Riccardo Rebonato, Professor of Finance, EDHEC-Risk Institute, EDHEC Business School is specialist in interest rate risk modelling with applications to bond portfolio management and fixed-income derivatives pricing. **He gives you his insights on the inverted yield curve and unveil the latest estimates of the EDHEC Bond Risk Premium Monitor with a comparison of 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.

*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 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**.

*Riccardo Rebonato is Professor of Finance at EDHEC Business School. He was previously Global Head of Rates and FX Research at PIMCO. He also served as Head of Front Office Risk Management and Head of Clients Analytics, Global Head of Market Risk and Global Head of Quantitative Research at Royal Bank of Scotland (RBS). Prior joining RBS, he was Head of Complex IR Derivatives Trading and Head of Head of Derivatives Research at Barclays Capital. Riccardo Rebonato has served on the Board of ISDA (2002-2011), and has been on the Board of GARP since 2001. He was a visiting lecturer in Mathematical Finance at Oxford University (2001-2015). He is the author of several books, in particular having published extensively on interest rate modelling, risk management, and most notably books on SABR/LIBOR Market Model pricing of interest rate derivatives, as well as on the use of Bayesian nets for stress testing and asset allocation. He has published articles in international academic journals such as Quantitative Finance, the Journal of Derivatives and the Journal of Investment Management, and has made frequent presentations at academic and practitioner conferences. He holds a doctorate in Nuclear Engineering (Universita' di Milano) and a PhD in Science of Materials (Condensed Matter Physics, Stony Brook University, NY).*