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Description

EDHEC is launching the EDHEC Bond Risk Premium Monitor in September 2017. Its purpose is to offer to the investment and academic communities a tool to quantify and analyse the risk premium associated with Government bonds (with an initial focus on US Treasuries).

We calculate the risk premium using two distinct methods: (i) a purely statistical method and (ii) a model-based method.

 

 

 

Term Premia Estimates

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.

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.

 

Highlights March2019/June 2019 - The (Many) Problems of an Inverted Yield Curve

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.

 

FAQs

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.

The EDHEC Bond Risk Premium Monitor is a suite of tools that can be used to estimate the risk premium embedded in US Treasury bonds of different maturities.

In general, the risk premium can be thought of as the compensation investors require in order to bear the risks entailed in holding an asset. More precisely, it is proportional to the covariance between the pay-off of a security and the consumption of the investor. If we proxy consumption with return on investments, the risk premium should be proportional to the covariance between the pay-off of a security and the return from a broad market index (for example, the S&P 500).

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.

A high risk premium suggests that, on average, one can expect to make money from investing in long-term bonds and funding at the short end. From an asset manager’s perspective, a high risk premium suggests that it is a good time to be ‘long duration’ with respect to the chosen bond benchmark.

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.

From an asset pricing perspective, if an asset ‘hedges’ the risk from the market portfolio, then it will command a negative risk premium (we pay for fire insurance above the actuarial odds). So, if bonds hedge equity risk very effectively (the Greenspan/Bernanke/Yellen ‘put’), investors may then be willing to accept negative risk compensation for their hedging properties. Less precisely, it is often argued that, in an environment of extremely low (real) returns, ‘hunger for yields’ can drive risk premia into negative territory.

There is ample evidence that the risk premium is not a constant, but rather that it depends on the state of the economy. In turn, some aspects of the state of the economy are reflected in the shape the yield curve – so, the magnitude and sign of the risk premium depends (in part) on the shape of the yield curve.

We calculate the risk premium using two distinct methods: (i) a purely statistical method and (ii) a model-based method.

The statistical estimate of the risk premium is based on the analysis of the returns made by investing in a long-maturity bond and funding the position at the short end of the yield curve (the ‘carry’ strategy). If forward rates were unbiased expectations of future rates, then, on average, the carry strategy would make no money. Once a time series of excess returns has been obtained, that time series can be regressed against a number of candidate return-predicting factors, and it can be determined whether any of these factors are statistically significant. It must be stressed that, in order to avoid data mining and ‘factor fishing’, it is very important to give an economic explanation for the return-predicting factor.

Different return predicting factors give similar, but not identical, estimates of the risk premia. The more complex the return-predicting factor, the better the in-sample fit, but the grater the danger of over-fitting (and therefore of poor out-of-sample-prediction). We present the predictions from a (small) number of return-predicting factors, and the average of the predictions.

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’).

The return-predicting factors were chosen on the basis of robustness (out-of-sample performance) and predictive power. We mainly focus on four factors:

  1. the Cochrane-Piazzesi (2005) ‘tent-shaped’ factor (III) ;
  2. the Cieslak-Povala (2010a, 2010b) cycle-based factor (IV) ;
  3. the ‘restricted’ Cieslak-Povala factor (V);
  4. the unconditional slope and the level cycle (VI).

We also present the average of the four predictions, which is arguably the most reliable estimator.

Statistical models implicitly assume that the future looks like the past. As, over the last few years, authorities have been engaged in unprecedented monetary operations (QE, negative interest rates, etc.), past regularities may not apply to the present market conditions. Purely statistical models can therefore be ‘tricked’ by spurious similarities with past yield curve configurations. This is where a model can help, by adding financial information to the purely statistical data.

The extra financial information comes from the so-called ‘blue dots’ – predictions by members of the Monetary Policy Committee of the U.S. Fed about the future path of the fed funds rate. So, with the statistical approach, we try to directly estimate the risk premium, and we obtain the expectations as a by-product. With the model-based approach, we try to estimate the expectations and we obtain the risk premia. (In both cases, we take the market yields as given.

The model used belongs to the class of affine models. It is unique, however, in that it allows the market price of risk to be stochastic: instead of being a deterministic function of the shape of the yield curve, it is still only correlated with the established return-predicting factors. This means that, given a particular shape of the yield curve, the market price of risk does not always have to assume the same value. This is particularly important given the atypical monetary conditions encountered in the last ten years or so.

(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.
(V) ibid
(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).

 

Publications

International Journal of Theoretical and Applied Finance
AFFINE MODELS WITH STOCHASTIC MARKET PRICE OF RISK

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 »

Author: Riccardo Rebonato
18 May 2017

 

Related articles

Fed's low confidence signals recession, Investors Chronicle, 17 January 2019

Is the yield curve telling us that a recession is around the corner?, EDHEC Vox, 10 January 2019

Why Is the Market Not Believing the Fed?, EDHEC-Risk, 12 April2019

 

 

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