Carry Trade: Beyond the Fama Regression
Richard Clarida
Josh Davis
Niels Pedersen
For Educational Purposes Only 2
The Agenda
Introduce the carry trade
Economics of the carry trade
Volatility and the carry trade Realized
Implied
Volatility regimes & Fama regressions
Relation to other macro factors
Conclude
For Educational Purposes Only 3
Introduction
Influential Works
Meese and Rogoff (1983),
Hansen and Hodrick (1980)
Cumby and Obstfeld (1981)
Fama (1984)
Recent Work
Burnside, Eichenbaum and Rebelo (2006)
Bhansali (2007)
Jurek (2008)
Brunnermeier, Nagel, Pedersen (2008)
For Educational Purposes Only 4
Carry Trade Returns
The return is interest rate differential net of FX depreciation
Exchange rate is high yielding currency per unit of low yielding
currency
Bloomberg Dataset: Currency Baskets
Citibank Dataset: USD Crosses
11 t
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t
H
tt xiir
For Educational Purposes Only 5
Source: Bloomberg, PIMCO
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10
100
150
200
250
300
Date
Car
ry i
nd
ex
Carry return portfolios
3v3 G10
3v3exJPY
3v3 exJPY/USD
For Educational Purposes Only 6
Summary Statistics
mean vol m/v mean vol m/v mean vol m/v
Time period 1990-2009
Basket
1 4.98 15.06 0.33 3.79 12.13 0.31 5.28 12.19 0.43
2 2.82 11.11 0.25 5.53 9.72 0.57 5.66 9.48 0.60
3 4.62 8.98 0.51 5.46 8.21 0.66 4.63 8.14 0.57
4 4.34 7.81 0.56 4.19 7.23 0.58 2.75 7.00 0.39
5 3.28 6.86 0.48 2.38 6.18 0.38
Note: m/v is mean return divided by volatility
Table: Balanced G-10 Carry Trade Strategy
All Currencies Excl. JPY Excl. JPY/USD
Sample for Illustrative Purposes Only
For Educational Purposes Only 7
FX Economics
FX implies restrictions on pricing kernels
Simple Affine Kernel Dynamics
Dynamics of Exchange Rate
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For Educational Purposes Only 8
EWMA Volatility and Carry Returns
92 94 96 98 00 02 04 06 08-3
-2
-1
0
1
2
3
Date
Z-s
core
s
Realized carry return and return volatility(log-inverse)
Correlation is 0.55 Realized return
Realized return volatility(log-inverse)
Source: Bloomberg, PIMCO
For Educational Purposes Only 9
EWMA Volatility and Carry Returns
mean vol m/v mean vol m/v mean vol m/v
High Volatility State
(above 75th percentile)
Basket
1 -9.75 20.72 -0.47 -2.76 15.61 -0.18 1.14 16.00 0.07
2 -5.01 15.55 -0.32 -1.48 12.75 -0.12 2.30 12.24 0.19
3 -1.89 12.47 -0.15 3.46 10.76 0.32 4.72 10.17 0.46
4 3.37 10.72 0.31 1.26 9.31 0.14 -0.67 8.60 -0.08
5 2.34 9.15 0.26 0.35 7.79 0.04
Low Volatility State
(below 25th percentile)
Basket
1 13.61 10.25 1.33 2.87 7.59 0.38 6.85 7.54 0.91
2 6.06 7.45 0.81 8.41 6.82 1.23 6.40 6.78 0.94
3 6.52 6.21 1.05 6.39 6.00 1.07 3.42 6.11 0.56
4 5.76 5.27 1.09 6.97 5.30 1.32 7.23 5.39 1.34
5 5.97 4.76 1.25 4.13 4.51 0.92
Note: m.v is mean divided by volatility
All Currencies Excl. JPY Excl. JPY/USD
Table: Balanced G-10 Carry Trade Strategy in high and low volatility states
Sample for Illustrative Purposes Only
For Educational Purposes Only 10
Nonparametric Regression
For Educational Purposes Only 11
Citibank Implied Volatility and Carry Returns
For Educational Purposes Only 12
GARCH Model
Due to Nelson (1991)
Symmetric Model d=0 : positive/negative returns increase conditional volatility
symmetrically
Asymmetric Model: d<0 : negative returns increase conditional volatility more
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For Educational Purposes Only 13
GARCH Results
Sample for Illustrative Purposes Only
E-Garch models of carry portfolios
Four vs Four Portfolio Japanese Yen vs US dollar
coefficient std.error t-stat coefficient std.error t-stat
Asymmetric model
Constant -0.018 0.007 -2.563 -0.002 0.014 -0.161
FVF{1} -0.323 0.056 -5.783 -0.025 0.035 -0.704
GARCH-V -0.031 0.003 -11.347 -0.003 0.001 -2.384
GARCH-V, lagged 0.029 0.003 8.296 0.003 0.000 6.956
C -0.692 0.073 -9.453 -0.306 0.128 -2.395
A 0.031 0.013 2.325 0.130 0.031 4.182
B 0.929 0.008 114.802 0.975 0.014 70.397
D -0.068 0.016 -4.199 -0.008 0.018 -0.438
For Educational Purposes Only 14
The forward rate as an unbiased predictor of the change
in the spot rate:
Do these loadings change in different volatility
environments?
11 t
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Fama Regression
For Educational Purposes Only 15
Fama Regression
Table: Fama Regressions for 3v3 baskets of high and low yielding currencies
Time period 1991-2009 Low Volatility High Volatility All
Coefficient on forward premium(b) -3.29 2.73 -2.10
std. error 4.31 2.41 2.86
R-square 0.00 0.01 0.00
Note: Low volatility states are below 25th percentile. High volatility states above the 75th percentile
Sample for Illustrative Purposes Only
For Educational Purposes Only 16
Fama Regression
Table: Fama regression for FX pairs against the US Dollar.
All Low Volatility High Volatility
AUD -1.40 -7.12 5.65
2.69 4.09 6.89
CAD -1.14 -0.72 -2.39
2.98 4.84 11.40
CHF -2.78 -3.84 3.55
2.56 4.64 6.22
EUR -3.07 -2.81 -1.13
2.17 3.49 5.27
GBP 0.87 -0.44 6.50
2.49 3.68 6.60
JPY -2.56 -1.21 -1.34
1.89 3.39 4.66
NOK 0.43 -1.67 11.27
1.59 2.21 6.46
NZD -1.52 -9.21 1.72
2.54 5.26 6.18
SEK -1.52 -2.46 5.33
1.79 3.24 5.06
Note: Table reports coefficient on forward premium and standard error
Sample for Illustrative Purposes Only
For Educational Purposes Only 17
Other Risk Factors
Other determinants of carry trade returns
Yield Curve Movements
Relative shifts in the level of curves
Relative shifts in the slopes of curves
Crisis vs. Non-crisis periods
LHLH slopeslopelevlevVixr 321
For Educational Purposes Only 18
Sample for Illustrative Purposes Only
Table: Local(fx pair) factors and exchange rate movements
Dependent variable is percentage change in exchange rate net of carry. Weekly data.
Bond factors and equity returns JPYUSD CHFUSD JPYNZD CHFNZD JPYAUD CHFAUD All
July 2007-Now
VIX(percent) -2.66 0.50 -8.34 -5.51 -7.55 -5.68 -4.10
t-stat -4.25 0.78 -7.00 -6.39 -6.68 -6.70 -14.58
Yield Curve Levels 2.91 4.11 2.85 1.16 9.11 6.27 1.70
t-stat 4.48 5.18 2.03 1.21 6.54 5.41 6.22
Yield Curve Slopes -1.73 -1.64 -3.91 -1.82 -3.55 -2.51 -1.13
t-stat -2.38 -2.51 -2.36 -1.60 -3.34 -2.87 -3.83
R-square 0.46 0.26 0.49 0.37 0.64 0.54 0.20
Non-Crisis Periods
VIX(percent) -0.64 -1.09 -1.69 -2.13 -1.54 -2.15 -2.51
t-stat -2.02 -3.46 -4.23 -5.79 -4.31 -6.63 -18.71
Yield Curve Levels 1.20 1.30 1.59 1.07 2.02 1.80 1.60
t-stat 4.37 3.54 3.81 2.44 6.54 5.27 12.15
Yield Curve Slope -0.79 -1.44 -0.61 -0.74 -1.43 -1.37 -1.15
t-stat -1.98 -3.49 -1.23 -1.69 -3.40 -3.57 -7.52
R-square 0.06 0.07 0.08 0.08 0.14 0.15 0.13
Note: VIX is percentage change in the US implied volatility index. 'Yield Curve Levels" and "Yield Curve Slopes"
refers to relative change in levels and slopes in high yield currency country relative to low yield currency.
Level is defined as the 10 year treasury yield and slope is defined as 10 year minus 2 year treasury yield.
For Educational Purposes Only 19
Conclusion
Volatility is a key determinant of carry trade returns
Realized / implied
Fama coefficients regime dependent
Level and slope related to currency risk premium