Gold Valuation Solved                            (& Gibson’s Paradox)                A Required Yield Theory ™ Mechanism  ...
The RYT GOLD Model• The model is not a fitted regression or error correction approach, but ratherbased on absolute theoret...
RYT GOLD Valuation•   The major novel advances from the conclusions reached in the referenced paper are: a) that    gold i...
RYT GOLD Valuation•   Data Used     – IMF World GDP Forecast; Actual GDP Growth; World Population: World Bank &       Madd...
Gibson’s Paradox Solution•   The solution is essential to understanding that: a) gold has a real yield; b) assets are pric...
Gibson’s Paradox Solution•   The observation is a paradox because standard Finance theory states that the rate    of inter...
Gibson’s Paradox Solution•   Investigators compute the real rate of interest essentially by subtracting the actual    or p...
Gibson’s Paradox SolutionTable I: Real Yield of Consol in Terms of Purchasing Power of Interest to NominalPrice           ...
Gibson’s Paradox Solution•   A fiat perpetuity is priced in a manner wherein the principal does not inherently    obtain t...
Gibson’s Paradox Solution•   For example, if the price level doubled and remained there (no inflation) the yield of the fi...
Gibson’s Paradox Solution•   Graph II: The British and world general price levels were determined according the QTM: the  ...
Gibson’s Paradox Solution•   For clarity, all three series, the world price index, the consol yield and the ratio of world...
Gold Valuation in Fiat Currency•   One issue with the Barsky-Summers analysis, and that of others addressing Gibson’s Para...
About•   Mainstream asset pricing theories are empirical failures (CAPM, APT, MPT, NPV etc.) as they    fail to describe h...
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Gold Valuation

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Gold Valuation Mechanism Discovered, Patented - A Required Yield

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Gold Valuation

  1. 1. Gold Valuation Solved (& Gibson’s Paradox) A Required Yield Theory ™ Mechanism www.RequiredYieldTheory.com• Required Yield Theory.com and its Nexxus Wealth Technologies, Inc. consulting and IP licensing arm announce the solution to GOLD valuation/Gibson’s Paradox and its forthcoming 12/2011 issuance of the first ever gold valuation patent; adding to its asset valuation portfolio. RYT ™ models gold, shown here in USD$ with < 16.4% absolute variance including its late 1970’s rise, fall, subsequent decade-long flat- line performance and recent parabolic rise. Bar none, this model is the most accurate and theoretically robust in the world. 1
  2. 2. The RYT GOLD Model• The model is not a fitted regression or error correction approach, but ratherbased on absolute theoretically derived macro economic principles that operateupon real-time public domain macro economic variables and asset-specificcharacteristics such as total above-ground world gold stock, expected world GDPgrowth and inflation• The model has been partially disclosed in the referenced patent and in a paperpublished in the Jrl. Of Investing• Gold’s value is determined by its unique relationship to world GDP: the supply ofgold does and must increase, long term, at the rate of population growth whichmeans that the above ground gold stock is constant per capita; and that worldGDP grows per Troy Oz. at the rate of GDP/capita/oz. 2
  3. 3. RYT GOLD Valuation• The major novel advances from the conclusions reached in the referenced paper are: a) that gold is more than a constant real store of value; b) that gold therefore has a real yield; c) that real, after-tax interest rates must therefore affect the price of gold in fiat currency; d) that RYT both predicts and solves Gibson’s Paradox.• This directly means that gold does have an economic yield per Toz. of world real and nominal GDP/capita/oz. Fiat currency has a yield of minus the inflation rate. Thus while the purchasing power of gold increases at the rate of world real GDP/capita against a basket of world real goods and services; fiat currency loses purchasing power at the rate of inflation. This condition sets up an exchange rate between gold and fiat currencies.• Furthermore, that because gold has a yield, like a bond, its price in fiat currency is also a function of the real yield required by capital markets. In the long run, gold returns are equal to those of the long Treasury bond and the stock market on a per share basis. (RYT has shown that the equity “risk” premium was caused solely by transient, non-sustainable factors)• As demonstrated in the referenced paper, the real gold price is also a direct function of the nominal fiat pre tax Required Yield as defined in that paper: the pretax fiat nominal yield required to return at least an expected real, after-tax return equal to long term, real, global per capita productivity growth; a constant in the range of 1.5% to 2.1% which is the real, after-tax Required Yield 3
  4. 4. RYT GOLD Valuation• Data Used – IMF World GDP Forecast; Actual GDP Growth; World Population: World Bank & Maddison World Data – IMF World Inflation Forecast; Actual Inflation Rate – World Gold Above Ground Stock; Mine Production: World Gold Council – US Exchange Rate: DXY and related measures – Treasury yields across the term spectrum; US and World – TIPS yields – Blue Chip Inflation Rate Forecast – Effective marginal capital gains, income, deferred tax rates 4
  5. 5. Gibson’s Paradox Solution• The solution is essential to understanding that: a) gold has a real yield; b) assets are priced in relation to a real, constant quanta (real, long run per capita global productivity growth (The Required Real, After-Tax Yield) of about 2.1%; c) including gold, the stock market, bond yield determination and the pricing of oil.• It is generally held that gold earns no inherent economic return – thus, one holds it at the expense of earning interest on a bond, or dividends and capital gains from stocks. An analysis of gold and bonds during the pure British gold standard (1821-1913) proves that gold does indeed earn such a return and is priced accordingly. Moreover, that this required yield or return, in real terms, appears to be a macroeconomic constant stemming from gold’s unique relationship to world GDP growth.• Background of Gibson’s Paradox: the Price of Gold Under the Pure Gold Standard• The British government’s consol bond traded freely – a perpetuity paying interest-only, convertible into a fixed amount of gold during an era when currency was fully convertible to gold at a fixed rate. Consol yields varied directly with the national general price level; (and correlated even more closely with the global price level); as first noted by the British economist Alfred Gibson in a 1923 article. John Maynard Keynes publicized this effect in his Treatise on Money (Keynes 1930). On page 198 of Volume Two he wrote: “The Gibson Paradox - as we may fairly call it - is one of the most completely established empirical facts within the whole field of quantitative economics though theoretical economists have mostly ignored it.” 5
  6. 6. Gibson’s Paradox Solution• The observation is a paradox because standard Finance theory states that the rate of interest should vary directly with the expected rate of inflation – not the level of prices. 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; for example.• A number of scholars have addressed Gibson’s Paradox including Irving Fisher, Jeremy Siegel, Bob Shiller and Tom Sargent. Among the most notable is the work of Robert Barsky and Lawrence Summers in their “Gibson’s Paradox and the Gold Standard” paper appearing in the Jrl. Of Political Economy, June, 1988 (link in first paragraph). 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.• The Real Rate of Interest During the Gold Standard 6
  7. 7. Gibson’s Paradox Solution• Investigators compute the real rate of interest essentially by subtracting the actual or proxy expected rate of inflation from the nominal consol yield (notably, without accounting for effective taxation of interest income). They then assume that capital markets required the resulting rate as the real return on long term investment. This measure indeed varied over the period and correlated inversely with the price of gold/consol. Required Yield Theory asserts that this proposed mechanism errs because the Required (real) Yield determined the consol yield. Also, because the price level under the gold standard was determined by the world total above ground gold stock in relation to world GDP; not fiat currency; and because the yield of a gold instrument is determined through an entirely different mechanism (gold must earn the Required real Yield inherently) than for a fiat instrument (wherein the yield maintains constant real purchasing power of the principal and provides a real after-tax Required Yield).• There is a major empirical problem with the academic thesis: the real purchasing power of the fixed consol interest as a % (yield) of the nominal consol price remained constant – as a mathematical result of the observed relationship among price level, consol yield and price (Table I). 7
  8. 8. Gibson’s Paradox SolutionTable I: Real Yield of Consol in Terms of Purchasing Power of Interest to NominalPrice The price index varies by time period with a correlated nominal yield. However, adjusted for purchasing power (divided by the change in the price index), the fixed interest amount earns a constant real yield/return on capital invested (price) over time. Why should the real yield in terms of goods and services purchasing power be constant?An objection may be raised that this simple example does not account for theproportional change in the purchasing power of the principal or price. Recall that thereal yield is the per unit of investment (oz. of gold) claim to real goods and services.In all cases, the amount of purchasing power of interest-adjusted units of real goodsand services in relation to each unit of capital remains constant: a constant, realrequired yield. Gold must inherently obtain this yield as this table shows. 8
  9. 9. Gibson’s Paradox Solution• A fiat perpetuity is priced in a manner wherein the principal does not inherently obtain the real Required Yield, but rather, must have its real purchasing power preserved and earn the real Required Yield through the interest. For example: a fiat perpetuity paying $2 in fixed interest with a 2% real required yield, no taxes and no expected inflation will be priced at $2/2% = $100. If inflation expectations rise to 2% from zero; then the price must fall to $50 so that the fixed $2 interest covers both the expected 2% inflation (loss of purchasing power of principal) and provides a 2% real return: $2/$50 = 4% which is the new nominal required yield. This happens because fiat securities require a return that keeps the purchasing power of the investment constant, while providing a real after-tax return. So, the yield is a function of expected inflation, as standard Finance theory states.• Gold however, must inherently earn the real Required Yield. This only occurs when the world gold stock is constant per capita and thus gold yields real per capita productivity growth. In other words, when the price index against gold is falling at this rate (gold’s purchasing power is rising at this rate). Thus, under a gold standard, if the price index is determined by the gold stock in relation to world GDP, the yield of a gold perpetuity must move with the price index, not rate of inflation, to assure that point to point, the return on invested principal. 9
  10. 10. Gibson’s Paradox Solution• For example, if the price level doubled and remained there (no inflation) the yield of the fiat perpetuity would fall to the point that only a real yield would result in terms of the prices of goods and services at that time (less than when the inflation began, due to the purchasing power loss during the period of rising inflation). However, in order for gold to maintain an inherent real yield, the real yield must hold in terms of the exact same basket of goods and services with no purchasing power loss, as at the time before the inflation began. Thus, the gold perpetuity yield remains unchanged and correlates with the price level. Its yield does fall with the price level, but only when the fall in the price level is greater than the rate of productivity growth.• The Barsky-Summers finding is an artifact of these valuation dynamics in that the real yield remains positive and constant in the face of unchanging actual or expected price level; which to them appears as zero inflation, then seems to climb with any cumulative inflation. While that inflation is occurring, the real yield appears to be rising because the yield level is additive with any sequential period of inflation. The reverse happens when the price level declines and there is deflation. The real yield appears to collapse under deflation as measured by conventional means; when in fact the per unit of investment real return in terms of goods and services again remains constant.• Basis for Gold’s Economic Return and Constant Real Rates• Under the pure gold standard, the global ratio of above-ground gold stock in relation to world real GDP (via Milton Friedman’s Quantity Theory of Money (QTM)) determined both the world price level and the nominal consol (long term) interest rate or yield, while the real required consol yield remained constant as shown above. (The actual consol yield included a tax dimension as well, which is beyond scope for this article, but which determined the yield so that that after-tax real required yield remained constant.) 10
  11. 11. Gibson’s Paradox Solution• Graph II: The British and world general price levels were determined according the QTM: the price level was a direct function of the ratio of the total above-ground world gold stock (money – all of it; since little else was money or credit) to world real GDP. The consol yield closely tracked the world price level. The sharp spikes and troughs in the price index tend to correspond to major world events such as large-scale wars and famines.• Graph II 11
  12. 12. Gibson’s Paradox Solution• For clarity, all three series, the world price index, the consol yield and the ratio of world above- ground gold stock to world real GDP (golden triangle series) have been indexed serially as of 1820. The world above ground gold stock and world real GDP relationship has been obtained and calculated by the author and is reproducible from publicly available data.• The relationship of the supply of above-ground physical gold to world real GDP determines its real yield. For reasons detailed in the Jrnl. Of Investing paper, the gold supply per capita remains and is expected to remain constant; thus per Troy oz., world real GDP increases at the rate of real per capita productivity growth; or about 2% long term (Lant Pritchett, World Bank; and others). Thus, gold yields or returns, world real GDP per capita growth – the same as the real return on labor (which is why an oz. of gold tends to always buy a good custom-tailored suit).• In the case where gold is also the monetary standard, and under the assumption that long term invested capital requires a real, after-tax return equal to long term per capita productivity growth (a known, long-standing empirical constant); than an instrument paying a fixed gold interest is required to obtain this real return. In order to obtain at least this return, the supply of gold cannot grow faster than population growth or its real return falls below the required yield – which is to say, the world price level fails to fall at a rate at least equal to the rate of productivity growth per capita. Only when the world price level is falling at this rate, is gold earning the required yield; and the supply of gold is growing at the rate of population growth.• A rising gold standard price level is driven by a rising supply of gold per capita; and a failure of gold to earn the required real yield. The nominal yield rises with the price level and does not fall if the price level remains constant, because only a price level falling at the rate of per capita productivity growth allows gold to obtain the Required Yield. This is the reason why, empirically, deflation has been observed during strict gold standard periods and baring discoveries of easily accessible large gold deposits. Of course, nominal wages in gold remain constant but the purchasing power per unit rises with productivity, again equating the returns to labor and capital. 12
  13. 13. Gold Valuation in Fiat Currency• One issue with the Barsky-Summers analysis, and that of others addressing Gibson’s Paradox, is not distinguishing between inflation in terms of gold and inflation in terms of a fiat currency in relation to gold and in which gold is priced – as impacting the price of gold and the rate of interest.• Note that a unit of fiat currency yields minus the rate of inflation in contrast to an oz. of gold which yields real global per capita productivity growth. The fiat currency unit loses purchasing power at this rate because, according to the QTM, the rate of inflation and the level of prices is a function of, and is positive because of, an excess of fiat currency vs. real GDP growth. In order for capital to be preserved and obtain a real return when invested in fiat currency-earning instruments, a real yield net of the effective applicable tax rate and inflation must be required by the market.• Consider two perpetuities under initial conditions of no taxation and zero expected inflation: one pays two dollars interest, and one two dollars worth of gold. If the required real yield is 2%; the price of each will be $2/2% or $100. However, if inflation expectations rise to 2%; the cash perpetuity must yield 4% in order to make principal whole for its loss of purchasing power and earn a 2% real return – the price falls to $50. The gold perpetuity has not experienced fiat currency induced inflation erosion of purchasing power and yields a nominal 4% inherently and 2% real. As a result, its nominal price remains constant in terms of gold. However, in relation to fiat currency, its price doubles. This can be seen by comparing the ratio of the present values of two cash flow streams: one is the value of holding a dollar losing purchasing power at 2% per year; while the other maintains or gains real purchasing power. The price of the latter in terms of the former must double. Essentially, a fiat long term bond obtains the real required yield through interest reinvestment and compounding; while a unit of gold obtains this required yield inherently through its constant relationship to real global GDP growth. Gold pricing is further subject to certain interest rate derivatives, aspects of exchange rates, world gold stock, world growth and world actual and expected inflation. 13
  14. 14. About• Mainstream asset pricing theories are empirical failures (CAPM, APT, MPT, NPV etc.) as they fail to describe how asset prices actually behave, and are theoretical failures not only because of the empirical flaws, but because they offer no definitive link between asset returns and valuation to the macro economy e.g. growth, nor do they show how the valuation of all assets relate to each other beyond correlations. RYT is the first general theory of asset valuation which has so far been proven for fiat and gold standards and for stocks, bonds, gold and oil. RYT stipulates exactly what macroeconomic and asset-specific factors determine valuation and through what mechanism. It is not a correlation-derived or fitted model. It is has also been issued the only patents ever for an entirely new asset valuation mechanism. Three published academic journal papers articulate many aspects of the Theory.• Intellectual Property Notice• Required Yield Theory ™ and RYT ™ are trademarks. Required Yield Theory is patented in the US 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 global jurisdictions. Public domain formulas may not be used in computer applications in whole or part without license from the author. Asset managers wishing to learn about the applications for gold, stock, bond and oil valuation may contact the author. Formulae and data will be provided under NDA for evaluation. 14

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