium is shown to emerge fully, specifically and episodically from just three transient factors: EPS growth above long term GDP/capita growth; after tax long bond yield below GDP/capita growth, and change in P/E (valuation) – without a risk premium. The earnings/price (E/P) ratio is shown to lack an embedded premium and appears anchored to GDP per capita growth. An aggregate stock market after-tax return model is proposed that balances return with GDP growth; which existing models do not. Long term investors (IRA, 401k, endowments, buy and hold strategies and pension plans) have no historical negative return risk over their investment-divestment horizon, enjoy the lowest effective tax rate, are the largest equity holder block with common economic attributes, and may therefore determine valuation by being the highest sustainable bidders.

Why There Is No Inherent Equity Premium: The Total Market Return vs. The Per Share Return – Introduction

This paper shows that apart from a rising price-earnings ratio (P/E) which is an obvious but transient source of the equity premium (EP), the EP emerges only when, and to the extent that, one or more of the following hold: EPS growth is above its long-term average equal to GDP per capita growth, the after-tax long Treasury bond yield is less than GDP per capita growth. The relationship of both EPS growth and long T-bond yield to GDP per capita growth is theoretically and empirically discussed in Faugere-Van Erlach (2009) and is therefore beyond scope here; but serves as a basis for findings. Faugere-Van Erlach make the case for EPS growth delimited by GDP per capita growth and after tax long bond yield generally resolving to long term GDP per capita growth when market forces apply.

It can be argued that if an arbitrary benchmark was chosen in relation to which EPS growth and bond yield are both measured, a respective divergence would also correlate to the equity premium. However, both the correlation and magnitude of change are essential and cannot both happen without at least a large determining role played by growth. This paper shows that both hold when the association is made to GDP growth; and that use of the pre-tax EPS growth (capital gains proxy) and after-tax bond yield are necessary for reasons explained in the next section. Any other benchmark results in degraded correspondence of values between the actual and expected equity premium.

Relating the EP to GDP growth raises two fundamental questions. First; the accepted measure of the equity premium return is much greater than GDP growth. Thus, there does not appear to be a reason from this viewpoint that the EP should be a direct function of GDP growth alone. Second, standard Finance theory holds that the EP to bond yield is a major determinant of the equity premium as compensation for greater return risk stemming from price volatility. For these reasons, the findings in this paper are unexpected and changes in the risk premium should appear as discontinuities in either or both of the specified correlation or its magnitude if a risk premium is operating. However, no such effect is found.

This paper begins by showing that the accepted measure (per share capital gain plus fully reinvested dividend yield) of the EP return, and its implication for stock market wealth accumulation, cannot be reconciled with GDP growth on either a before or after-tax basis due to both magnitude and infeasibility of full dividend yield reinvestment at the market level in much slower new share growth. However, the aggregate stock market return can be reconciled with GDP growth. The second section shows that the long term equity investor faces no return risk and enjoys the lowest effective tax rate, represents the largest shareholder block as defined by common economic attributes, and thus may arguably be the highest sustainable bidder. This obviates the impetus for a risk premium and sets the stage for why the EP should be a function of EPS growth and bond yield divergences from GPD per capita growth alone.

Third, the E/P or valuation of the stock market is shown to be directly related to pre-tax GDP per capita growth with no embedded risk premium. Thus the after-tax expected return equates to long term nominal growth per capita. The last section shows how the equity premium is determined from P/E change, earnings growth and bond yield inverse respective divergence from GDP per capita growth. An explanation for the variability of the P/E is offered by Faugere-Van Erlach (2009).

Equity Premium

Equity Premium
Exhibit 3: Total US Stock Market Value vs. GDP 1946-2000

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