Currency risk premia: Perceptions of downside risk and deviations from benchmark values

• Author: Joshua Stillwagon,Steven Furnagiev
• DOI: http://doi.org/10.1002/ijfe.1647
• Date: 01 January 2019
• Published date: 01 January 2019

Received: 17 February 2017 Revised: 27 January 2018 Accepted: 26 June 2018

DOI: 10.1002/ijfe.1647

RESEARCH ARTICLE

Currency risk premia: Perceptions of downside risk and

deviations from benchmark values

Steven Furnagiev1Joshua Stillwagon2,3

1Center for People, Politics, and Markets,

Goucher College, Baltimore, Maryland

2Economics Division, Babson College,

Babson Park, Massachusetts

3INET Program on Imperfect Knowledge

Economics, New York,NY, USA

Correspondence

Joshua Stillwagon, Economics Division,

Babson College, Babson Park, MA 02457.

Email: jstillwagon@babson.edu

Funding information

Institute for New Economic Thinking

JEL Classification: F31

Abstract

This paper examines the empirical performance of an alternative model of the

currency risk premium. This model relates risk not to the variance of returns

but rather to potential crash risk based on the deviation, or “gap,” between the

exchange rate and perceptions of its benchmark value. The model is testedusing

a novel data set of traders' exchange rate forecasts, from 1986:08 to 2013:09. The

forecast data eliminate the need for a joint hypothesis about expectations forma-

tion through direct measurement of the market's ex ante premium. To measure

the benchmark value, rather than use purchasing power parity, we relate it to

recent levels through a moving average. Strong support is found for the pre-

diction that the premium comoves positively with the “gap” measure of risk,

according to cointegrated vector autoregression analyses for all four markets

examined. This result is robust for moving averages from six to 24 months and

when controlling for exchange rate volatility.The findings suggest how investors

assess downside risk ex ante, at least in part, and may rationalize the application

of certain technical analysis.

KEYWORDS

CVAR,exchange rates, IKE gap model, risk premia, survey data, technical analysis

1INTRODUCTION

Explaining foreign exchange returns remains one of

the central challenges in international finance, branded

the excess returns puzzle. This puzzle stems from the

ubiquitous rejection of traditional risk premium models

founded on the rational expectations hypothesis (REH)

and expected utility theory (EUT).1The problem is that

standard measures of the risk premium, such as the volatil-

ity of consumption or asset supplies, are insufficiently

variable, requiring implausible degrees of risk aversion.

These models are also inconsistent with frequent sign

reversals in the premium, or alternating periods when the

premium is positive or negative in value (Mark & Wu,

1998; Lewis, 1995). This result has led to numerous stud-

ies that attribute excess returns instead to systematic and

persistent forecasting errors.2It is possible though that

the problem lies, also or instead, with the specification

of risk preferences. Psychologists have in fact uncovered

substantial evidence that the predictions of EUT are incon-

sistent with the behaviour of actual individuals towards

risky gambles (Kahneman & Tversky, 1979; Tversky &

Kahneman, 1992).

In this paper, we test a new portfolio balance model

of the currency risk premium, the imperfect knowledge

economics gap model of Frydman and Goldberg (2003,

2007), which replaces EUT with endogenous prospect the-

ory (EPT). EPT builds upon traditional prospect theory

(Kahneman & Tversky, 1979)—which includes the find-

ing that participants are “loss averse” receiving much

greater disutility from a loss than utility from an equal

Int J Fin Econ. 2019;24:33–48. wileyonlinelibrary.com/journal/ijfe © 2018 John Wiley & Sons, Ltd. 33

34 FURNAGIEV ANDSTILLWAGON

magnitude gain—but allows for the degree of loss aver-

sion to be endogenous to position size. When incorporated

into a standard portfolio balance model, EPT allows Fryd-

man and Goldberg (2003) to relate the market's premium

to participants forecasts of potential losses, or downside

risk, from speculation. To represent these forecasts, Fry-

dman and Goldberg appeal to a lost insight of Keynes

(1936) that market participants tend to view potential

losses in light of deviations of asset prices from benchmark

values.3

The gap model generates novel time-series implications

for the properties of excess returns.In particular, the model

recognizes the existence, and importance, of both bulls and

bears in real-world financial markets. Frydman and Gold-

berg (2003) derive a market premium that depends on the

difference between how those betting on an appreciation

(bulls) and those betting on a depreciation (bears) respond

to the gap. The intuition is that as a currency becomes

further overvalued, bulls (betting on a continued appreci-

ation) will become more concerned about the potential for

a reversal (i.e., they perceive greater downside risk) and

the losses it would generate. Bears (betting on a reversal),

meanwhile, become less worried about a further move-

ment against them (i.e., they perceive less downside risk).

Consequently, bulls raise and bears lower the premium

they require in order to retain their open positions. It is

through this asymmetry that as the gap rises (or falls), so

too does the market's premium.

Using the gap between current and benchmark levels

has also been advocated by Edmund Phelps as a new

means of assessing systemic risk, including in an open

letter to Gordon Brown and other leaders of the G20

(April 1, 2009).4Arguably, however, the gap measure of

risk remains an intuitive yet seldom tested hypothesis in

exchange rate modelling; as such, it requires more suf-

ficient testing including extensions that examine more

recent data.

The gap model is similar to specifications of risk prefer-

ences employed elsewhere in the literature. For example,

De Grauwe and Grimaldi (2006) derive and conduct sim-

ulations for a heterogeneous agent model, where fun-

damentalists become less risk averse as the currency

moves further away from the fundamental value. It is

also similar in nature to the crash risk of Brunnermeier,

Nagel, and Pedersen (2009), where ex post returns to the

carry trade are positive on average but subject to nega-

tive skew (or crash risk). In Brunnermeier et al. (2009),

they do not elaborate on the mechanism through which

investors assess the potential for downside risk ex ante,

which provokes investors to require the excess return or

premium to begin with, whereas the gap model does.

Survey data are ideal to investigate this ex ante risk

behaviour.

One of the chief obstacles to fully surmounting the

excess returns puzzle is that the vastmajority of studies use

ex post returns, which are made up of both an expected and

unexpected component. In order to explain ex post returns

in light of a risk premium, which pertains to the expected

portion, we need a hypothesis about the unexpected part

as well. These studies invoke the REH auxiliary hypoth-

esis that forecast errors of expectations are white noise,

enabling researchers to proxyexpected returns with ex post

returns. The consequence, however, is that it cannot be

discerned whether the rejection of these models derives

from violations of REH, an inadequate specification of

risk preferences (EUT), or both. By using survey data to

measure the market's ex ante excess returns, this paper

avoids the joint-hypothesis nature of most tests and pro-

vides for a more direct assessment of risk preferences. Sur-

vey data allow for myriad forecasting strategies, whatever

they may be, from fundamentalist to chartist approaches

and the incorporation of noneconomic news and cen-

tral bank announcements, which are inherently difficult

to model.

Numerous studies have used survey data to test whether

expectations are rational and whether a general risk pre-

mium is present (i.e., expected returns do not equalize).5

Veryfew studies however have examined the determinants

of the time-varying risk premium found in survey data to

illuminate market participants' risk behaviour.Prior stud-

ies to do so use data spanning only to 1997 (Frydman &

Goldberg 2007; Stillwagon 2015, 2018). Since then, vol-

ume in the foreign exchange market has exploded from

$1.53 trillion in 1998 to $5.34 trillion in 2013 Bank of I. S.

(2013), a common currency was implemented in the Euro

area, and the world has undergone its greatest economic

crisis in nearly a century. Given these dramatic, transfor-

mational occurrences, another contribution of this study

is to update those initial analyses of the survey-data based

risk premium with an extra 15 years of data.

The survey data employed here characterize 3-month

ahead forecasts, surveyed monthly by FX4Casts from

August 1986 to September 2013, and cover the spot

U.S. dollar exchange rate against the Japanese yen,

Swiss franc, British pound, and Canadian dollar. The

survey-based forecasts are collected from nearly 50 major

financial institutions, and, according to the 2013 BIS tri-

ennial report, these four currency pairs account for over

a third of all FX transactions.6The breadth of the survey

and currency cross section in this case provides an expan-

sive analysis of currency risk premia, ideal for testing the

Imperfect Knowledge Economics (IKE) gap model.

In formulating the gap model, Frydman and Goldberg

incorporated Keynes' (1936) discussion of liquidity pref-

erence as behaviour towards risk. Keynes argued that a

low interest rate left “more to fear than to hope” (in