Long-term interest rates are a series of future short-term rates

I know the title to this post is exactly the kind of thing that is going to garner this post a million page views but the concept I am describing is important because it is ultimately what determines why debt-induced depressions are deflationary in nature.

Now, Steve Waldman has a post up over at interfluidity called “The long bond does the limbo” which does a good job of teasing out some interesting aspects that have led to record low interest rates. Steve mentions three theories on interest rates, one that has been proved wrong by events and two others that are supported by the data. The first ‘correct’ one is the one I want to highlight in this post.

One theory of long-term interest rates is, I think, definitively refuted. This is the joint hypothesis that 1) long-term real rates include a mostly stable real yield plus a premium for expected inflation; and 2) expected inflation is a function of the growth of the monetary base. If you believe in a stable real yield, then you’ve got to concede that investors’ now expect deflation despite an explosion of the monetary base.

The facts strike me as consistent with two different views. In one account, long rates are pinned by arbitrage to the expected path of short-rates plus a risk premium, and market participants have become increasingly certain that nominal interest rates will be very low for a very extended period. In a second account, important clienteles of investors do not consider money issued by the Fed and debt issued by the Treasury, particularly long-term debt, to be close substitutes. These investors have basically been starved of new Treasury supply, and so have bid up bond prices, in order to draw supply from the inventory of investors less wedded to maturity.

What Steve is pointing to in the underlined bit is the expectations theory of interest rates. I ran across a good (mathematical) explanation of it. Let me quote that definition and give you my interpretation of what it means:

Source: Encyclopedia of Banking & Finance (9h Edition) by Charles J Woelfel

(We recommend this as work of authority and you can order it here)

A theory that purports to explain the shape of the yield curve, or the term structure of interest rates. The forces that determine the shape of the yield curve have been widely debated among academic economists for a number of years. The American economist Irving Fisher advanced the expectations theory of interest rates to explain the shape of the curve. According to this theory, longer-term rates are determined by investor expectations of future short-term rates.

In mathematical terms, the theory suggests that:

(1 + R2)2 = (1 + R1) x (1 + E(R1))


R2 = the rate on two-year securities,

R1 = the rate on one-year securities,

E(R1) = the rate expected on one-year securities one year from now.

The left side of this equation is the amount per dollar invested that the investor would have after two years if he invested in two-year securities. The right side shows the amount he can expect to have after two years if he invests in one-year obligations. Competition is assumed to make the left side equal to the right side.

The theory is easily generalized to cover any number of maturity classes. And however many maturity classes there may be, the theory always explains the existence of longer-term rates in terms of expected future shorter-term rates.

The expectations theory of interest rates provides the theoretical basis for the use of the yield curve as an analytical tool by economic and financial analysts. For example, an upward-sloping yield curve is explained as an indication that the market expects rising short-term rates in the future. Since rising rates normally occur during economic expansions, an upward-sloping yield curve is a sign that the market expects continued expansion in the level of economic activity.

Financial analysts sometimes use this equation to obtain a market-related forecast of future interest rates. It can be rewritten as follows:

E(R1) = [(1 + R2)2 / (1 + R1)] – 1

The equation suggests that the short-term rate expected by the market next period can be obtained from knowledge of rates today.

Here’s what is happening:

  • The Federal Reserve is a monopolist. The US government, as monopoly issuer of its own currency, has given the Fed monopoly power in the market for base money. The Fed exercises this monopoly power by targeting the overnight rate for money, the fed funds rate.
  • Any monopolist can only control either price or quantity, not both. And the Fed wants to target rates i.e. price. It can’t do that unless it supplies banks with the reserves they desire to make loans at that rate. That means that they must be committed to supplying as many reserves as banks want/need in accordance with the lending that they do subject to their capital constraints. Failure to supply the reserves means failure to hit the federal funds rate target.
  • Markets know, therefore, that the Fed, as a monopolist, will always be able to hit its federal funds target now and in the future. Therefore, future overnight rates reflect only future Fed Funds target rates as set by the Federal Reserve. This means that future expected overnight rates reflect only market-determined median expectations of future Fed Funds target rates as set by the Federal Reserve (plus a risk premium).
  • Long-term interest rates are a series of future short-term rates. All I need to do to mathematically represent any long-term interest rate is smash together a series of short-term interest-rates over the long-term period. For example, I wrote in May 2010 about the five-year bond: “Bootstrapping the yield curve is simply the math used to translate these three-month zero-coupon prices into a series of expected future 3-month interest rates. Doing this would mean we have a full term structure of interest rates every three-months out to five years.”

The bottom line: if long-term rates don’t reflect the expected path of short-term rates, you have a sure fire arbitrage opportunity.

What does this mean for an indebted economy? Take Japan as an example:

In an indebted economy, in which private sector liabilities have built up to levels not supported by the economy’s future cash flows, we are faced with a combination of four options: pay down debts via accumulated savings, inflate away the value of debts, renege in part or full on the promise to repay by defaulting or through debt forgiveness, or transfer the debt burdens onto the public balance sheet. Socialising losses will always be the preferred method of dealing with this problem of large private sector debt burdens.

But socialising losses increases public sector debt to GDP quickly.

In the countries like Spain, Ireland, the US, and the UK, where the property markets seized up the most, governments also socialised the most losses. For example, Ireland now has government debt to GDP well over 100% from a relatively benign 25% mark before the crisis. In the US, Simon Johnson estimates that government debt to GDP increased 40% as a direct consequence of the financial crisis.

The Sovereign Debt Crisis and Currency Sovereignty

Being a monopoly issuer of your own currency makes socialising losses much easier. When people ask “Why Italy and why not Japan?”, it is clear that currency sovereignty is a defining factor. Nevertheless, currency sovereignty is no panacea; unless policy makers close the public sector funding gap quickly, government debt-to-GDP rises to levels where interest payments take up a large percentage of government expenditures. At that point, either government must deficit spend to supply the same amount of real resources to other government-funded activities or real resources to those other government-funded activities must be curtailed. This is the scenario Japan faces.

  1. Japan’s long-term rates reflect private portfolio preferences as determined by expected future interest rates (see Market discipline for fiscal imprudence and the term structure of interest rates). So 10-year rates are low because expected inflation and expected future short-term rates are low.
  2. Japan’s Debt to GDP is over 200%, meaning that any uptick in expected future short-term rates due to inflation would be disastrous in terms of interest due.
  3. So, to avoid this scenario, Japan must leave short-term interest rates at near zero percent or risk the crowding out of public spending that higher interest payments would entail. Only if the debt to GDP ratio declines significantly can it relax this stance.

That’s my take here. Japan has failed to make the necessary reforms and is now trapped in a zero rate policy. This is the cautionary tale for the U.S. and Europe that Bass is pointing to. But, where he sees insolvency, I see perpetual zero rates, money printing and currency debasement. Bass talks about short rates going up from this. Often the bond vigilante talk ignores the reality that the Fed can manipulate rates. The Fed could, if it wanted, decide to offer unlimited liquidity for a specific price (interest rate) somewhere on the curve as it does for Fed Funds. Moreover, longer term bond yields are only market representations of future short term yields.

Kyle Bass on Japanese Insolvency and Systemic Risk in the Global Economy

The Japanese scenario is a fundamentally deflationary one and the expectations theory of interest rates is key to why.

Japan socialised losses by holding down real interest rates to allow private sector debtors time to work off their debt. Without reforming the financial sector, banks eventually became zombies because net interest margins shrank and shrank with interest rate expectations. This is how quantitative easing and permanent zero are toxic to bank net interest margins and create a deflationary outcome. Eventually debt deflation sets in – to the point where even attempts at currency debasement fail. This is why QE won’t work and why the US crisis is deflationary in nature.

  1. Dave Holden says

    Fascinating analysis – it why I read here!

  2. StephenM says

    This statement is false:

    The bottom line: if long-term rates don’t reflect the expected path of short-term rates, you have a sure fire arbitrage opportunity.

    Thus leaving much of the commentary open to question. As to why it is false – show me the “sure fire arbitrage opportunity”.

    1. Edward Harrison says

      Stephen, your comment makes no sense. Arbitrage is the single most fundamental concept in investing to converge prices to the accepted market price. Stated simply, if you believe the market price does not reflect your view of the expected path of short-term rates, you simply bet against that price. You will be proved right or wrong when future policy rates are set. That is the “sure fire arbitrage opportunity”. In fact, it is the aggregation of individuals making those bets that DETERMINES the market price.

      Why would you insist otherwise?

    2. Edward Harrison says

      Just to put this another way, even if you believe in a semi-strong form of the efficient market hypothesis, what I am saying is true.

      “If the market prices do not allow for profitable arbitrage, the prices are said to constitute an arbitrage equilibrium or arbitrage-free market. An arbitrage equilibrium is a precondition for a general economic equilibrium. The assumption that there is no arbitrage is used in quantitative finance to calculate a unique risk neutral price for derivatives.”

      And I am not arguing for the EMH here. I am just saying that the market price reflects the aggregated collective wisdom of market participants. To the degree you believe the price of longer-dated risk free assets is not in keeping with expectations of the future policy rate path, go into the futures market, buy some Treasury strips, etc. There are a hundred ways to bet against that by re-creating an asset with identical cash flows that does not trade at the same price. Those markets have to converge. And even if they DO follow the no arbitrage principle, you as an individual have an arbitrage by being able to use those derivative markets to make a bet that the market prices don’t reflect the likely future policy path.

  3. StephenM says

    I was just preparing my respsone to your first reply which will come through later.

    If I can “re-create” the cashflows of one one asset using other assets that deliver a different NPV (and for no additional functional risk). Then I have an arbitrage and can make riskless money. Or, in other words, the market is not in equilibrium. This sort of event can occur relatively frequently and is often driven by the “preferred habitat hypothesis”.

    What I can’t do is define my own forward curve (based on my expectations), price other assets off my curve and trade against my prices in the expectations that I will automatically generate value.

    In your commentary, there is leap in reasoning from

    “To the degree you believe the price of longer-dated risk free assets is not in keeping with expectations of the future policy rate path”….which is based on a mismatch between your expectations and market expectations.


    ” There are a hundred ways to bet against that by re-creating an asset with identical cash flows that does not trade at the same price. Those markets have to converge”….which is based on trading against pure market inefficencies.

    The first is a sure pathway to financial disaster and we have regularly seen the explosive results. The latter provides some opportunity for profit.

    1. Edward Harrison says

      So, I think we agree. Correct me if I am wrong.

      Bill Gross was following a premise similar to your premise one, that the price of longer-dated risk free assets is not in keeping with his own expectations, what you called “mismatch between your expectations and market expectations.” What I am saying is that large bond markets ipso facto reflect future expected policy paths because derivatives markets – that reflect the market price/yield of future expected policy rates – create very few market inefficiencies to arbitrage against .

      1. StephenM says

        Hi Ed, I think we agree on this point. And I agree that with your following statements.

        I have worked in a number of businesses where some sizeable financial markets directional bets have failed spectactularly.

    2. Edward Harrison says

      Just to add to my previous comment, the no arbitrage principle is important in how rates come to reflect future policy rate expectations.

      That said, I think some bank traders had gotten in the habit of making implicit directional bets. Markets DO largely follow the no arbitrage principle, And, yes, you as an individual have an arbitrage by being able to use derivative markets to make a bet that the market prices don’t reflect the likely future policy path. But that is a directional bet which can fail very badly.

  4. flow5 says

    Failure to supply the reserves means failure to hit the Fed funds rate target.

    No, reserves in the inter-bank market are always available at a price. If that price (rate), exceeds the target, the FED always adds reserves. The FED has been targeting interest rates since 1965.

    1. Edward Harrison says

      You’re not saying anything different than I am. Why do feel the need to comment?

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