**Overview**

The most important topic in finance, and for investors, is valuation: how and why it changes.

This article shows theoretically and empirically that there is a scientific universal valuation principle linking at least the stock market, bond yield and gold to the macro economy through real per capita GDP growth. It is based on four published peer-reviewed finance journal papers, several patents (the only ones issued for an entirely new valuation mechanism) and a number of related articles. Unlike CAPM, discounted cash flow and related models, this principle is highly empirically successful (90%+ valuation accuracy over multi-decade time periods), directly links asset valuation and return to GDP growth, and uses no "risk" premium or necessary reference to Treasury yields.

My purpose is to encourage scientific discussion and investigation that goes beyond mere correlations and addresses the necessary linkages among GDP growth, tax and inflation targeting policy, monetary policy, and asset valuation and return. Also, to enable investors to assess the factors that impact stock market and gold valuation, and bond yield determination.

## Current State

For stocks, it's all about what causes the price/earnings ratio to change, and its inverse, the earnings yield. The Treasury bond yield is thought to be generally controlled by the Federal Reserve at the short end; combined with inflation and real growth expectations at the long end. There is no accepted valuation mechanism for gold; and many notable investors, including Warren Buffett, denounce any economic role for gold.

All stock valuation models hold that the earnings yield must be made up of some combination of the risk-free rate (Treasury long bond yield) + a premium for risk of relative equity return volatility.

- How all this links to GDP growth is not in the models
- Nor are effective tax rates
- Nor is it shown how risk can drive return (as opposed to growth which certainly does drive return e.g. EPS growth)
- The risk premium is estimated for the future and measured ex-ante; but there is no formal model of precisely what factors determine its magnitude or cause it to change
- Academic studies show that total equity return (capital gains + dividend yield) far exceed not only Treasury yields but also GDP growth itself (Shiller, Siegel, Ibbotson and Chen)
- How stock market return can vastly exceed GDP growth is never explained
- None of these models actually work: they don't model the actual value of the stock market well. See Eugene Fama and others on the failure of CAPM.
- Even Ed Yardeni's proposed "Fed Model" has long since broken down (this tries to link the T-bond yield to the earnings yield).

For these reasons, various historical and statistical studies of the P/E are tracked such as Shiller's CAPE measure. There are no theoretical or empirical models of precisely what factors determine the P/E other than ex-ante measures of the "risk" premium. Hence appeals to "animal spirits" (in investors) by Shiller, Keynes and others.

All of this leaves Finance and Economics as social, not hard sciences because no actual principles have been discovered underlying the mechanics of asset valuation and return.

**The Evidence of a Universal Valuation Principle**

Stock Market

How does the observed pre-tax return comprised of capital gains + dividend yield at the investor level compare to the actual *entire* stock market return? Does the whole stock market return match that of an investor reaping capital gains and fully investing dividend yield? What is the role of dividends and why and under what circumstances are they paid?

Stock market return findings from Siegel, Ibbotson and Chen and others show compounded 1926-2000 returns of about 11% compared to GDP growth of 6.5%; which would imply the market return exceeded GDP growth by a cumulative 17.5X! Did this really happen?...no, it did not at the whole market level.

The equity (RISK) premium of about 5.4% is calculated from an average long T-bond yield over the period of about 5.3%. Standard Finance theory holds that this equity premium is due to the higher risk (volatility) of stocks vs. Treasuries.

Using Fed Funds Flows data available from 1946, the value of the entire stock market compared to GDP is constant except for changes in the P/E. The stock market is comprised of existing shares + *net new share *growth.

Fig. 1: Stock Market vs. GDP 1946-2000 vs. P/E

Source: author

Of course, if a single investor owned the entire stock market in 1946, their dividend yield could only be reinvested in net new share formation. What is the rate of net new share formation vs. dividend yield?

Two approaches provide the same answer: about 1.1%, which is the same as population growth. Standard & Poor's has limited data which approximates this share growth rate. A more complete answer can be arrived at be examining the value of the entire stock market, EPS growth and GDP growth.

GDP growth is comprised of inflation, population growth and real per capita productivity growth. Now, EPS growth, net of US foreign investment and earnings therefrom; and foreign investment and market share growth in the US; exactly matches GDP per capita growth.

Fig. 2: EPS and GDP per Capita Growth Indexed to 1926

Source: author

Since the ratio of the entire market value to GDP is constant except for P/E change which cannot indefinitely move in just one direction (Fig. 1); and EPS growth = GDP/capita growth; then net new share growth MUST equal population growth. This is true for many reasons: net new investors emerge at the rate of population growth and must have new shares to buy; if shares grow much faster or slower than population growth than EPS growth would be slower or faster than GDP growth, creating a major imbalance between growth and capital formation.

Further evidence that the value of the stock market is bound by GDP is found by looking at the ratio of corporate net worth at market value to GDP; which is constant. Corporate net worth includes retained earnings; where the dividend payout ratio over time is relatively constant. Thus, the market value of retained profits grows with GDP; which includes all new companies formed.

Fig. 3: Corporate Net Worth at Market vs. GDP

Source: author

Of the 4.2% pre-tax average dividend yield 1926-2000; only 1.1% could have been reinvested in net new share formation; with the balance accumulating as a cash pool. After accounting for capital gains and dividend tax (two tax layers vs. one for bond interest) and the feasible dividend reinvestment, the equity premium to GDP growth is eliminated and the premium to the long T-bond yield is greatly reduced.

Some academics have tried to argue that stock returns are real while the bond yield is nominal; but both returns are certainly nominal: EPS and dividends are both nominal quanta paid in fiat money which loses value at the rate of inflation; just like bond interest.

At the market level, after tax dividend yield covers capital gains taxes, leaving nominal EPS growth as the sustainable after-tax nominal investor return. EPS growth of course equals GDP/capita growth which is inflation + productivity (real per capita GDP) growth. This fully balances stock market return, GDP growth and taxation; and leaves real per capita productivity growth as the real long-term after-tax return to investors (which is also the same real return to labor). Return on capital and labor must balance since income growth is the largest source of investment capital.

Many studies show that long-term real per capita GDP or productivity growth is a constant (about 2%): e.g. Pritchett.

Individual stocks cannot be valued differently from the market as a whole. The question is how? How is the marginal equity bid formed and who dictates it?

Without perfect ability to predict stock market movements, the highest possible marginal bidder must be the long-term investor-divestor because: a) they face the least return variability risk over their long horizon; and b) have the lowest effective tax rate. However, they can only be assured of obtaining a real, after-tax return equal to long term real per capita productivity growth IF they ALWAYS bid so as to obtain a real, expected, after-tax return given each current set of market expectations about inflation, EPS growth, GDP growth and effective taxation….that is: in relation to a macro-economic constant.

The valuation model (Fig. 4) based on this is 92% accurate using only point-to-point market expectations about the above variables since 1970 when reliable data became available. A related paper was published from NYU by a co-author and me showing precisely how and why this theory works for stock market valuation and Treasury bond yield determination. Since then, I have enhanced this model to show the effects of long-term sub-par expected real GDP growth and the market requirement to offset lower expected real EPS growth through a higher required after-tax dividend yield to obtain a 2% real after-tax return.

This latter effect also explains why the "Fed Model" has failed and why similar comparisons between long T-bond yields and the E/Y or earnings yield have diverged since long term real growth expectations have fallen.

Fig. 4: The Required Yield (RY) Valuation Model vs. SP500 1970-4/2019

Source: author

Bond Yield

The intermediate to longer term T-bond yield is a direct function of GDP/capita growth and effective tax rates as figures 5 and 6 show; using Federal Reserve data. Especially notable is the real after-tax yield compared to real per capita GDP growth (Fig. 6).

The above-referenced paper shows how the T-bond yield is determined through the relationship between short to intermediate term real per capita growth expectations vs. long term growth.

Fig. 5: GDP Growth vs. Long T-Bond Yield

Source: author

Fig. 6: Real GDP/Capita vs. Real After-Tax T-Bond Yield

Source: author

Return on capital, equity or debt, is determined by GDP per capita growth. Because stock market investors who comprise the bulk of investable capital, the long-term investors, have a much longer investment-divestment horizon (50+ years) than even long T-bonds (20-30 years); they can be assured of obtaining on average the long term real per capita productivity rate of about 2% after tax. This is less certain over bond term horizons, and therefore the after-tax real bond yield will generally be less than the after-tax stock market long term return.

Thus, there is an equity return premium; but not an equity risk premium.

Since the 2008 Financial Crisis, central banks have purchased bad loans that should have been allowed to default and reduce the pool of capital; increasing their assets from just over $3T in 2007 to over $14T. By comparison, total world non-financial bond debt is estimated to be $187T by the Institute for International Finance. This is over $22T of incremental capital created (at least $11T that should have disappeared + $11T of new debt to buy it)…not counting cross-defaults that would have materialized.

This $22T of marginal debt created since 2008 could be as much as 30% of total non-financial world debt growth. The surplus of capital necessarily reduces the return on capital from future growth; thus causing abnormally low bond yields that we are seeing now. Furthermore, the low real return on capital must spill over to the return on labor and real economic growth - both of which are far below historical rates and expected to remain so long after the 2008 crisis.

Gold

Gold has no apparent interest or dividend stream payable in fiat money - so, the academic and financial communities have no mechanism to assess its actual value or even relative value. Former Fed Chair Ben Bernanke has publicly told Congress that he and the Fed economics teams don't understand how gold is valued.

Nothing has changed.

How is the value of fiat money determined? We know that its purchasing power falls with inflation. Fig. 7 shows that the ratio of M3 (a no longer published broad measure of money supply) to real GDP closely correlates with the CPI (consumer price level - a measure of inflation increase) …and arguably causes it.

Thus, the excess of money creation by the Fed vs. real goods and services growth determines the rate of inflation or purchasing power loss.

Fig. 7: M3 to Real GDP Ratio vs. CPI

Source: author

What about gold? Fig. 8, based on data I have compiled, shows the same relationship holds true for gold. This data covers the pure world gold standard when there was a calculated world price index in terms of gold.

Fig. 8: Gold Standard World Price Level vs. Above Ground Gold Stock/World Real GDP Ratio

Source: author

However, the total above ground gold stock grows with population growth (for reasons I won't go into here); which means that world GDP increases at the rate of world GDP/capita per unit of gold; or at real per capita GDP growth per unit.

Some researchers claim that gold is merely a constant real store of value: Roy Jastram and the World Gold Council and Erb and Harvey.

However, they study the price and purchasing power of gold in terms of British and US currencies (Fig. 9); not in terms of global purchasing power. For the periods in question:

Fig. 9: Purchasing Power of Gold in US and UK Currency 1560 - 2008

Source: Jill Leyland in the LBMA's Alchemist Issue 56

But, these currencies appreciated against other currencies because Western Europe/England and the US more than tripled their shares of world GDP:

Fig. 10: Country and Regional Share of World GDP 1500 - 2005

Source: Ian Bremmer of Eurasia Group Working Paper

Therefore, in order for the purchasing power of gold to have remained constant in UK and US currency terms, it must have greatly appreciated in global purchasing power.

Let's now look at a very famous pure World Gold Standard phenomenon: Gibson's Paradox. In so doing, it will become very evident that gold inherently obtains a real yield (growing share of world goods and services per unit) …just as fiat currency inherently obtains a negative real yield (falling purchasing power) due to their respective stock to GDP relationships.

Gibson's Paradox

John Maynard Keynes coined the term Gibson's Paradox as being one of the most important unexplained phenomenon in all of Finance and Economics. Standard Finance theory states that the rate of interest should vary directly with the expected rate of inflation - not the *level* of prices. However, during 1820 to about 1910, the British government's consol bond - a perpetuity paying fixed interest-only and convertible into a fixed amount of gold during an era when currency was fully convertible to gold at a fixed rate, paid a yield that varied directly with the national general price *level* (and even more so with the global price level). (Fig. 11)

Fig. 11: from Barsky & Summers' "Gibson's Paradox and the Gold Standard" here. World Price Level Co-Varies with the UK Consol Yield

Source: Barsky-Summers (1988)

The observation is a paradox because a constant expected general price level implies zero inflation and thus should cause a fall in interest rates from a prior period of positive inflation expectations. Under the gold standard, a constant price level did not influence the yield of the consol. The consol yield varies with the price level; thus, a doubling of the CPI doubles the yield and so on. A flat CPI - zero inflation - surprisingly, leaves the consol yield unchanged.

A number of eminent scholars have addressed Gibson's Paradox including Irving Fisher, Thomas Sargent, Robert Shiller and Jeremy Siegel. Among the most notable is the work of Robert Barsky and Lawrence Summers in their "Gibson's Paradox and the Gold Standard" paper (1988). They posit that gold prices varied inversely with changes in real interest rates - which effect, however, they cannot consistently find under fiat monetary systems as they state in their paper. Under their theory, real rates first change, then impact the price of gold, which then translates to a change in the price level in terms of gold.

Barsky-Summers view the nominal rate as essentially the real rate because of the lack of serial correlation of inflation and because nominal rates showed no predictive power for future inflation; thus, they assume no inflation premium was embedded in nominal rates; making them essentially real. Therefore, they assume that a rising consol yield was evidence of a rising real required interest rate which in turn caused gold, which they viewed as a durable good, to fall in price because of the rising return available from alternative competing assets.

However, Fig. 8 shows that the *world price level; and thus consol yield*, were in fact a direct function of gold stock and world GDP - totally independent of any real interest rate causality. A close look at the yield in terms of purchasing power evidences a constant real yield in terms of purchasing power of the interest payment in relation to the nominal consol price (Fig. 12).

Fig. 12: Gold Standard Relation of Price Level, Consol Yield and Purchasing Power of Consol Interest to Price Expressed as a Yield

Source: author

Note that if a 2% consol yield at time 0 (price level of 100) bought 2 units of goods and services (a 2% real yield in terms of goods and services) and the price level doubled to 200, the nominal yield doubled to 4% because the consol price fell in half; but the purchasing power of the fixed interest fell in half as well; which left the real yield a constant 2% (1 unit of goods and services purchasing power over half the price (50) as before). If in fact gold is *required* to obtain a real *inherent* yield equal to its long term average of about 2% which is the long term rate of real per capita growth, then a constant new doubled price level results in a doubled nominal yield in order to maintain the required constant 2% real yield. The logic holds for any combination of price level and associated consol yield where the price level is a function of gold and real GDP.

For gold to have a real yield (growing share of global goods and services) equal to long term real per capita productivity growth, the world price level in terms of gold must be *falling* at the rate of per capita productivity growth. Thus, a *constant* price level means gold is *failing to earn its required return* and so the yield of the consol cannot fall. This is because gold must *inherently* obtain a real yield; in contrast to fiat investment instruments which must pay fiat money interest or dividend payments or a growing share of equity earnings in relation to which price is set. A fiat perpetual bond, if it is to offset purchasing power erosion of the principal due to inflation, and earn a real after-tax return of say 2%; must yield (2% + i)/(1-t) where (I) is the expected inflation rate and (NYSE:T)) is the effective tax rate.

During the Gold Standard, the valuation of gold was clearly based on the requirement that gold earn a constant rate of growth of real yield; which is a growing share per unit of goods and services (the constant rate being long term real per capita productivity growth). Building upon this, a very effective theoretical and empirical gold valuation model in terms of fiat currency can be built. Gold is valued according to at least five functions:

- Gold's cumulative real value results from its cumulative above ground stock relationship to world real GDP;
- Its cumulative additional nominal value derives from world fiat inflation;
- A change in fiat inflation expectation should result in a directionally consistent and proportionate change in gold price in fiat currency since gold's real yield is unaffected by fiat inflation;
- A change in medium to long term market required real yield in relation to 2% (the long term real per capita productivity growth rate and long-term real gold yield) should cause an inverse proportionate change in gold price;
- The local or national gold price should also be an inverse function of changes in the global GDP-weighted real purchasing power of the local currency

This resulting model is shown in the author's recent Jrl. of Investing paper (Fig. 13)

Fig. 13 Required Yield Model of Gold Valuation 1978 - 2015

Source: author

This model exhibits an average absolute variance from 1978 - 2015 of 12.02% with R-squared of .967; and 8.3% absolute variance from 2005 to 2015.

An earlier though incomplete model of gold valuation co-authored by the author with Dr. Christophe Faugere demonstrates the same principle determining the stock market P/E and the valuation of gold in a 2005 paper Price of Gold Jrl. of Investing.

The model in Fig. 13 states that the change in gold price must be according to the formula:

- Pt+1/Pt = (It+1/It) x (G
_{wr}/A_{s})t+1/(G_{wr}/A_{s})t x 1/(Y_{r}t+1/Y_{r}t) x 1/(Ct+1/Ct) x (R_{y}t+1/R_{y}t) - Where:
- P is the local price of gold at a time (T); I is the world consumer price level;
- (G
_{wr}/A_{s}) is the ratio of world real GDP to the world above ground gold stock; - Y
_{r}is the world tax-adjusted real intermediate to long term real after-tax interest rate; - C is the domestic real exchange rate in terms of world purchasing power;
- R
_{y}is the world required yield where R_{y}= (r + i)/(1-t); where r is the long term real world GDP per capita growth rate, i is expected world inflation, t is the effective weighted tax rate on investment income and return. The R_{y}assures an expected after-tax real return equal to at least world long term real per capita GDP growth (Faugere-Van Erlach (2009))

How All Three Assets Relate to GDP Growth

Fig. 14: Equivalency among GDP, Stock Market, Gold and Bond Yield

GDP | Stock Market | Gold | T-Bond Yield |

Population Growth | share growth | above ground stock growth | |

Inflation | EPS growth | inherent price appreciation/purchasing power growth | yield determined based on expected GDP/capita over bond term/(1-tax rate) |

Real per Capita Productivity | |||

after-tax dividend yield covers capital gains tax |

Source: author

The above diagram shows how the components of GDP growth map to the attributes of each of the stock market, gold and bond yield. All three, through their respective attributes, are valued in relation to a macro-economic constant of about 2%: long term real per capita productivity growth.

The body of work referenced here proves this theoretically and empirically with the most accurate asset valuation models in print to the author's knowledge.

Why Valuation Changes and Today's Stock Market and Gold Price

Stock Market

The stock market P/E moves inversely with the expected inflation rate and with changes in effective investor taxes (so that a constant real after-tax earnings yield is maintained). It also moves directly with intermediate term expected GDP growth resulting in below 2% real per capita GDP growth - meaning, the P/E falls enough to cause the after-tax dividend yield to compensate for the expected shortfall to the 2% long term growth of real per capita productivity. This is happening now.

Gold

The world price of gold generally rises at the rate of world per capita GDP growth. Its value moves directly and proportionately with changes in the expected inflation rate through the Required Yield mechanism; inversely with local GDP-weighted currency and inversely with the real economic yield as evidenced by expected intermediate real per capita GDP growth or TIPS yields.

Both the stock market and gold are correctly valued based on current macro-economic expectations.

Intellectual Property Notice

Stock market valuation and bond yield determination patent rights are protected by patent 7725374B2.

Gold valuation patent rights are protected by patent 8095444B2

Other patents covering all three asset classes are pending.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.