Sunday, September 8, 2019

Low bond yields

Why are interest rates so low?

Here is the 10 year bond yield, by itself and subtracting the previous year's inflation (CPI less food and energy). The 10 year yield has basically been on a downward trend since 1987.  One should subtract expected 10 year future inflation, not past inflation, and you can see the extra volatility that past inflation induces. But you can also see that real yields have fallen with the same pattern.

There is lots of discussion. A falling marginal product of capital, due to falling innovation, less need for new capital, a "savings glut," and so forth are common ideas. The use of government bonds in finance, the money-like nature of government debt among other institutional investors and liquidity stories are strong too. And most of the press is consumed with QE and central bank purchases holding down long term rates. I hope the steadiness of the trend cures that promptly.

Along the way in another project, though, I made the following graph:

The blue line is 10 times the growth rate of nondurable + services per capita (quarterly data, growth from a year ago). The red line is the negative of an approximate measure of the real return on 10 year government bonds. I took 10 x (yield - yield a year ago), and subtracted off the CPI.

Look at the last recession. Consumption fell like a rock, while the real return on long-term bonds was great. That real return came from a double whammy: long term bonds had great nominal returns as interest rates fell, and there was a big decline in inflation.  No shock, there is a "flight to quality" in recessions, along with a sharp decline in nominal rates. From a foreign perspective, the rise in the dollar added to the return of long-term bonds. The graph suggests this is a regular pattern going back to the almost-recession of 1987. In every recession, consumption falls, interest rates fall, inflation falls, so the real ex post return on government bonds rises.

Government bonds are negative beta securities. At least measured by consumption or recession betas.  Negative beta securities should have low expected returns. They should be less even than real risk free rates. I haven't seen that simple thought anywhere in the discussion of low long-term interest rates.  

Making the graph, I noticed it was not always thus. 1975, 1980, and 1982 have precisely the opposite sign. These were stagflations, times when bad economic times coincided with higher inflation and higher interest rates. Likewise, countries such as Argentina which go through periodic currency crises, devaluations, and inflations, flights to the dollar, all associated with bad economic times, should have the opposite sign. There is a hint that 1970 was of the current variety.

One could easily make a story for the sign flip, involving recessions caused by monetary policy and attempts to control inflation, vs. recessions involving financial problems in which people run to, rather than from, money in the recession.

In any case, the period of high yields was associated with government bonds that do worse in recessions, and the period of low yields is associated with government bonds that do better in recessions and have a negative beta. I haven't really seen that point made, though I am not fully up on the literature on time-varying betas in bond markets.

In any case, if we want to understand risk premiums in bond markets, this sort of simple macro story might be a good starting point before layering on institutional complexities.


  1. A very interesting idea, John, that can potentially at least partially explain fall in yields from era of stagnation to era of dominant demand shocks. There has been some formal work on this idea:

    Campbell, John, Adi Sunderam, and Luis Viceira (2009), “Inflation Bets or Deflation Hedges? The Changing Risks of Nominal Bonds”, NBER Working Paper 14701.

  2. I am reminded by a remark by Fisher Black "We know the correlation between stocks and bonds is .3 , we just don't know the sign."

  3. I am reminded of a remark by Fisher Black "We know the correlation between stocks and bonds is .3, we just don't know the sign."

  4. This is great stuff. I incorporate hedging value a bit differently, with M-GARCH models of correlations/betas w.r.t. the S&P 500. Today there measures are low, but by my rough regressions accounting, comprise ~10 bps of the 110 bp rally YTD. Happy to forward charts & deets (

  5. This seems pretty compelling. If we think of the drop in the 10-year rate as the result of changes in (1) expected inflation, (2) risk free real rate, and (3) beta risk premium, it looks like (1) and (2) aren't enough to explain the 10.3 ppt drop in the 10-year since 1982. Using Cleveland Fed inflation forecast and real rate data, it looks like (1) accounts for about a 3.8 ppt drop and (2) accounts for about 5.2 ppt. So there's roughly 1.3 ppt of decline in the 10-year (since 1982) left to be explained, perhaps by a drop in the 10-year’s consumption beta.

  6. I enjoyed reading this post. My job market paper examines the time-varying correlation between real bonds and the equity market: It uses a New-Keynesian model with long-run risk subject to the ZLB and shows that the ZLB can endogenously produces time-varying equity-bond market correlations.

  7. "One could easily make a story for the sign flip, involving recessions caused by monetary policy and attempts to control inflation, vs. recessions involving financial problems in which people run to, rather than from, money in the recession."
    indeed, a nice recent attempt at quantifying a story of this type (with no financial frictions, just differences in the willingness of the Fed to fight inflation) by Dongho Song at JHU: Bond Market Exposures to Macroeconomic
    and Monetary Policy Risks

  8. The discussion on negative betas reminds me of Taleb's ideas on antifragility, in the sense that government bonds in the current era can be characterized as having antifragile qualities due to their dependence on negative news to achieve better yields. It's an interesting way to think about why rates are low.

  9. Economics, resource allocation [of scarce resources], is a trade off between efficiency and productivity, or stability and growth, for optimum economic performance; and these trade offs are not constants in their performance but cycle depending upon the needs and wants in a society. The reason we have had lowering interest rates over several decades is because of public policies we have been following coming out of the excessive inflationary spirals of the 1970s, and especially since the fall of communism in Europe and the takeoff of globalization where the U.S. prominence on the world stage has been supreme. We have had a long period of the ‘Great Moderation’ until the Financial Crisis of 2008, with minor crises prior to that; and we have emerged from 2008 with the old ways intact. What we have learned over this period is that the U.S., in providing the global financial and economic leadership, can do this much better if policies promoting economic stability are emphasized over promoting greater economic rates of growth. So, the use of monetary policy has preempted the promotion of fiscal policy and monetary policy has tried to put range bounds on economic performance; not too warm, not too cold. The reduction in volatility, especially long-term volatility, has resulted in a steady decline in long-term bond rates, with the concomitant result of lower interest rates and yields along with long term trends of declining rates of economic growth.

    Our economic sphere does not work independently of our political sphere. In our political sphere stability can be associated with status quo and growth can be associated with the vitality that is needed for a society to make changes when it faces challenges that will propel it toward progress. In the trade off between stability and growth we need to put a little more emphasis on growth and less on economic stability. [I don’t think the Chinese or anybody else could keep up with us if we had higher rates of growth by promoting less of our consumer sector and more of our technical sector, technical services as well as the making of things.]

  10. Another Explanation:

    "The Fed Can’t See Its Own Shadow: Its asset purchases are squeezing nonbank lending and sinking long-term bond rates." By Andy Kessler on Sept. 8, 2019

    That’s the market for repurchase agreements, or “repos,” a form of short-term borrowing. Mr. Snider calls it “collateralized interbank borrowing.” One party puts up collateral such as a bond, and is paid for the value of that asset on the promise to buy it back later at a higher price. It can be overnight, 90 days or more. Often that collateral is lent out again, creating a money supply outside traditional fractional-reserve banking. It’s huge—today nonbank lenders hold more total assets than traditional banks do.

    But shadow banking has issues. In times of stress, the repo market demands better or “pristine” collateral, usually longer-term U.S. debt, of which there often isn’t enough. In 2013 I wrote about a shortage of collateral for the repo market and how Fed buying was squeezing the shadow banking system. Mr. Snider recalls the moment as well: “They were stripping the repo market of the best collateral as well as lesser-traded issues. They still had to buy up repo collateral to keep up the ruse that they were ‘printing money’ they weren’t.” The lack of inflation is proof that the total money supply has barely grown.

    So what should they do? Encourage the Treasury to issue more of the long bonds the market is demanding: 30- or even 100-year. Feed the beast. Then stop quantitative easing: It doesn’t work and soaks up collateral. Next, stop paying interest on reserves. Maybe even create a nontradable “Treasury-R” to act as reserve currency elsewhere, freeing up more bonds.

  11. Also true apparently for stocks

  12. "Bond beta" requires accurate definition if the concept is to be useful. Beta is defined as Cov(X,Y)/Var(Y), where X is the total return on security x and Y is the total return on security y, typically a proxy for all capital assets, including but not limited to common stocks, preferred stocks, bonds, debentures, notes, commodities, land, artworks, etc.

    A "bond beta" would see X represent the total return on the bond in the period, and Y represent the total return on the asset market proxy which would include the the market weighted total return on bond x. It follows that the market index would include both stocks and bonds that are tradeable in the period specified.

    Given the market value of all tradeable bonds greatly exceeds that of all tradeable equities, it is difficult to imagine a "negative beta bond" being encountered. Note that "beta" is a measure of non-diversifiable risk, specific risk having been eliminated through portfolio construction (MPT).

    However, if the manager errs and constructs his proxy for all capital assets by limiting the index portfolio only to equities, it is conceivable that he would find "negative beta bonds". By restricting his proxy index to a subset of the total asset market, namely to equities traded on a stock exchange in the USA, his finding of "negative beta bonds" would not be at all remarkable.


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