interest rate modeling getco
TRANSCRIPT
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Work on Term structure
modeling
Sankha Banerjee
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Introduction Background Modeling Results Summary
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The?
Panic of 2008
Whatassetshaveheldtheirvaluebest US Treasury bills (stable value)
Nominal US Treasury bonds (increasing value) WhyhavenominalTreasuriesbeensuch good hedges?
Flight to quality helps safe assets, but why are nominal Treasuries regarded as safe?
They have no credit risk, but they do have inflation risk
Have nominal Treasuries always hedged investors against other risks?
Understanding Bond Risks Thislectureexplorestime-variationininflation risk and its effect on the
nominal Treasury yield curve
TheanalysismakessomeuseofTIPSdata but TIPS are not the main focus
Attheend,abriefanalysisofcurrencies along the same lines
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What do we know from the 2008?
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US Treasury bills and Nominal US Treasury bonds hold their value during a high
volatility event
They act as good hedge, and the phenomenon of "Flight to quality helps safe
assets.
Why are nominal Treasuries regarded as safe? They have no credit risk, but they
do have inflation risk
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Time series of the stock-bond covariance and the CAPM beta of the 10 year nominal bond
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Time series of the stock-deflation covariance and the CAPM beta of deflation
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Time series of the US 10-year inflation-indexed yields
Estimated time series of the real rate
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Time series of the real bond second moments
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Time series of the nominal bond second moments
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Estimated time series of permanent and transitory components of expected inflation
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Estimated time series of covariance of the inflation with interest rate.
Response of the nominal expected excess returns to covariance of the inflation with
Interest rate.
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Estimated time series of expected excess returns for 10 year nominal bonds.
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Response of the yield curves to covariance of the inflation with Interest rate.
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Changing Conventional Wisdom
Late1970sandearly1980s:
Bonds are exposed to the risk of stagflation Avoid them unless the term premium
is high
2000s:
Bonds are hedges against the risk of deflation Anchor to windward Hold them even at a low term premium
Changing CW reflects changing reality Bonds as hedges in 2007-2008
Changing Inflation Behavior
The changesinmeasuredbondrisksappear to be related to changing behavior of
the Phillips Curve WhenthePhillipsCurveisstable(early 1960s, 2000s), inflation falls when
unemployment rises
Then bonds do well in bad times and hedge macroeconomic risk
WhenthePhillipsCurveisunstable(1970s and early 1980s), inflation and
unemployment move together (stagflation)
Then bonds do badly in bad times and are risky
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Term structure modeling
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Real stochastic discount factor (SDF):
xt
is real rate:
zt
drives time-variation in volatility of SDF:
xt
and zt
follow AR(1) processes:
d i k d d li l
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Modelling the Yield Curve
Changingbondriskdoesseemtomatterover the long run
Intheshortrun,however,thereareother influences on the yield curve
Tocaptureitsmovements,weneedto consider more traditional factors as well:
The real interest rate
Investor attitudes towards risk Expected inflation Campbell,Sunderam,andViceira2008 undertakes this project
A Bond Pricing Model
Weconsiderfivefactorsthatmoveindifferent ways:
Real interest ratext(transient)
Risk aversion zt(persistent)
Long-run expected inflation t (permanent) Temporary expected inflation t(transient)
Covariance of inflation with recession t(persistent, can change sign)
Thefivefactorsarenotdirectlyobserved,so we back out their implied values from data we
do observe
Nonlinear Kalman filtering
I d i B k d M d li R l S
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Fisher equation Inflation risk premium
I t d ti B k d M d li R lt S
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Date
CAPMbeta
Introd ction Backgro nd Modeling Res lts S mmar
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Stagflation risk
Deflation risk
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Implications for the Yield Curve
Weplottheyieldcurveatthesamplemeanofall the state variables
Thenwevaryeachstatevariabletoitssample minimum and maximum, while holding the
other state variables at their sample mean
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This variable is the main innovation of our model, and plays important role:
(t)2 drives time variation in the conditional volatility of both realized
inflation and expected inflation.
zt tdrives time variation in the covariance of the real economy with
inflation, and thus determines nominal bond risk premia.
This covariance (and thus bond risk premia) can switch sign as ttakes
positive or negative values (zt is always positive in the data)
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Nested Models
Both ztand tconstant
Two-factor affine yield model of Campbell and
Viceira (2001, 2002).
Both real bond risk premia and nominal risk premia are constant. ztvarying and tconstant
Three-factor affine yield model ((Bekaert et al.,
2004, Buraschi and Jiltsov 2006, Wachter 2006).
Both real bond risk premia and nominal bond risk premia vary with aggregate risk
aversion
ztconstant and tvarying Single-factor affine yield model for the real term structure, and a linear-quadratic
model for the term structure for nominal interest rates.
Constant real bond risk premia, time-varying nominal bond risk premia.
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Estimation
Maximum likelihood via nonlinear Kalman filter because state variables are
unobserved.
UnscentedKalmanfilter(JulierandUhlmann 1997, Wan and van der Merwe 2000,Koijen and Binsbergen 2008)
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Observed Variables
Nominalyieldcurveatmaturities3months,1 year, 3 years, 10 years
TIPSyield
Realized inflation Equityreturnsanddividendyield(proxyforrisk aversion)
Realized bond variance and bond-equity covariance in daily data
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Implications for the Yield Curve
Realinterestrateandtemporaryexpected inflation move the short end
Riskaversionmovesthelongend
Permanentexpectedinflationmovestheyield
curve up and down in parallel
Inflation-recessioncovariancedrivesthe curvature of the yield curve
Implications for the Yield Curve Fixed-incomepractitionersanalyzetheyield curve using level, slope, and curvature factors
Theydonotrelatethesefactorstoexternal market conditions
Ourmodeldoes:
Real interest rate and permanent expected inflation
drive the level factor
Real interest rate, risk aversion, and temporary expected inflation drive the slope factor
Inflation-recession covariance drives the curvature factor
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Implications for Bond Returns Whathappenswheninvestorsbecomemorerisk averse?
Ifbondsarerisky,theninvestorssellbothstocks and bonds
Ifbondsarehedges,theninvestorssellstocks and buy bonds (flight to quality)
Thusmovementsinriskaversionamplifythe covariance of bonds and stocks
If the covariance is positive, it becomes more positive
If the covariance is negative, it becomes more negative
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Implications for Term Premia
Expectedexcessbondreturns(termpremia)are determined by