The Myth of a “Risk-free” Government Bond Rate



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Let us imagine an economy burdened with a nefarious, covert clique of counterfeiters.  This group (perhaps with the letter “G” painted on the back of their shirts) desires to steal real output from the stolid producers of real output.  They accomplish this by sometimes printing fraudulent paper money (one sub-group of them) and sometimes by issuing debt (another subgroup of them) or fraudulent IOUs promising interest and principal payments during the future in return for “borrowing” real output from naïve lenders.  Of course, since they really are producing nothing of value, themselves, they realize it will actually be impossible for them to pay off the debt they have issued and they have no intention of doing so.  However, they don’t want the gravy train of stolen output to actually come to an abrupt end with a default on their debt—it’s too lucrative and too much fun.  What to do?


Saving the day, a bright member of their gang suddenly realizes that the two cliques can actually cooperate to their joint benefit.  They can buy back the debt they issued by printing yet more worthless currency to repurchase it—so long as the public is naive or stupid enough to accept the entire fraudulent, synergistic scheme.  They go so far as to label these actions “open market purchases”.   Of course, these illicit activities actually result in some artificial “market” rate of interest on their dubious bonds.  That peculiar lending rate is just an accidental result of the cumulative behavior of the issuers of the worthless currency and the fraudulent debt.  To think of this rate as some sort of “risk-free” benchmark seems absurd.  After all, it can easily be manipulated by both the thieves supplying the “bonds” as well as the resultant inflation rate of prices in terms of the counterfeit currency. How could anyone be so silly as to think this interest rate was particularly important or meaningful—that it was some sort of meaningful “benchmark”?  Clearly, no one would be so blind as to think of it as some sort of a “risk-free” rate of return.  In fact, if this nefarious clique of counterfeiters and fraudulent borrowers threatened to desist, pack up, and exit our imaginary economy, the remaining honest producers surely should and would applaud. It would be strange if they could be panicked at the clique’s threatened shutdown of operations and wonder how their economy could go on without them.


Now, in comparison, let us consider the economy we actually live in.  But wait… it appears the two economies are not so different.  If you are a skeptic about the real value to our economy of public goods and government services, then you may agree.  We have a central bank that issues worthless currency at whatever level it chooses and usually issues it by the means of buying back previously issued treasury debt.  The combined scheme is used to finance government spending—either purchasing economic output directly or transferring wealth or claims on output from those who voted against the political incumbents to those who voted for them.  That is the traditional spoils system or “public choice theory” of representative democracy.  In so doing, our economy strongly resembles the hypothetical one that we previously imagined.   Surprisingly, many of us consider the peculiar borrowing rate determined by Fed and Treasury collusion and manipulations to be particularly meaningful.  If it’s not, what should we use for a logical “benchmark” rate of return?


We can think of two candidates.  First, if you live in an economy that enjoys an average rate of growth of say 3% from year to year, then expecting such a future return on wealth or savings that you loan to another is not such a farfetched idea.  In fact, it seems reasonable to expect it as a reward for deferring your own consumption for one year.  Another logical benchmark is the rate of return to a piece of productive capital.  After all, if you choose not consume all the output you produce, then you would likely consider “investing” it.   That is, creating a tool that will make you able to produce more output in the future.  The expected average rate of return to an investment in such a tool or piece of productive capital also seems a logical benchmark rate of return.


Let us suppose that the annual average rate of growth of our real economy is some rate, n.  Secondly, let us define the real average rate of return to a piece of productive capital as r(k).  It may or may not surprise you that there is a strong, logical argument, in a transparent economy in which individuals try to maximize their sustained level of prosperity, these that two rates will tend to converge toward or to equal each other.  That is, r(k) = n.    (Forget about a “risk-free” rate of return.  There isn’t one.  In an uncertain world, you won’t find it anywhere—especially not as a promised rate of return of government bonds or bank accounts.)  To see how and why the real return or marginal product of productive capital should converge to the growth rate of the economy, you may want to read our book (Capital as Money).  Alternatively, you can follow the brief argument sketched out below.  It was first made by originally by an economist named James Tobin and is popularly referred to as Tobin;s “Q.”


Suppose we consider a very simple economy where output can be either immediately consumed or invested in order to create capital or an investment good that helps produce more output in the future.  A simple intuitive example is corn—it can either be eaten as current consumption or dried and planted in order to produce more corn in the future.  In this very simple economy, suppose that the price (in terms of whatever monetary good is being used) of a unit of output steered toward consumption is P.  The price of the same unit of output steered toward the creation of future production or capital is P(k).      Further let us suppose that the real natural rate of return or interest in this economy is, in fact, just its average annual growth rate, n.  For simplicity, suppose there is no inflation of the price of consumption goods and that P is therefore expected to be stable.    Then the equilibrium price of a piece of capital will be nothing more or less than the sum of the expected returns to that piece of capital over future periods discounted to a present value using the real interest rate, n, and stated in terms of the price of a typical piece of output.  Thus, in annual periods,




(1)     P(k) =   P*r(k)/(1+n)+P*r(k)/ (1+n)^2 +P*r(k)/ (1+n)^3… +P*r(k)/(1+n)^i…




P(k) = the price of a unit of output used to create a piece of productive capital


P = the price of a unit of output used for current consumption


r(k)= the real marginal product of a piece of output turned into a capital good (in terms of output)—expected to be constant.


n = the real rate of growth of the economy.


A^b means that A is raised to the power of b.


i = refers to the ith period or year.


It turns out that equation (1) can become, without too much ado (using some re-arrangement and the algebra of the sum of an infinite geometric series);




(2)    P(k)/P = r(k)/n




What is the intuition of equation (2)?  It is surprisingly simple (and hopefully a major reason why James Tobin was awarded the Nobel prize in economics). The ratio P(k)/P, or Tobin’s “Q” provides a clear and elegant behavioral explanation of optimal capital investment.  First, suppose that a unit of output turned into a capital good is currently more valuable to the market than the same piece of output turned into a consumption good.  Then P(k) > P or Tobin’s Q >1.  If this condition is true, it is also true that r(k) > n.  In that case, current output will be steered by the marketplace toward the production of more capital goods.  Until what?  Until the marginal product of capital falls, thereby converging to the growth rate of the economy.  At that point of market equilibrium r(k) = n and Q =1.   This is the same result as the “golden-rule” capital intensity of the Solow neoclassical growth model (for further explanation you should read Capital as Money).  On the other hand, if the current market value of a unit of output invested to create a capital good is less than the value of same unit of output consumed as a consumption good, then P(k) < P or Tobin’s Q <1.  Thus, output will naturally be steered away from investment and toward consumption by the marketplace.  Until what?  Until capital becomes scarce enough in production that its marginal product rises to r(k) = n and Q once again is equal to 1.  Thus, a logical, rational market mechanism exists in a free-market economy that tends to drive us toward the optimal market-determined capital-intensity or aggregate level of investment.  Notice this mechanism has nothing at all to do with government or central bank manipulation of interest rates.  In fact, when such distractions exist, all that can be said for them is that they will tend to thwart or confuse the capital market in realizing the optimal level of productive capital creation.  It is this always present decision of all individuals and all economies of whether to consume or invest at the margin that causes us to recommend that units of broad productive capital should, in fact, be our medium of exchange and natural store of value—that capital should be our money.


This beautiful and elegant picture grows cloudier when we introduce sustained fiat money growth and inflation.  We would like to say that fiat money growth is perfectly neutral in exerting real economic effects upon the real return to capital, investment and the capital-intensity of the economy over the long run.    Unfortunately, the design of our ham-handed tax system, either by accident or intention, allows no such benign result.


To see why, consider the following thought experiment.  Suppose you own a stock during a period where its market price exactly doubles.  Unfortunately, during the same period the average price of all other goods, including the consumer price index, exactly doubles as well.  Realizing that your stock price appreciation has just kept pace with general inflation, you conclude that the real capital gain on your stock is precisely zero.  Carefully noting that fact on your tax return when you sell your shares, you report to the IRS that since there was no real capital gain on your shares, you owe no real tax—especially since the government or central bank’s monetary policy was responsible for the sustained rate of inflation in the first place.   Good luck with that completely reasonable argument!  Since capital taxes are typically not indexed to inflation, this is an important reason why a rise in the interest rate, taken alone, should generally exert a negative effect upon the future returns to a stock (growth or value).  Most rises in market interest rates simply reflect a rise in the actual or expected inflation rate.  In terms of equation (1), above, an increase in expected inflation does not net out in the effect on the numerator (P growing at the inflation rate) and the effect on the denominator (the discount rate becoming (n + Inflation rate)) because r(k) is reduced by taxes that are not inflation-neutral falling upon the real rate of return to capital.  In addition, there is nothing neutral about our witches’ brew of asymmetric tax rates. They will generally exert real distorting effects everywhere, including the split between investment and consumption.


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