Global Asset Prices' Common Principle:
Required Yield Theory
Christophe Faugère, Ph.D. & Julian Van Erlach, MBA
© May, 2004Many academics and practitioners share the view that since financial markets do not behave according to the most advanced theoretical models, investors must lack rationality. In fact, experience and the news media show that greed and fear seem to occupy the front-seat row in matters of stock market price determination and sometime manipulation.
Both the supply and demand sides of capital markets are perceived through the tainted lenses of either malicious or irrational behavior of market makers or investors. None of this brings peace of mind nor does it boost investors' confidence in the overall investing process. Fortunately, there is light at the end of the tunnel of confusion and despair.
While the quality of corporate information and the integrity of trading practices are legitimate issues, new research shows that the behavior of broad financial markets is marginally a function of human emotion. In fact, that behavior is governed to a large extent by unavoidable mathematical relationships - laws, if you will. Many practitioners may relate to this claim as an impossibility given the lack of success of past attempts to discover such principles. On the other hand, many more will find relief in proving to themselves that this new paradigm works.
A Clue for a Unifying Valuation Principle
Before presenting and proving a general, unified asset valuation theory, we first offer evidence that our claim holds water. The evidence is in the similarity of how multiple asset classes such as bonds, stocks and gold are priced.
Consider the following simple graph showing a close relationship between the indexed real gold price, the SP500 forward earnings to price (E/P) ratio and the 10-year Treasury yield for the 1979-2003 period on a quarterly basis.
While the relationship between the forward E/P and the Treasury yield is currently known as the "Fed Model", the link to real gold prices is new; and the relationship to a new concept: Required Yield or RY is new as well. We will demonstrate that these relationships are not accidental since they are inextricably tied to the macro economy and the ultimate driver of wealth and the human standard of living: global real productivity per capita.
Graph 1: Real US Gold Prices, Treasury Yield, the E/P and Required Yield 1979-2003
A General Theory of Asset Valuation
Straightforward intuition and logic tell us that asset prices should somehow relate to economic growth. Certainly profits and interest are generated from the macro economy. The simple formula for Gross Domestic Product or GDP growth is: Population growth + Inflation + Real Productivity per Capita (RPC). This mathematical truism tells us that on a real per-capita basis, neither wages nor capital can earn a return greater than RPC in the long-term aggregate. But what short-term effect assures that this condition holds?
In simplest terms, our Required Yield Theory (RYT) states that most major asset classes are essentially priced at a nominal yield (the Required Yield) that returns a real after tax yield equal to long-term, global, real productivity per capita. Although this rate may vary from country to country, this figure has been on average about 1.5% for the developed world (Pritchett 1997).
Irving Fisher and a Real Yield
In 1930 Irving Fisher considered the possibility of a required real interest rate. However, Fisher was unable to prove this, to derive what that real yield might be, to link it to stock return or the P/E. But, his intuition leads to an absolute truth: neither capital nor labor total real long-term compounded returns can exceed real per capita productivity. Furthermore, the mechanism that exists to always assure this is that asset prices are always priced in relation to this constant.
On our way to demonstrate this new valuation theory, we must stop and address a fundamental issue of Finance, which plays a key role in making our valuation theory come together neatly.
A Revision of Long-Term Total Equity Returns and the Equity Premium
Financial academics and practitioners generally believe that the nominal compounded total equity (SP500) return for the 75 years 1926 - 2000 was about 10.9% compared to 5.28% for 10-year Treasury average yield. The resulting apparent equity return premium of 5.6% is believed to compensate investors for the extra risk manifested in a greater relative price volatility of stocks.
The total stock return of 10.9% is comprised of a 6.42% compounded return from capital gains plus essentially 4.46% additional return due to the assumption of 100% dividend yield reinvestment and returns from dividends on dividends. GDP grew a compounded nominal 6.44% and earnings per share or EPS grew 5.05%.
By implication, total stock-related wealth compounded by 4.5% in excess of GDP for 75 years, resulting in cumulative wealth 21 times greater than GDP; an impossibility. Furthermore, profit itself cannot compound faster than GDP; yet, it must have both supported EPS growth of 5% AND dividend reinvestment in new shares of 4.5%. Therefore, it had to compound by at least 9.5%, or 3% faster than GDP.
In reality, net new shares cannot compound faster than population growth (1.2%) so that EPS compounds at the rate of GDP less share growth. Thus, 100% dividend reinvestment could not have occurred at the aggregate for there simply are not enough shares or wealth creation. Additionally, dividends must compound themselves, in addition to the initial capital investment.
The only way an investor can temporarily achieve greater than GDP compound total return is by indeed reinvesting dividends; but, this means that investor is increasing his/her market share of the total market. This is because any reinvestment of dividends is an increasing accumulation of share per capita, which means there are less shares per capita for other investors. Remember that shares grow with the population. Therefore those investors that reinvest increase their share of the total market. That process cannot continue indefinitely for they too will come to own the entire market and their return again drops to the rate of GDP growth.
Fed Funds Flows, available since 1946, provide additional confirmation. Total compounded capital gains and dividends are not merely the dividend yield added to the compound capital gain. From a starting base of stock market value and prior accumulated dividends paid, one adds the cumulative dividends paid through an ending period, such as 2003, and the value of the total market at that time. The resulting compound return must and does closely approximate GDP growth.
The inescapable conclusion is that the long-term compound return is precisely equal to GDP growth. Since shares increased at about the rate of population growth, the compound return per share is GDP - share growth or about 5.24%; which in turn is equal to the average risk-free 10-year Treasury yield of 5.28%. Ultimately, the relevant measure of return is per capita which is the same as per share.
On a per-capita basis, there is no equity premium in the long run. But what about risk? Doesn't more risk require a greater return? Consider junk bonds: they pay a higher yield but their total return, net of principal losses, cannot exceed Treasuries in the long-term. The stock market value is more volatile than the prices of Treasury bonds, but it's per share total return is not greater. By the laws of compounding, asset total return cannot exceed GDP growth in the long term.
The existence of a sustained premium of any sort creates a conundrum since compounding in excess of GDP growth is allowed, and there is inherent uncertainty as to valuation since measuring this premium has proven elusive. If there is in fact no premium in the long run, then a very precise valuation of the broad equity market, bond yield and gold price can be specified, as follows.
Our academic working papers: A General Theory of Stock Market Return and Valuation, and The Price of Gold: A Required Yield Theory, set the theoretical and empirical foundation for this article.
Our Required Yield Theory (RYT) predicts that equities are valued to generally yield a real, after-tax yield based on expected earnings and inflation equal to the long-term rate of real, per-capita productivity. For brief periods of time, stock prices may diverge from the values predicted by RYT due to the presence of short-term expectation divergence among investors. However, in the long-term, these aggregate divergences must net to zero since the equity premium must be zero.
A simple form of the resulting equation is:
Expected Equity Index Value = (Expected EPS - blended dividend and capital gains taxes)/(Expected CPI + RRY of 1.5% + Excess Treasury yield)
The excess treasury yield is present in this formula since investors price equity so that it gives them the highest return between a current T-Bond and the real long-term productivity per capita.
The widely used but academically shunned "Fed" Model simply compares an equity index earnings yield to the 10-year Treasury yield without accounting for tax differences, EPS growth, real yield, or the so-called equity "risk" premium. RYT provides a theoretical basis for both T-bond yield and stock market yield; not stock yield in terms of bond yield.
Graph 2 compares the actual SP500 P/E based on forward EPS quarterly for 1970 - 2003, adjusted for changing income tax rates, to the RYT-predicted P/E which is essentially 1/(Expected Inflation + R) where R is long-term real productivity per capita of 1.5%.
Graph 2: RYT-Predicted and Market Forward P-E 1970-2002
Compound long-term total real stock return per aggregate share cannot exceed real long-term per capita productivity and is generally priced to yield this return based on expected inflation, taxes and earnings. Real bond yield cannot exceed productivity either; or it becomes impossibly decoupled from real GDP growth per capita.
Thus the standard risk-free 10-year Treasury yield should comprise that nominal return which after taxes and expected inflation yields the long-term, per-capita productivity rate. At (capital) risk bond yields must in addition include an expected default premium plus administrative costs of the debt issue (declining over history due to automation). Note that at-risk bonds cannot yield more than treasuries in real, after-tax terms in the aggregate, and after defaults net of recoveries and related costs, else this return too would impossibly decouple from real GDP.
An 18-year quarterly depiction of the nominal 10-year Treasury yield is shown below compared to the RYT-predicted yield taking into account expected one year forward inflation and averaged capital gain and income taxes (at the highest marginal rate then in effect). The result for the period of 72 observations is an absolute average variance from actual yield of less than 6.5%.
Graph 3: RYT and 10-Year Treasury Yield 1985 - 3/2003
Gold has been the symbol of wealth and adornment for millennia. Indestructible and beautiful, it serves as ornament, currency and shelter in turbulent times. Yet, there is no formal theory that explains its value.
Many researchers show that gold and stocks exhibit virtually no correlation. Furthermore, as a store of real value, gold has not done well in the last 25 years; having fallen in both nominal and real terms while the CPI more than doubled.
But this makes sense in light of RYT. The link between RYT and gold, and therefore stocks and bonds is subtle but direct. RYT states that for gold to be a store of value its real price must vary inversely to the stock market P/E and the yield on T-bonds. While gold is a pure store of real value, stocks experience growing real earnings (equal to productivity), gold experiences zero real price change in the long term. Nevertheless, the required yield governs the real gold price in the same way that it governs the market P/E.
Essentially, as asset prices change due to a changing RY, gold remains constant, but its real price in terms of depreciating or appreciating financial assets changes. In Graph 4 we show the indexed real price of gold vs. RY and the US dollar against a basket of major currencies. USD-denominated gold price is only affected by a foreign exchange basket when that basket shifts in value for reasons other than relative national RYs. The US RY alone accounts for more than 85% of the variation of the real domestic price of gold. RY and FX effects together explain more than 92% of the change in the real price of gold.
Graph 4: RY, Real Gold
RYT also requires that the global amount of gold per capita remain essentially constant and that gold, as a share of total wealth, must decline in real terms at the rate of productivity growth.
Graph 5: Indexed SP500 Forward E/P vs. Real Gold Price, Quarterly, 1986-2004
Since the gold/silver price relationship is quite stable, we posit that RYT holds for silver valuation as well. Graph 6 shows the indexed nominal gold and silver price relationship.
Graph 6: Gold and Silver Indexed Nominal Price Relationship
We have briefly demonstrated a global, general theory of asset valuation that links asset prices to the macro economy, solves the equity premium puzzle, makes falsifiable predictions about asset prices and yield, given macro economic expectations, and is readily reproducible.
Our review of aggregate, per capita long-term total returns has shown that both stock and bond returns were equivalent, and equal to GDP per capita on a pre-tax basis. However, since the early 1980's, empirical evidence shows that 10-year Treasuries have yielded a nominal return that results in an essentially constant 1.5% after-tax return. This requires that the nominal pre-tax yield exceed GDP per capita.
We believe that bond investor sophistication has increased over time, and that the government recycles interest taxes to pay the yield in excess of GDP per capita. Private borrowers however, must pay this yield out of profits. Secondly, we believe that this yield results from arbitrage with the total equity return available to an initial investor who obtains both stock capital gains and dividends when making his or her first investment in stocks. This effect results in a temporarily greater than aggregate pre-tax compound return to initial investors only. It is precisely this effect that investors have recognized and required of the bond market in recent decades, making borrowing more expensive.
RYT is a foundation for a stream of new research based on these principles. Fundamental market dynamics may now become comprehensible to all investors who will grow more comfortable in managing their savings. Policymakers may now rely on these tools to improve their stewardship of economies. What once seemed mysterious becomes familiar…and manageable.
About the Authors: Christophe Faugère, Ph.D. is Assistant Professor of Finance at the State University of New York at Albany Business School; and Research Associate at the Center for Institutional Investment Management. Julian Van Erlach, MBA, is CEO of Nexxus Wealth Technologies, Inc.
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