Fig 1: The 10-year term premium estimated by the Cochrane-Piazzesi, the Cieslak-Povala, the Slope &Cycle, and the EDHEC Stochastics Market price of Risk models.
The inversion of the US Treasury yield curve is creating headaches in many quarters, not least in the estimate of risk premia. All the best-trusted models (including the slope, the Cochrane-Piazzesi, the Cieslak-Povala – some of these used, or at least quoted, by the Fed) are giving nonsensical answers, estimating risk premia as negative as -5% or more for the 10-year yield. See these model estimates in Fig 1. What is happening? If taken literally, these models would imply future rates at such negative levels to make the German Bunds look like high-yielders.
The problem is that historically the inversion of the yield curve has been associated with poor returns for bonds, ie, a low or even negative risk premium. The traditional risk-premium models, trained as they are on 50 years of past history, have learnt this pattern, and they blindly apply it to the present market conditions. Unfortunately, past history knows close-to-nothing about the possibility of Quantitative Easing. In the present monetary conditions, these QE expectations almost mechanically engineer an inverted yield curve, which the models then interpret as harbinger of poor bond returns.
Interestingly, the EDHEC Stochastic Market Price of Risk model, which does not use this mechanical link between the shape of the yield curve and the risk premium, produces a very different, and much more reasonable, assessment of the bond risk premium. From an investor perspective, this is still nothing to get too excited about, as the EDHEC SMPR prediction of the risk compensation is around zero; however, once a bit a convexity is factored in, at least the number make sense, and do not imply future Fed funds of -5%.
This, of course, raises the Bernanke conundrum, who famously said that QE should not work in theory, but does work in practice. What did Chairman Bernanke mean, and what is the relevance of this conundrum?
To understand the issue in its essence, let’s forget for a moment risk premia and convexity. In this simplified world, yields are just the (expected) average of the future path of the Fed funds rate. Now, if the Fed were totally credible, once forward guidance has been given, buying long-dated bonds should have no effect on yields whatsoever: suppose that the Fed signalled rate at 2% until the end of time, but bought long-dated bonds so as to push their yields below 2%. Then the shrewd investor would just short the long-dated Treasury bond and lend at 2% (we are neglecting convexity here), and by bond maturity would reap a riskless profit. Of course, by shorting the ‘expensive’ bond, it would push its yield back up towards 2%, negating the QE efforts of the Fed.
This is all true in theory. However, the ‘arbitrage’ would take 10 years to materialize, and many an ‘arbitrage’ have had to be unwound before the clever investor could reap her profit. So, QE, and QE expectations, do change the shape of the yield curve, adding distortions to its shape not fully captured by a pure-expectation-plus-risk-premium picture of the yield curve. The most convincing interpretation of the current shape of the yield curve is therefore that the market expects the Fed to respond to a recession by engaging in QE sooner rather than later.
EDHEC is launching the EDHEC Bond Risk Premium Monitor in September 2017. Its purpose is to offer to the investment and academic community a tool to quantify and analyse the risk premium associated with Government bonds (with an initial focus on US Treasuries).
The following FAQs provide detailed explanations of what it can offer.
For a precise definition, see Cochrane (2001), Asset Pricing, Princeton University Press, or Rebonato (2018), Bond Pricing and Yield Curve Modelling – A Structural Approach, Cambridge University Press, Chapter 15.
In the case of (riskless) bonds, the risk premium is associated with the strategy of being ‘long duration’, (i.e. of funding a long position in a long-maturity bond by shorting a short-maturity bond). The strategy is often referred to as a ‘carry’ trade.
Risk premia provide timing (rather than cross-sectional) investment information. They answer the question, “Is today a good (bad) time to be long duration?” They do not answer the question, “Given that I have to be invested today, which bond gives the most attractive expected return?”
Risk premia also allow the market expectations about the future path of the short rate (Fed funds) to be extracted from the market yields.
We stress that changes in risk premia are more reliably estimated than the level of risk premia (the ‘slopes’ of the regressions have tighter confidence bands than the ‘intercepts’).
We also present the average of the four predictions, which is arguably the most reliable estimator.
(I) Strictly speaking, one should also take convexity into account. For a discussion, please refer to Rebonato (2018). Bond Pricing and Yield-Curve Modelling – A Structural Approach, Cambridge University Press, Chapters 20-21.
(II) See Rebonato (2018). Bond Pricing and Yield-Curve Modelling – A Structural Approach, Cambridge University Press, Chapter 24.
(III) See Cochrane, J. H. and M. Piazzesi (2005). Bond Risk Premia. American Economic Review 95(1): 138-160; for technical details, and the regression coefficients, see https://www.aeaweb.org/aer/data/mar05_app_cochrane.pdf (accessed on 25 November 2014).
(IV) Cieslak, A. and P. Povala (2010a). Understanding Bond Risk Premia. Working paper – Kellogg School of Management and University of Lugano, available at
https://www.gsb.stanford.edu/sites/default/files/documents/fin_01_11_Cie..., accessed on 5 May 2015, and Cieslak, A. and P. Povala (2010b). Expected Returns in Treasury Bonds, working paper, Northwestern University and Birbeck College, forthcoming in Review of Financial Studies.
(VI) Hatano, T. (2016). Investigation of Cyclical and Unconditional Excess Return Predicting Factors. MSc thesis – Oxford University.
(VII) See Rebonato (2018). Bond Pricing and Yield-Curve Modelling – A Structural Approach, Cambridge University Press, Chapter 25 for a discussion of this point.
(VIII) For a chapter-length description of affine models, see, Piazzesi M. (2010), Affine Term Structure Models, Chapter 12 in Handbook of Financial Econometrics, Elsevier, or Bolder, D. J. (2001). Affine Term-Structure Models: Theory and Implementation, Bank of Canada, Working paper 2001-15, available at http://www.bankofcanada.ca/wp-content/uploads/2010/02/wp01-15a.pdf , accessed on 11 August 2017. For a book-length treatment, see Rebonato (2018), Bond Pricing and Yield-Curve Modelling – A Structural Approach, Cambridge University Press.
(IX) For a detailed description of the model, see Rebonato (2017). Reduced-Form Affine Models with Stochastic Market Price of Risk, International Journal of Theoretical and Applied Finance(forthcoming).
In this paper we discuss the common shortcomings of a large class of essentially-affine models in the current monetary environment of repressed rates, and we present a class of reduced-form stochastic-market-risk affine models that can overcome these problems. In
particular, we look at the extension of a popular doubly-mean-reverting Vasicek model, but the idea can be applied to all essentially-affine models.
Read more »
By accessing this tab via the website, users signal their agreement with the conditions and clauses set out below and pledge to abide by them.
The purpose of these sections is to showcase and present academic research only. It seeks to provide information concerning non-investable indices and a database that may be used for research purposes. None of the information may be considered as constituting an offer of products or services, particularly of financial products, on the part of EDHEC-Risk Institute, nor as a solicitation to purchase or sell securities or any other investment product.
EDHEC-Risk Institute does not offer any online services, nor any benefits and makes no pledge whatsoever to maintain the continuity of its research production.
EDHEC-Risk Institute reserves the right to amend these conditions at any moment without notice, with publication of the new conditions being deemed to constitute notification to users and indicate their consent.
The general structure of this website, as well as the texts, graphics, images, sounds and videos that comprise it, are the property of EDHEC-Risk Institute. Any representation and/or reproduction and/or exploitation of the content and services proposed by Investment Solutions, either partially or in full, by any process whatsoever, without prior written authorisation from EDHEC-Risk Institute is strictly forbidden and liable to constitute an infringement of articles L 335-2 et seq. of France’s Intellectual Property Code (Code de la propriété intellectuelle).
Any representation and/or reproduction and/or exploitation of EDHEC-Risk Institute’s trademarks, either partially or in full, in any manner whatsoever, is totally prohibited.
This website is designed for personal ends and not for commercial purposes.
EDHEC-Risk Institute may in no case be held liable for any form of direct or indirect loss, nor any other prejudice in any form whatsoever, resulting from the use of this section or the impossibility of using it for any reason whatsoever, whether such liability is or is not contractual, tortious or quasi-tortious or if founded on the principle of liability without fault or other, and even in the event that EDHEC-Risk Institute may have been warned of the eventuality of such loss or prejudice.
-EDHEC-Risk Institute may not be held liable for the use of the information available in this website; EDHEC-Risk Institute does not guarantee that the information is free from error; consequently, any use that users make of the information is done so at their own risk;
-none of the elements contained on the site constitute asset allocation advice, financial or investment advice or advice of any other nature;
-none of the indices on this site shall be used or referenced as a benchmark by any financial instrument, financial contract or investment fund where such use or reference falls within the scope of Regulation (EU) 2016/1011 of the European Parliament and of the Council of 8 June 2016 on indices used as benchmarks in financial instruments and financial contracts or to measure the performance of investment funds and amending Directives 2008/48/EC and 2014/17/EU and Regulation (EU) No 596/2014 and EDHEC-Risk Institute shall not be responsible for any such use or reference.
-the projections presented are based on simulations; past performances in no way guarantee future performances. The information provided may in no way be deemed to represent investment guarantees or investment-return guarantees.
This list is not limitative.
This tab may contain hypertext links to other sites on the internet. The links towards these other resources lead you to exit this site.
These links and sources of information are provided for users purely for informational purposes only. EDHEC-Risk Institute has no authority over the content of characteristics of these other resources and may in no case be held liable for their content or for any loss or prejudice that may result from their use.
Users must take the necessary precautions to ensure that the said resources do not contain any viruses or any other malicious elements.
The user hereby accepts the characteristics and limits of internet, and recognises in particular that:
EDHEC-Risk Institute does not assume any liability for the services accessible by internet and does not exercise any control in any form whatsoever over the type and characteristics of the data that might transit via its server centre.
The user recognises that the data circulating on internet is not protected, particularly against possible misappropriation. Communication of any information deemed by the user to be sensitive or confidential is done so at the user’s own risk and peril.
The user is solely liable for the use of data that he/she consults, searches and transfers on Internet.
The user recognises that EDHEC-Risk Institute does not possess any means of controlling the content of the accessible services
Both this site and its terms and conditions of use are governed by French law, wherever the place of use. In the event of any dispute, and after the failure of all attempts to find an amicable solution, the French courts of Lille shall be the sole ones competent to adjudicate such disputes.