Has the Duration Risk Premium Turned Negative?

This is an old post. Over the last few years, we have considerably improve our modelling of the US Treasuries yield curve. See Our Guide to Understand (And Trade) The US Treasuries Yield Curve.

22 October 2018

As stressed recently by the BIS in its quarterly bulletin, “In recent years, government bond yields have not always responded predictably to macroeconomic or monetary policy news. Long-term yields in the United States remained stubbornly low even as the Federal Reserve initiated a series of interest rate hikes away from zero starting in late 2015. Analysts have debated the causes and implications of a flat, or even downwards-sloping, term structure at a time of broadly robust growth.”1 An interesting point is that this recent surprise was in fact the sheer repetition of what happened in the previous cycle of Fed tightening a bit more than 10 years earlier. As stressed by Federal Reserve Chairman Alan Greenspan in his February 17, 2005, testimony before the Committee on Banking, Housing, and Urban Affairs of the U.S. Senate: “For the moment, the broadly unanticipated behavior of world bond markets remains a conundrum. Bond price movements may be a short-term aberration, but it will be some time before we are able to better judge the forces underlying recent experience”.

Indeed, there are many signs that this famous and still unresolved “conundrum” started even earlier2. Over the last 25 years, investors were more often than not surprised by how long-term rates behaved in many countries. In general, according to surveys on expectations, analysts have judged long-term rates to be too low relative to the bond market fundamentals and have expected them to rise sharply in the coming year. But months after months the opposite has happened and until recently long-term rates were on a long declining trend. This disconnect between expectations and the reality has been particularly strong in the US since the beginning of the century and for euro rates since the mid-90s (see the following graph based on the monthly surveys done by “consensus economics”).

Since January 2000, 10-year rates on US treasuries were on average expected to rise by 61 bp in the coming year while they actually fell on average by 18 bp. As far as German bunds are concerned, an average ex ante expected rise of 41 bp was followed by an average ex post decline of 27bp.  The mistake was of the same order of magnitude in the two countries (around 79 versus 68 basis points).  

These observations raise many different questions that we’ll try to answer in this post.

At a fundamental level, what is this repeated conundrum telling us about the markets’ efficiency and the way investors price risks? In other words, how is it possible that investors have been surprised for so long?

Yet for most investors, there is a more pressing interrogation that is to assess what kind of risk premia have been left in the currently low long-term interest rates. After all these recent and older surprises, is it possible that duration risk premia may have turned negative, i.e. that the return on long-term safe government bonds may be in the future lower than the return provided by short-term monetary instruments? Could this be the “new normal”?

In our view, it is not possible to answer these two related questions without making a clear distinction between three of the four different sorts of risk premia one can encounter in financial discussions: the “spot” risk premia, the “valuation” risk premia and the “embedded” risk premia (see The Four Risk Premia).

We’ll defend the view that the key “spot” risk premia on long term bonds have indeed turned negative many years ago and that this structural shift should not be seen as a real surprise. Yes, there is probably a “new normal”. But the markets’ reckoning has been slow and at time chaotic: as investors and analysts failed to adjust rapidly the “valuation” risk premia they use, the “embedded” risk premia have been rather sticky. Only recently, the “embedded” risk premia on key long-term bonds seem to have fallen around 0 (US treasuries) or even below (German bunds).

Moreover, it seems likely that this chaotic process of risk premia adjustment from the “spot” to the “embedded” is not over. There are many reasons to expect the US yield curve to become significantly inverted in the coming few years. Yet, looking at the more distant future, we’ll see that these flat or inverted yield curves may face some resistance, since they would raise some very interesting questions regarding the optimal public debt’s structure and the evolution of pension systems.

The “spot” risk premia on long-term bonds have turned negative long ago…

Remember that the “spot” risk premia are the short-term risk premia that we all encountered in finance textbooks while studying the Capital Asset Pricing Model (CAPM). They are the expected short-term excess expected returns over treasury bills that investors require to hold risky assets.

“Spot” risk premia are not supposed to be stable. As far as long-term bonds are concerned, there are many reasons why they may have changed in the recent decades (see Why Risk Premia Vary):

  • Starting in the late 1980s, after a catastrophic decade of inflation in the 1970s, the improving credibility of most central banks reduced considerably the risk of holding nominal bonds. We’ll see later that this is probably the most important structural change.
  • The ageing of the population may have increased the demand for long-term instruments. Short-term bills are very dangerous investments for long-term investors since they have no guarantee at which rate they may be able to reinvest their holdings in the future.
  • The recurrence of financial crisis tends to create on average a negative correlation between the price of bonds and equities (when equities collapse, there is a flight to safety and the price of the safest government bonds increase). In some way, the “betas” of government bonds have turned negative in many countries. In the Capital Asset Pricing Model, negative betas lead to negative risk premia…

  • More recently, Quantitive Easing in many countries has reduced the supply of bonds that investors must absorb. This should also push downward the duration risk premia on bonds.

Thus, with the benefit of hindsight, most analysts probably believe that “spot” bonds’ risk premia required by investors have been on a declining trend over the last 10 or even 20 years. Yet, is it possible that “spot” risk premia have even changed sign and become on average negative?

From a theoretical perspective, yes, they can!

In finance theory, in order to have a negative “spot” risk premium on an asset class, you need this asset class to provide a hedge relative to the risks threatening the overall well-being of the average investor. The CAPM is a specific application under some rather restrictive hypothesis of this key principle. In other words, seen from a theoretical perspective and with perfectly efficient financial markets, the key question should be the following: are rising long-term interest rates good news or bad news for rational people involved in financial markets? If rising long-term rates are on average bad news, considering all the risks born by the average investor, the duration risk premia should be positive. Adding more bonds to the average portfolio increase its risk and investors must be compensated for that. This was clearly the situation when the central banks were lacking credibility and when the movements of long-term rates were mainly driven by changes in inflation expectations. Higher inflation was at the time very bad for the average investors and thus holding bonds was seen as increasing their risks.

When inflation expectations are well anchored, the sign of the normal duration risk premia is much more ambiguous and depends a lot on the relative weight of long-term and short-term investors. For most rational long-term investors, rising long-term interest rates are very good news even if they trigger some short-term apparent paper losses on their current holdings of bonds. As long as they are “cash-flow” positive, i.e. they will need to invest in financial markets some new saving or the redemptions of the bonds they have in portfolio, they will clearly benefit from higher interest rates. Indeed, we should listen to what the rational Germans say when they cry for higher interest rates in order to help their savers penalized by the irresponsible policy of the ECB! If we were all German and hopeful for higher rates, the duration risk premia on bonds should be negative…

More generally, most analysts would probably agree that higher real interest rates are generally a healthy sign that the medium-term economic prospects are improving, that productivity is growing and that the society is on average getting richer. In other words, higher long-term interest rates are generally good news and not only for the Germans… All in all, it is thus very tempting to argue that contrary to decades of markets’ wisdom influenced by the risk of inflation, the normal duration “spot” risk premia should be negative whenever central banks are perfectly credible.

Yet, there are several “market failures” and “economic policy failures” which can trigger positive “spot” risk premia on bonds despite impeccable central banks… With “bounded rationality”, some long-term investors may not be able to absorb serenely the apparent paper losses on their bond portfolio and spot all the true longer-term benefits of higher rates. And even with rational investors, higher interest rates due to an irresponsible fiscal policy rather than improved medium-term economic prospects are not that good for anyone… Also, there is a delicate issue of intergenerational risk-sharing: higher productivity and interest rates can be good for the future generations, but not for the current one if the government has issued a lot (too much?) of very long-term bonds (we’ll come back briefly at the end of this post on intergenerational risk-sharing and the optimal public debt policy).

Thus, let’s give the current markets’ wisdom a chance and accept that the normal sign of the duration “spot” risk premia is still ambiguous in our current environment. Is there any way to have some more empirical information on where they stand? Of course, there are: we can use expectations surveys to get some insight on what sort of excess return investors require on bonds.

In the following graph, we used the expectations gathered by “consensus economics” over the last (almost) three decades and we extract the implicit one-year excess return over a risk-free investment. These estimates take into account the carry which benefits, or not, bonds investors depending on the shape of the yield curve.

For many reasons, the result is quite volatile3. Thus, it seems quite clear that the “spot” risk premia on US treasuries and German bunds have now been negative for a long period. Using a moving average over two years, the US duration risk premium has been negative since March 1998 and the German since June 1997. Over the last two years, this smoothed “spot” risk premia has been on average -3.2% in the US and -1.8% in Germany4.

The most interesting point is that while these “spot” risk premia have indeed fallen deeper into negative territories over the last few years, the change of sign was not recent. They were already negative at the time Alan Greenspan mentioned the bond conundrum, long before the 2007-2009 financial crisis. This illustrates the point that the fundamental factor behind changing duration “spot” risk premia was probably not Quantitative Easing, but rather the rising credibility of central banks which made considerably more attractive an investment in long-term nominal bonds.

It is important to note that there is another place to look at for some indices on the duration “spot” risk premia. There has been for long a very liquid and efficient future markets for 3-month interbank rates, both in dollars and euros (or deutschemark before the creation of the common currency). Quite often, analysts use these futures prices to judge what are the market’s expectations regarding future short-term rates, i.e. monetary policy decisions. Yet, as in all futures markets, the prices you get are a mix of true expectations and risk premia. If investors need to be compensated for the risk of higher short-term rates in the future, they will buy the future contracts at a lower price than their true expectations: the expected profit will bring the risk premium they need. In other words, these futures prices will signal higher rates than really expected when the duration risk premia are positive, and lower rates than expected when the duration risk premia are negative. Thus, to get an insight on the duration risk premia it is possible to compare the prices on these contracts and the “true” expectations revealed in surveys like the monthly polls made by “consensus forecast” since 1989. This comparison is done in the following two graphs.

Before commenting the results, we must make three important caveats:

  • There is a credit risk premium in interbank rates as in time of trouble, investors may fear that some banks may collapse. Thus, when you buy a Eurodollar or Euribor future contract, you take the risk that rates will rise in the future due to a larger credit risk premium. Thus, these contracts are not as good as safe government bonds as a hedge against financial crisis. As a result, the “spot” risk premia on these futures are likely to be significantly higher than the spot risk premia on long-term government bonds. Indeed, in time of financial crisis, it is perfectly possible to have negative “spot” risk premia on long-term bonds and positive “spot” risk premia on futures based on interbank rates.
  • Even if we make abstraction of the credit risk premium embedded in interbank rates, we should note that the risk on long-term bonds and short-term rates futures are not perfectly correlated. Yields and prices on long-term bonds depend both on the future path of monetary policies and on the duration risk premia required by investors. This complex relationship is described in detail in Our Yield Curve Model. In our model, on average over a long period, broadly half of the action in the government bond market is coming from news on monetary policies and the other half is coming from varying risk premia. Thus, the risk premia, positive or negative, are here to compensate for two different sorts of risks: a tighter monetary policy than expected in the future or a higher duration risk premium. As far as one-year ahead short-rates futures are concerned, one can show that the relative weight of the two sorts of risks is not at all the same: these contracts are much more exposed to changing view on monetary policies than to changes in duration risk premia5. As long-term bonds and Eurodollar or Euribor one-year ahead futures contracts don’t support exactly the same risk, the risk premia on the two instruments should not be perfectly correlated, especially in times of financial crisis.
  • Finally, in the survey done by “consensus economics” for the US market, the analysts are not questioned on next year interbank rates, but on US treasury bills. Thus, we have added to their answers the difference between the current risk-free yield on treasury bills and the 3-month interbank rate (i.e. we have added the current TED spread6). Yet, in times of financial crisis, investors probably don’t expect this credit risk premium to stay stable over the coming year.

All in all, the analysis of risk premia on Eurodollar or Euribor contracts are interesting but it should be recognized that they may give a biased view of the true duration risk premia on government bonds, especially in times of markets’ instability. Yet, the graphs show for the US a clear structural shift at the beginning of the century. Over the period 1989-2002, the future market was pricing Eurodollar rates one-year forward on average 43 basis points above the expectations as revealed in the survey we use. Over the next 15 years, they were priced 24 basis points below, i.e. the related risk premium became negative. Thus, the analysis of Eurodollar contracts reinforces a lot the view that the duration “spot” risk premium has turned negative a long time ago in the US.

The message is much less clear in Europe, with a lower risk premium than in the US on average in the first period (a 20-basis points difference between forward rates and expectations) and a risk premium close to 0 but not negative over the last 15 years. Yet, as the “spot” risk premia on Euribor contracts are likely to be on average significantly above the risk premia on German bunds (among the kings of safe assets…), this result doesn’t contradict the view that the “spot” risk premia on long-term bunds have also turned negative many years ago.

A slow reckoning: the “embedded” duration risk premia have only recently been close to or below 0…

As explained in the Four Risk Premia, the “embedded” risk premia reflect how risks are priced in financial markets. They are the excess returns that investors can reasonably expect in the long term on the various asset classes compared to a rolling investment in “risk free” short-term government bills. Thus, to estimate them, one has to start with a scenario on future monetary policies (i.e. the expected return on a rolling investment in bills) and has also to establish a scenario for the various fundamental variables driving the other assets’ future returns (corporate profits, equilibrium exchange rates…).  The relationships between the current prices, the current “embedded” risk premia and the related fundamentals are described by the well-established valuation models (“discounted cash flows” model for equities, the “expectations hypothesis” model for safe government bonds and the “overshooting” model for currencies).

Compared to other asset classes, extracting the “embedded” risk premia on safe government bonds (i.e. for countries with very little risk of default) is rather straightforward. The long-term  pay-off of bonds is fixed (contrary to equities or currencies) and the “embedded” risk premia depend only on the expected path of monetary policies. Dealing with equities and currencies adds a lot of uncertainties on corporate profits and equilibrium exchange rates (and default rates as far as corporate bonds are concerned).

They are several surveys which help to estimate how the average investor asses the future path of monetary policies. Moreover, in the US, the Fed is very helpful by providing a detail analysis of how its board sees the most likely scenario for short-term rates in the short, medium and long terms (the famous “dot plots” published four times a year). Finally, the shape of the yield curve may help to estimate how the markets see future monetary policies. Obviously forward rates should not be taken at face value since they are impacted by risk premia. We have just discussed this key issue. Yet, the arbitrage made by investors insure that the risk premia on bonds of various maturities are not independent. Thus, the contribution of risk premia to the shape of the yield curve is constrained and it may be possible to use these “arbitrage constrains” to extract an estimate of what markets expect regarding monetary policies. Yet, this is a rather complex affair that we discuss in more details in Our Yield Curve Model.

A recent paper in the BIS quarterly bulletin makes a good job at comparing the results of the various approaches used to extract the “embedded” risk premia on long-term bonds in the US and the eurozone (here they chose the French OATs rather than the German bunds). There are some disagreements over some specific periods, but overall the messages are quite convergent. In the following graphs, we take the result of one of the yield curve models they used. The history of the “embedded” risk premia would be rather similar if we were using expectations drawn from surveys rather than the output of a complex yield curve model.

In the US, the “embedded risk” premium on the 10-year US treasury declined a bit around the time Alan Greenspan mentioned its “bond conundrum” and then stabilized until the financial crisis of 2008-2009.  Then, the “embedded” risk premium became quite volatile and declined brutally in 2011 when the Fed decided to increase its Quantitative Easing operations. Since then the “embedded” US risk premium has been around 0 (or slightly negative according to most of the other approaches). In other words, long-term rates have been quite close to the average expected short rate: over the last few years, the US yield curve has exhibited a positive slope, but only because markets had been expecting the Fed to tighten the US monetary policy and raise short rates in the future. There was not significant embedded risk premium.

In the eurozone, the impact of QE at the beginning of 2015 was even more pronounced. The “embedded” risk premium became significantly negative in “core” countries (Germany, France…): current long-term rates are significantly below the average expected short rate over the coming 10 years if we share the mainstream scenario regarding the ECB’s future monetary policy (i.e. a progressive normalization of interest rates starting in the second half of 2019).

Thus, in both zones, we have observed the same phenomenon. Firstly, there was a sort of downward rigidity of the “embedded” risk premia: they declined in the early 2000s before the financial crisis, yet they stayed significantly positive despite the “spot” risk premia having turned negative a long time ago. Secondly, central banks’ QEs have apparently succeeded at provoking a sharp downward adjustment of these “embedded” risk premia in the aftermath of the financial crisis. QEs seem to have been a very efficient instrument to reduce sharply the long-term borrowing costs!

How to explain these different phenomena, i.e. a sort of disconnect between the “embedded” and the “spot” risk premia for many years and a sudden adjustment of the “embedded” risk premia triggered by QEs?

We believe that the key to answer this question is to look at the behavior of fundamentalist investors over this period and how they may have adapted the “valuation” risk premia they use as key inputs. Remember that the “valuation” risk premia are the risk premia that investors and analysts use as benchmarks when they judge if markets are correctly valued or not. As explained here, if for a given asset class, the “embedded” risk premium is above the “valuation” risk premium, the assets will be considered cheap and fundamentalist investors will advise to buy this asset class. Conversely, a low “embedded” risk premium relative to the “valuation” risk premium will lead to an overvaluation diagnosis.

In normal times, “valuation” risk premia are obviously a very important determinant of “embedded” risk premia. All the fundamentalists investors are playing actively to close the gaps between the two. Thus, as long as fundamentalists are a dominant force, the pricing of financial asset is very unlikely to look unusual: “embedded” risk premia will be close to the “valuation risk premia” and there will be no apparent “conundrum”. Yet, the situation may look rather different if fundamentalists become unable to stabilize some markets that become driven by other investment techniques, for example those based on the analysis of charts and momentum. Whenever the fundamentalists capitulate, the pricing of financial assets can become quite volatile and the “embedded” risk premia may wander in surprising territories.

In our view, before QEs took place, fundamentalist investors were mostly using inaccurate “valuation” duration risk premia, but most of them were able to persevere in their mistake and did NOT fully capitulate. There were many signs of a very strong demand for long-term government bonds, as illustrated by the “conundrum” highlighted by Alan Greenspan. The negative “spot” risk premia revealed by expectations survey should also have alerted fundamentalist investors that “this time was different”… for real. Yet, they mainly kept the failed markets’ wisdom that long-term bonds were riskier that short-term bills, and wrongly predicted that long rates would rise to a more normal level in the following year (see again the first graphs of this post).  As a result, during most of the early 2000s, fundamentalist investors were wrong footed by the behavior of long-term rates. There were many periods when the market behaved in a strange manner (with “technical” movements triggered by the interaction between fundamentalist and other sorts of investors), but there was no massive capitulation of the fundamentalists despite the losses triggered by short positions in the bond market. In some way, the day of reckoning was probably postponed by the good apparent economic situation of the years 2005-2006 prior to the financial crisis. Monetary policy was tightened more than expected and at last there was some moderate increase in long-term rates that seemed to validate the systemically bearish view of the (this time lucky) fundamentalist investors.

This situation of mispricing, which continued in the immediate aftermath of the financial crisis, created a perfect setting to make QEs very effective. On the one hand, the buying of bonds by central banks pushed “spot” duration risk premia even more in negative territory. It increased the disconnect between the positive “valuation” risk premia used by most fundamentalist investors and the sharply negative “spot” risk premia resulting from the huge excess demand for safe bonds. On the other hand, QEs forced fundamental investors to revisit their long-held assumptions relative to the “valuation” duration risk premia. The clear objective of this policy was indeed to support the economy by reducing these risk premia and reduce the cost of long-term debts to favor investments. Thus, the “risk premia” questions took center stage and it was no more possible to fudge the issue by repeating that long-term bonds were more risky than short-term bills as they have always been.

For all these reasons, QEs were responsible for a long delayed but massive capitulation of fundamentalist investors. They didn’t really change their “valuation” risk premia. They rather concluded that markets were distorted by the activity of central banks and that it was no more safe to try to stabilize long-term rates using traditional fundamental analysis. They mainly stopped to take short positions in bonds when they were judged too expansive, and they let the embedded risk premia collapse.

Now the tricky question is the following: how are markets likely to price duration risk now that the central banks have either reversed their QE policy (the Fed is in a Quantitative Tightening mode) or intend to stop it at the end of 2018 (the ECB).

Are inverted yield curves the “new normal”? Probably, despite some likely changes in the management of public debts and pension systems….

In our view, the reversal of QEs is unlikely to drive in the foreseeable future the “spot” duration risk premia in positive territory. As we have already stressed, “spot” risk premia were probably negative long before central banks started to expand their balance sheets. The main reason why “spot” risk premia are negative is probably because we are in a world with a lot of long term saving and a world where most of the changes in bonds prices come from changes in real interest rates rather than from changes in inflation. 

The situation is less clear cut as far as “embedded” risk premia are concerned. The “embedded” risk premia should reflect the current “spot” risk premia and their future likely changes (see again The Four Risk Premia). Thus, in the future “embedded” risk premia should also be negative: as a result, yield curve should be inverted if there is no tightening expected in monetary policies (obviously, when short rates are expected to rise, the yield curve may have a positive slope even if the “embedded’ risk premium is negative).

Yet, we are not sure that fundamentalist investors have already fully learnt the lessons of many years of yield curve “conundrum”… In the future, the end of QEs may convince many of them to declare the end of “markets’ distortions” and take again some large short positions on long-term bonds whenever the “embedded” risk premia seem too low. In other words, many may have temporarily capitulated, but have they changed their view of the “valuation” risk premia they should use when they will feel the time is right to make a comeback? We don’t think so and we would expect the chaotic process of risk premia adjustment to continue in the coming few years with some volatility in the bond market.

As long as central banks are in the tightening mode of the business cycle, it is likely that many fundamentalist investors not fully aware of the “new normal” will be tempted to reintroduce some short positions in the bond market. A flat yield curve will look for them as an anomaly and they will attribute it to some hypothetical mistakes made by other investors (suspected of underestimating the ongoing tightening of monetary policies). Thus, the return of fundamentalist investors may well push higher long-term interest rates in the coming few months.

Yet, the end of this tightening cycle may sooner or later serve as a new wake-up call for fundamentalist investors using positive “valuation” risk premia. In the US, according to most forecast (including the Fed’s “dot plots”) the peak of short rates may happen in 2019, or 2020 at the latest. At that time, we will not be surprised to observe a sharply inverted yield curve in US treasuries.

Is it possible to be more specific about how “sharp”, this inversion could be? Not really. And indeed, we would like to stress how difficult it is to estimate precisely what should be today the “valuation” and “embedded” risk premia in a hypothetical world of sophisticated fundamentalists. As explained several times, these premia should be based on the current “spot” risk premia with a realistic scenario for its future evolution. But, on the one hand, with the current expectations surveys, we got a rather imprecise estimate of the current “spot” premia7. And on the other hand, it is also difficult to forecast how they could evolve.

In particular, an inverted yield curve would probably trigger many reactions which could push progressively higher the risk premia. Indeed, over the last two years, the “spot” risk premia revealed by surveys has been on average -3.2% for the 10-year US treasury and -1.8% for the 10-year German bund. It is difficult to believe that such extreme negative levels may be sustainable in the long term.

First, the management of public debt would probably adapt. Currently, in many countries, the average duration of public debts is relatively limited (often around 7 years). As a result, public finances are exposed to the risk of rising interest rates in the future. Bearing this interest rate risk may make sense whenever “embedded” risk premia are strongly positive, i.e. whenever the cost of short-term debts is significantly lower than the cost of long-term debts. But it would be absurd to keep the same duration if “embedded” risk premia were to turn structurally negative. Thus, we may see in the distant future a significant increase of the duration of public debts which would push higher long-term rates. This lengthening of the duration of the public debt would make particular sense in the countries which belong to the Eurozone: indeed, we argue here that such a consolidation of public debts should be one of the key pillars of any reform of the Eurozone.

Second, a sharply inverted yield curve would probably accelerate the demise of the traditional defined benefits pension plans sponsored by private companies. They are currently huge buyers of very long-term bonds in order to match their long-term liabilities. Sharply negative “embedded” risk premia would create strong incentives to lower the duration of their portfolios in order to get a higher return, but this would create a dangerous maturity mismatch between the assets and liabilities. At the end of the day, such a situation would probably accelerate the shift from defined benefit pension plans towards defined contribution plans where the risks are born by the workers (see here for an analysis of pension systems and the best ways to “harvest” risk premia).

In the distant future, structurally inverted yield curves would probably lead to a higher supply of long-term debts and a lower demand from pension institutions. Thus, they are obvious limits to how inverted yield curves may become, but only the future will say where are these limits!

Version of October 22, 2018

  1. “Term premia: models and some stylised facts”, Benjamin H Cohen, Peter Hördahl and Dora Xia, BIS Quarterly Review, September 2018

  2. See “Greenspan’s Conundrum and the Fed’s Ability to Affect Long-Term Yields”, Journal of Money, Credit and Banking, March 2018, Vol.50(2-3), pp.513-543. This paper “shows that the connection between the 10-year yield and the federal funds rate was severed in the late 1980s, well in advance of Greenspan’s observation”. In an article published in the French statistical institute’s review in October 1990, we also discussed and tried to explain the surprising behavior of yield curves in the late 1980s (see “Primes de risque et politique monétaire”, In: Economie et statistique, N°236, Octobre 1990. pp. 7-23).

  3. Some of this volatility could be real, as the “betas” of bonds is also quite instable, see the correlation between the S&P500 and US long-term rates above. Yet, it seems likely that the use of expectations surveys introduces some noise in the measurement of the “spot” risk premia. There are at least three reasons why surveys may sometimes lead to an imprecise estimate of the average “E(zbondst)-  rt” across investors.  Firstly, they are often based on a relatively small number of respondents. Moreover, Consensus Economics surveys mainly economists who may not be perfectly representative of the actual investors. Secondly, these respondents generally give their most likely scenario: when risks are not symmetric around this central forecast, their answers will lead to biased and unstable estimates of E(zit). Thirdly, when financial markets’ economists are questioned, they often give their official forecast as published in their latest newsletter. When prices have recently moved significantly, their last official forecasts may no longer reflect their true expectations.

  4. In these estimates, the one-year risk-free rate is an interbank rate. The “spot” risk premia would be slightly less negative using the one-year rate on government bonds.

  5. Indeed, this is this fundamental discrepancy that helps yield curve models identify the origin of shocks impacting the whole yield curve. See Our Yield Curve Model.                                                                                                                                                                                                                   
  6. In fact, as the TED spread is sometimes quite volatile, we have added the average of the TED spread over the previous three months.                                             
  7. Mainly because the panel of respondents is often rather small and because they are questioned on their most likely scenario and not on their expected average scenario. In this paper about “The Role of Transparency For a Better Princing of Risk” we argued at the end of the 90s for new surveys coordinated by central banks which would allow more accurate estimates of “spot” risk premia (see Appendix 1).