carry trade: beyond the fama regression richard clarida ... · carry trade: beyond the fama...

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


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)


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

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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


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


FX Economics

FX implies restrictions on pricing kernels

Simple Affine Kernel Dynamics

Dynamics of Exchange Rate

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EWMA Volatility and Carry Returns

92 94 96 98 00 02 04 06 08-3

-2

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1

2

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Date

Z-s

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s

Realized carry return and return volatility(log-inverse)

Correlation is 0.55 Realized return

Realized return volatility(log-inverse)

Source: Bloomberg, PIMCO


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



Nonparametric Regression


Citibank Implied Volatility and Carry Returns


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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GARCH Results


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


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


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



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



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



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.


Conclusion

Volatility is a key determinant of carry trade returns

Realized / implied

Fama coefficients regime dependent

Level and slope related to currency risk premium

carry trade: beyond the fama regression richard clarida ... · carry trade: beyond the fama...

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