TADC, London Business School, 2010
Monetary Policy and the Uncovered Interest Rate Parity Puzzle by David Backus, Federico Gavazzoni, Chris Telmer and Stanley Zin Discussion by Anna Cie´slak University of Lugano Institute of Finance
May 14, 2010
c TADC-LBS ( 2009 Anna Cie´slak)
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The carry trade ⊲ Carry trade C1. Fed and $ C1. Asymmetry C2. MP and vol C0. Other Literature
Impressive performance compared to S&P SR=0.362 p.a.:
23 developed countries G10 countries
Mean
Std
SR p.a.
Skew
0.181 0.217
0.934 1.327
0.637 0.567
-1.106 -1.012
See Ang & Chen (2010); sample 1975-2009
In short picking up nickels in front of steamrollers: you have a long run of small gains but eventually you get squashed Economist, 22.2.2007 Why should policy makers care about carry trades? i. More complicated conduct of monetary policy ii. Currency dislocations iii. Large exposure to fundamental risk factors, systemic risk due to unwinding carry positions [e.g. $ carry trades, 2009] This paper asks a very important and topical question. c TADC-LBS ( 2009 Anna Cie´slak)
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C1. Fed and the dollar Carry trade C1. Fed and $ C1. Asymmetry C2. MP and vol C0. Other Literature
⊲
We are attentive to the implications of changes in the value of the dollar for inflation and inflation expectations and will continue to formulate policy to guard against risks to both parts of our dual mandate, including the risk of an erosion in longer-term inflation expectations. The Federal Open Market Committee will strongly resist an erosion of longer-term inflation expectations, as an unanchoring of those expectations would be destabilizing for growth as well as for inflation. — Ben Bernanke, Jun 3, 2008
c TADC-LBS ( 2009 Anna Cie´slak)
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C1. Asymmetry in monetary policy rules $/EUR
Carry trade C1. Fed and $ C1. Asymmetry C2. MP and vol C0. Other Literature
$/EUR
1⋆ I estimate: yt+n − yt1⋆ = a + b log ft+n /ft
⊲
⋆
+ εt+n
n = 1m
n = 2m
n = 3m
n = 4m
US
b t-stat R2
-0.2 -2.6 4.8%
-0.2 -2.7 5.0%
-0.2 -2.5 4.0%
-0.2 -2.0 2.9%
Ger
b t-stat R2
-0.1 -1.6 1.4%
-0.1 -1.1 1.1%
-0.1 -0.9 1.1%
-0.1 -0.8 0.8%
∗
I use sample 1975–2009; all variables standardized; data: Datastream, BOE, Bundesbank, and Fed H.15 c TADC-LBS ( 2009 Anna Cie´slak)
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C1. Asymmetry in monetary policy rules $/EUR
Carry trade C1. Fed and $ C1. Asymmetry C2. MP and vol C0. Other Literature
$/EUR
1⋆ I estimate: yt+n − yt1⋆ = a + b log ft+n /ft
⊲
⋆
+ εt+n
n = 1m
n = 2m
n = 3m
n = 4m
US
b t-stat R2
-0.2 -2.6 4.8%
-0.2 -2.7 5.0%
-0.2 -2.5 4.0%
-0.2 -2.0 2.9%
Ger
b t-stat R2
-0.1 -1.6 1.4%
-0.1 -1.1 1.1%
-0.1 -0.9 1.1%
-0.1 -0.8 0.8%
...or a VAR in annual lags: Xt+1 = µ + ΦXt + εt+1 , 1 = one year $/♦ ♦ $ where Xt = yt , yt , ft , ♦ = {EUR (Ger), GBP}
Φ$/EUR
1.06
(13.6) 0.44 = (4.4) ×
−0.24 (−3.3)
0.49 (4.9)
×
0.18
(2.8)
0.21 (2.8) 0.72 (8.8)
Φ$/GBP
0.99
(11.3) 0.35 = (3.3) ×
(1)
−0.22 (−2.9)
0.51 (4.8)
−0.29 (−2.7)
0.15
(2.0)
0.20 (2.6) 0.63 (6.3)
∗
I use sample 1975–2009; all variables standardized; data: Datastream, BOE, Bundesbank, and Fed H.15 c TADC-LBS ( 2009 Anna Cie´slak)
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C1. Asymmetry in the longer run $/EUR
1⋆ ∆yt+m = α + β∆ ln ft
+ εt+m ,
a. β (standardized)
0.4
∆ = yoy change, ⋆ = {US, Ger} b. R2
0.15
US Ger
0.3 0.1 Ger
0.2
US
0.05
0.1 • = significant coeff. 0 10
15
20 25 30 Months ahead, m
35
40
0 10
15
20 25 30 Months ahead, m
35
40
Over longer term Fed strikes balance between its objectives [growth and inflation] Weakening dollar today suggests higher short yields in the future [inflation expectations
channel] Monetary policies are tied [convergence of international bond markets] Suggestion. The asymmetry assumption requires empirical verification and more discussion of its limitations c TADC-LBS ( 2009 Anna Cie´slak)
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C2. Monetary policy shock and volatility Average realized volatility
130
bps p.a.
120
In the last 20 years... low in-
flation, Fed focussed on unemployment and growth
Easing
110
Easing cycles associated with Unconditional
high volatility/uncertainty as the spectrum of economic scenarios widens
100 90 80 1
Tightening
Fed watches the amount of 2
3
4
5 6 7 Yield maturity
c TADC-LBS ( 2009 Anna Cie´slak)
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9
10
11
uncertainty in the market
6
C2. Monetary policy shock and volatility Average realized volatility
130
bps p.a.
120
In the last 20 years... low in-
flation, Fed focussed on unemployment and growth
Easing
110
Easing cycles associated with Unconditional
high volatility/uncertainty as the spectrum of economic scenarios widens
100 90 80 1
Tightening
Fed watches the amount of 2
3
4
5 6 7 Yield maturity
8
9
10
11
uncertainty in the market
In your 2-factor affine base-case model: it
=
τ + τ1 πt + zt (Taylor rule)
(2)
πt
=
(3)
zt
=
vt
=
a + a1 zt + a2 vt (Taylor + SDF consistent) √ ϕz zt−1 + vt−1 εt (monetary policy shock) θ¯v + ϕv vt−1 + σv wt (volatility)
where εt ⊥wt ⇛ under assumptions, UIP coeff = c TADC-LBS ( 2009 Anna Cie´slak)
(4) (5)
ϕv τ1
6
C2. Monetary policy shock and volatility In your 2-factor affine base-case model: zt
=
vt
=
√ ϕz zt−1 + vt−1 εt θ¯v + ϕv vt−1 + σv wt
where εt ⊥wt . Under assumptions, UIP coeff =
c TADC-LBS ( 2009 Anna Cie´slak)
φv τ1
(6) (7)
, ϕz does not matter
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C2. Monetary policy shock and volatility interact Now... let me make Fed shock correlated with uncertainty, realistically ρ < 0: √ zt = ϕz zt−1 + vt−1 εt √ vt = θ¯v + ϕv vt−1 + σv vt−1 wt
(6) (7)
where shocks interact Covt−1 (εt , wt ) = ρ
c TADC-LBS ( 2009 Anna Cie´slak)
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C2. Monetary policy shock and volatility interact Now... let me make Fed shock correlated with uncertainty, realistically ρ < 0: √ zt = ϕz zt−1 + vt−1 εt √ vt = θ¯v + ϕv vt−1 + σv vt−1 wt
(6) (7)
where shocks interact Covt−1 (εt , wt ) = ρ i. not so transparent anymore, even under symmetry and ϕz = 0: UIP coeff =
a2 ϕv a2 ϕv − 1/2 (a21 + a22 σv2 + 2a1 a2 ρσv )
(8)
where a1 is as in the base case, a2 is a nonlinear function of ρ ii. under assumptions, persistent monetary shock ϕz > 0 starts to matter for cov(mean,vol) of log SDF, i.e. for UIP Suggestions. One parameter more, but might give interesting implications. Provide comparative statics for different models models, especially when they get complex.
c TADC-LBS ( 2009 Anna Cie´slak)
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CG. Other comments Carry trade C1. Fed and $ C1. Asymmetry C2. MP and vol C0. Other Literature
C3. The world volatility factor... is an important channel empirically i √ − log nit+1 = ... + λ(ςw ) wt εit+1
⊲
but is shut by the symmetric case. Why ϕv = 0, ϕw = 0.997? C3’.
Related
literature...
Lustig, Roussanov, and Verdelhan oderlind (2009) [predictability of FX premia], Christiansen, Ranaldo, and S¨ (2010) [regimes in risk expose of carry trades, volatility and liquidity], Menkhoff, Sarno, Schmeling, and Schrimpf (2010) [global FX volatility], Ang and Chen (2010) [yield curve factors], ...
C4. Term structure implications... of an affine model: Ptτ = a(θ, τ ) + (xt , vt , wt )′ b(θ, τ )
where θ contains structural parameters, may be hard to justify empirically: one of the state variables needs to inherit the persistence present in the data
c TADC-LBS ( 2009 Anna Cie´slak)
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Literature Ang, A., and J. S. Chen (2010): “Yield Curve Predictors of Foreign Exchange Returns,” Working Paper, Columbia and UC Davis. Backus, D. K., S. Foresi, and C. I. Telmer (2001): “Affine Term Structure Models and the Forward Premium Anomaly,” Journal of Finance, 56, 279–304. Bekaert, G., M. Wei, and Y. Xing (2005): “Uncovered Interest Rate Parity and the Term Structure,” Working paper, Columbia, Fed Board of Governors, Rice. Christiansen, C., A. Ranaldo, and P. S¨ oderlind (2010): “The Time-Varying Systematic Risk of Carry Trade Strategies,” Journal of Financial and Quantitative Analysis, forthcoming. Clarida, R., J. Gali, and M. Gertler (2001): “Optimal Monetary Policy in Open versus Closed Economies: An Integrated Approach,” American Economic Review, P&P, 91, 248–252. Lustig, H., N. Roussanov, and A. Verdelhan (2009): “Predictable Currency Risk Premia,” Working Paper, UCLA, Wharton and MIT. Menkhoff, L., L. Sarno, M. Schmeling, and A. Schrimpf (2010): “Carry Trades and Global Foreign Exchange Volatility,” Working paper, University of Hannover.
c TADC-LBS ( 2009 Anna Cie´slak)
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