深度研究：巴黎銀行R周期介紹

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4、 disclosures at the end of this reportDEEP DIVE | GLOBAL5 April 2019Introducing BNP Paribas Cyclical-RKEY MESSAGESCyclical-R is BNP Paribass new fair value model for 10-year government bond yields. Our approach is to combine cyclical variables with the well-known R* framework.KEY MESSAGESCyclical-R

5、is BNP Paribass new fair value model for 10-year government bond yields. Our approach is to combine cyclical variables with the well-known R* framework.The model indicates when 10y yields appear too high or low compared with economic fundamentals such as growth andinflation.The model currently indic

6、ates that yields in Germany and the UK appear around 15bp too low. History suggests that convergence back to fair value tends to take between three to twelve months.The decline in 10y yields in other developed markets has been in line with softening growth and inflation in recent months.BNP Paribas

7、Cyclical-R builds on two academic approaches for bond yields, R* and the Taylor rule, combining them with econometric techniques to provide a fair value that bond yields have tended to track over time.Backtesting suggests that deviations from fair value are temporary, with an overshoot of 10y yields

8、 historically lasting around three to twelve months (see page 4).BNP Paribas Cyclical-R provides systematic signals based on the current macro economic situation. They will be used as an input into BNP Paribas analysis but may not always be aligned with our views, which might take other factors into

9、 consideration.Summary of Cyclical-RUSGermanyFranceUKJapanCanadaAustraliaCyclical-R (%)2.480.160.481.27-0.061.662.44Deviation (bp)5-15-10-1534-54Z-score0.2-0.8-0.5-1.7SignalNeutralYield to riseNeutralYield to riseNeutralNeutralYield too low, butstatistical confidenceis low%Fig. 1: BNPP Cyclical-R fo

10、r US10y yieldFig. 2: BNPP Cyclical-R for 10y Bund yield%Sources: Bloomberg, Macrobond,BNP ParibasSources: Bloomberg, Macrobond, BNPParibas HYPERLINK mailto:michael.sneyd Michael Sneyd, Head of Macro Quantitative & Derivatives Strategy | BNP Paribas London BranchBNP Paribas Cyclical-R: standing on th

11、e shoulders of giantsCyclical-R builds on existing fair-value tools. There are limited academic based tools for assessing the fair- value for rates over a 3-12 month horizon. The most popular models are the risk neutral rate of interest known most commonly as r* - and the Taylor rule. We have taken

12、guidance from these approaches establish a framework for assessing 10y bond yields based on macroeconomicfundamentals.R* and long-term variables. While the R* estimate can be referred to as the policy rate a central bank would have if an economy were running in line with its potential GDP and had re

13、ached its inflation target, it has also proved a useful indicator for super-long bond yields, given that these are less likely to be impacted by cyclicaldynamics.The most popular literature on R* by Lauchbach and Williams (2003) describes the main drivers of interest rates over the long term. The pa

14、per indicates that the real R* is determined largely by the potential growth rate, but also finds an impact from the shift in time preferences, due largely to changing demographics (we will publish more on this topic at a laterstage).This factor causes R* to deviate from a simple estimate based on p

15、otential GDP growth alone, and means the nominal R* can, over time, deviate from a simple calculation of potential GDP growth plus a central banks inflation target. The paper describes the factor as “unobserved” or “other determinants” of the neutral rate, We take this into consideration in our Cycl

16、ical-Rmodel.The Taylor rule and cyclical variables. The Taylor rule is a calculation usually used to assess short-term interest rates, but we find that its components the output gap and inflation gap by themselves have better predictive power for interest rates.Cyclical-R is estimated on monthly dat

17、a, using original vintage data where possible. To generate a monthly GDP series, we interpolate GDP using our economic strength index our daily-frequency tracker of the strength of economic data using the Chow-Lin interpolation technique. This approach also provides a simple now- cast estimate, so t

18、hat each fair value point incorporates the latest assessment of the economy.Fair values are estimated using constrained maximum likelihood regressions, with the coefficients constrained to be economically intuitive and to avoid overfitting the model. The variables are estimated in levels, resulting

19、in estimated cointegrated relationships between the variables and the 10y bond yield, similar to our approaches used in BNP Paribass short- and medium- term FX fair-value models, STEER and CLEER.Co-integration theory states that non-stationary variables tend to move together over time, with deviatio

20、ns from each other being temporary. Relationships between the variables and yields also tend to change over time, which we incorporate by estimating relationships using a three- year rolling regression.Sources: Bloomberg, Macro HYPERLINK mailto:michael.sneyd Michael Sneyd, Head of Macro Quantitative

21、 & Derivatives Strategybond, BNP ParibasFig. 3: US HLW R* andotherdeterminantsFig. 4: Eurozone HLW R* and otherdeterminantsSources: Bloomberg, Macro HYPERLINK mailto:michael.sneyd Michael Sneyd, Head of Macro Quantitative & Derivatives Strategybond, BNP ParibasSources: Bloomberg, Macrobond,BNP Parib

22、asSources: Bloomberg, Macrobond, BNPParibasFig. 5: US Taylor rule estimate BNP Paribas Cyclical-R: Combining existing approachesSummary of long-term variables: Based on R* literature we incorporate the following variables:Potential real GDP growth: Estimated using a rolling Hodrick Prescottfilter*.T

23、rend inflation:To turn real R* into a nominal gauge, academic literature suggests using the central banks inflation target. To make our model more responsive to long-term shifts in inflation, use a long-term trend, also calculated using a Hodrick-Prescottfilter.Unobservable structural factor: The “o

24、ther determinants” factor in the 2017 Holston- Laubach-Williams R* model (HLW). We capture this by the difference between our simple nominal R* estimate (potential GDP growth plus trend inflation) and market rates over the long term. our view, these variables have been driven by a combination of qua

25、ntitative easing and the impact of demographics leading to high savingrates.*The Hodrick Prescott filter which is easy to use and interpret is also renowned for over-fitting when calculated in sample. To avoid this we use an expanding HP filter, eg the trend is estimated on only the information that

26、 was available at the point of time that the fair value was estimated.Summary of cyclical variables: Based on the Taylor Rule and our observation of rate market drivers, weinclude:Output gap the difference between current GDP growth and potential GDP. A component taken from the Taylor Rule to indica

27、te how the monetary policy stance is likely to respond to an economys cycle. A more positive (negative) output gap should correspond with higher (lower) yields. We produce a “l(fā)ive” gap by extrapolating GDP using our Economic Strength Index(ESI).Inflation gap the difference between the current inflat

28、ion rate and the long-term trend of the inflation rate. Also from the Taylor Rule to capture how the monetary policy stance is likely respond to the current level ofinflation.Excess liquidity a variable to capture non- standard operations by a central bank, mainly QE. Where significant, rising exces

29、s liquidity puts downward pressure on yields. Our testing of various specifications suggests the stock of excess liquidity is a better indicator for a 10y yield than the flow, or the change in, excessliquidity.Equity market performance Incorporated capture the impact of market sentiment on bond yiel

30、ds, using the 6m change in equity market performance. A decline/rise in equity prices has historically tended to correspond to lower/higher bondyields.Fig. 6: US basic nominal R* estimate (trend growth and inflation)Fig. 7: Real-time output gap estimate for US HYPERLINK mailto:michael.sneyd Michael

31、Sneyd, Head of Macro Quantitative & DerivativesStrategySources: Bloomberg, Macrobond,BNP ParibasSources: Bloomberg, Macrobond, BNP HYPERLINK mailto:michael.sneyd Michael Sneyd, Head of Macro Quantitative & DerivativesStrategyTesting the Cyclical-R frameworkOverall, our backtesting suggests the BNP P

32、aribas Cyclical-R model could add value when assessing G7 bond yields over a horizon of 3-12 months.When building models, we favour a simple model based on academic theory, as models that try to capture everything can result in overfitting.It is therefore important to have an indicator that tells us

33、 when the model is working and we should or should not put emphasis on the models outputs.We have achieved such an indicator by running a co- integration test on the model at each point in time to show whether or not the variables have a co- integrated relationship with the bond yield (Figure 1).If

34、they do not, the fair value and the 10y yield may not realign with each other, resulting in the model likely being less predictive. The periods in which co- integration does not hold are indicated by lighter shading on the fair-value plots.To assess Cyclical-Rs capacity to provide an accurate indica

35、tion of fair value, we run a simple trading strategy of buying/selling the bond* when yields are more than one standard deviation above/below fair value. The position is held until convergence with fair value has been achieved, or the co-integration filter signals that realignment is lesslikely.Fig.

36、 8: Co-integration statistic for US modelIf the fair value and explanatory variables are not co- integrated when the deviation takes place, a signal is not entered. The results are shown in Figures 9-11.This indicative strategy has given a reasonable performance, with an overall Sharpe ratio for tra

37、ding futures of 0.54. It typically takes between three and six months for a yield to move back towards its fair value, although it can take up to 12 months.The performance for trading the overshoot of a yield above its fair value is better than positioning for a yield to rise when it has overshot be

38、low its fair value a long- bond only strategy has a Sharpe ratio of 1.13.Some of this difference can be explained by the impact of carry and roll being positive when positioning for a yield to decline, but negative when positioning for arise.The difference could also be due to the downward trend in

39、yields over the past 20 years enhancing the performance of long positions. However, as long positions were held over average for 15% of the time since 2000, we do not think this is the case. Rather, it appears that a sell-off in bond markets is easier to fade than arally.*We use BNP Paribas excess r

40、eturn series to capture the performance of the signals.These hypothetical, past performance simulations are the result of estimates made by BNP Paribas, as of a given moment, on the basis of parameters, market conditions, and historical data selected by BNP Paribas, and should not be used as guidanc

41、e, in any way, of future performance. The above graph is for illustrative purposes only.Fig. 9: Cumulative returns of portfolioPortfolio returns, 10% target vol350300250P-value above 0.05 indicates lower likelihood that yields converges to Cyclical-R value200P-value above 0.05 indicates lower likeli

42、hood that yields converges to Cyclical-R value150100500Feb-00Feb-04Feb-08Feb-12Feb-16Long & short bondsLong bond onlyShort bond onlySources: BNP ParibasSources: BNP ParibasFig. 10: Performance statistics (Sharpe ratio)Long & short bondsLong bond onlyShort bond onlyCu260i.e. position on overi.e. posi

43、tion onLong & short bondsLong bond onlyShort bond onlyCu260i.e. position on overi.e. position oni.e. position on240and undershoots ofovershoot of 10yundershoot of 10y10y yieldsyieldsyieldsUS0.690.790.26Germany0.160.73-0.23France*-0.56-0.56UK0.070.48-0.22Japan0.490.680.01Canada0.350.74-0.33Fig. 11: C

44、umulative returns of long-only strategymulative returns, 10% target vol220200180160140120100SS HYPERLINK mailto:michael.sneyd Michael Sneyd, Head of Macro Quantitative & DerivativesStrategyAustralia0.050.35-0.1880 HYPERLINK mailto:michael.sneyd Michael Sneyd, Head of Macro Quantitative & Derivatives

45、StrategyAustralia0.050.35-0.1880Portfolio0.541.13-0.18Jan-00Jan-05Jan-10Jan-15Notes: Performance based on BNPP excess return series for 10y bonds. *Excess returns series for France starts in 2012ources: BNP Paribas USGermanyUnitedKingdomJapanCanadaAusSources: BNP ParibasCyclical-R results: German an

46、d UK yields too lowA snapshot of Cyclical-R values and deviations are shown in Figure 12. The current fair values are based on information available up to 4 April 2019. The largest deviations are currently in Germany (-15bp), UK (-15bp) and Australia (-54bp), with the model signalling that UK and Ge

47、rman yields are likely to rise over the coming months.For the 10y Bund yield, the Cyclical-R value has declined by 25bp over the past six months, driven largely by softening inflation, and currently stands at 0.16%. Prior to this decline, our estimate of basic R* had been rising due to inflation and

48、 growth trends improving, while it also appears that the size of ECB excess liquidity is suppressing the Bund yield. The current Cyclical-R value of 0.16% suggests the yields move into negative territory was an overshoot. This result differs from our recently-updated Intrinsic HYPERLINK /Singletrack

49、CMS_DownloadDocument?uid=2effff59-0ae2-4f73-a30e-3ec1e37aa690&docRef=9c21ecf0-95dc-482c-8f40-e681a11d017e&jobRef=39df6f13-791c-4439-a823-31ede521c2af Value model (Our Bund yield Intrinsic Valuation model turns negative, 28 March 2019) because of the longer-term focus ofCyclical-R.Cyclical-R signals

50、that the UK 10y yield has recently been at its largest overshooting level since shortly after the UKs referendum to leave the EU in 2016. The yield is currently trading 15bp below its fair value of 1.27%. As a result, the model suggests that the UK 10y yield is likely to rise from current levels.The

51、 US 10y Treasury yield has been moving lower broadly in line with its cyclical fundamentals, according to Cyclical-R, and its fair value is currently 2.48%. Over the past 12 months, the model suggests that the decline in US excess liquidity, caused by the Feds balance sheet shrinkage, has added 40bp

52、 to the value of the 10y yield. However, the softer economic backdrop has reduced the fair-value by slightly more than this amount (46bp, see figure 15).Cyclical-R identifies Australias 10y yield as having the largest overshoot, trading 55bp below its fair value of 2.44%. However, the model shows le

53、ss confidence that the yield will rise (indicated by the light shading in Figure 32), which reflects that drivers outside of our model are currently important for Australian bonds.The Cyclical-R values from France, Japan and Canada have all declined over the past few months, resulting in these marke

54、ts trading broadly in line with their fair values.For France, our model picks up that OATs appear to have a higher sensitivity than Bunds to growth and soft equity market performance, resulting in a larger decline in the fair value, currently at0.48%.The decline in Japans 10y yield has broadly been

55、in line with its Cyclical-R fair value since the start of the year. contrast, the decline at the end of 2018 corresponded with the yield falling from elevated levels. The fair value is currently-6bp.The decline in Canadas 10y yields over the past six months has been fully in line its Cyclical-R fair

56、 value, and has corresponded with the decline in Canadas growth and inflation. The fair value is currently 1.66%, in line with the market yield (Figure 29).The signals from Cyclical-R are designed to provide insight into the bond market based on the current macroeconomic factor. Deviations from Cycl

57、ical-R tend take 3-12 months to converge back to the fair value and our backtesting suggests that they are a useful input when managing bond exposures, especially when yields overshoot above the Cyclical-R value. These output will be used as an input into BNP Paribas analysis but may not always be a

58、ligned with our views as these may take other factors intoconsideration.2.01.51.0Z-score deviation0.5Z-score deviation0.0-0.5-1.0-1.5-2.0Fig. 12: Cyclical-R values across G7, now vs 3m ago10y10yyieldstoohigh10yyieldstoolowUSGermanyFranceUKJapanCanadaAustralia 30-Nov-1803-Apr-19USGermanyUSGermanyFran

59、ceUKJapanCanadaAustraliaCyclical-R (%)2.480.160.481.27-0.061.662.44Deviation (bp)4.6-14.8-9.9-54.0Z-score0.2-0.8-0.5-1.7Yield too low, butModel signalNeutralYield to riseNeutralYield to riseNeutralNeutralstatistical confidence is low HYPERLINK mailto:michael.sneyd Michael Sneyd, Head of Macro Quanti

60、tative & DerivativesStrategy| HYPERLINK mailto:laurence.mutkin Laurence Mutkin HYPERLINK mailto:michael.sneyd Michael Sneyd, Head of Macro Quantitative & DerivativesStrategyBNP Paribas Cyclical-RFig. 13: Cyclical-R US 10y since 2001Fig. 14: Cyclical-R US 10y since2016Fig. 15: Contribution to changes