Differential risk premiums and the UIP puzzle

• Published date: 01 March 2021
• Author: Rita Biswas,Louis R. Piccotti,Ben Z. Schreiber
• Date: 01 March 2021
• DOI: http://doi.org/10.1111/fima.12314

DOI: 10.1111/fima.12314

ORIGINAL ARTICLE

Differential risk premiums and the UIP puzzle

Rita Biswas1Louis R.Piccotti2Ben Z.Schreiber3

1Department of Finance, School of Business,

University at Albany,SUNY, Albany, NY, USA

2Department of Finance, Spears School of

Business, Oklahoma State University, Stillwater,

OK, USA

3Information and Statistics Department with the

Bank of Israeland Bar-Ilan University,

Ramat-Gan, Israel

Correspondence

LouisR. Piccotti, Oklahoma State University,

SpearsCollege of Business, 460 Business Build-

ing,Stillwater, OK 74078, USA.

Email:louis.r.piccotti@okstate.edu

Abstract

We respecify the uncovered interest rate parity (UIP) conditions by

inverting the market price of the risk (Sharpe ratio) formula. Our

empirical model provides new insight indicating that violations to

the UIP stem from the existence of a risk premium in the exchange

rates and from observed market return differentials being a noisy

statistic of the markets’ expected return differentials in our respec-

ified model. Using an integrated macro-micro structure framework

for expected market return differentials improvesour model fit and

the validity of UIP.

KEYWORDS

Foreign exchange market, Order flows, Risk premium, Uncovered

interest rate parity

1INTRODUCTION

Exchange ratedynamics violating uncovered interest rate parity (UIP) have puzzled researchers for a number of years

(see Bakshi & Panayatov,2013; Farhi & Gabaix, 2016; Menkhoff,Sarno, Schmeling, & Schrimpf, 2012, for recent studies

regarding the profitability of the carry tradethat bets against UIP).1We advance the literature by demonstrating, given

reasonable assumptions, the sources of UIP violations, and we also relate currency risk premia to the exchange rate

disconnect puzzle.

We consider a multieconomymodel where an investor can allocate their wealth across different economies’ invest-

ment markets, each with its own price of risk (Sharpe ratio).2The price of risk formula can be invertedallowing us to

express the observedinterest rate as a function that is increasing in the market’s expected market return and decreas-

ing in the product of the risk price and the market return standard deviation. As a result, we are able to respecify the

UIP relationship by inverting the price of risk formula. This allows us to more finely examine why UIP tends to fail

empirically.

c

2020 Financial Management Association International

1Jurek (2014) further finds that crash hedged carry trade returns continue to be large indicating that peso problems cannot explain UIP violations. Brun-

nermeier,Nagel, and Pedersen (2008) determine that abrupt asset price movements can also be due to the unwinding of carry trade positions provoked by

speculators’liquidity constraints.

2Downsiderisk is beyond the scope of our paper and is left for future research.

Financial Management. 2021;50:139–167.wileyonlinelibrary.com/journal/fima 139

140 BISWASET AL.

Extant studies relating observed stock market returns to exchange rate changes include Hau and Rey (2006),

Malliaropulos (1998), and Solnik (1987), among others. However,there is a measurement error bias that results when

observed returns are used in the model specifications, rather than conditional expectationsof returns, which interest

rates are a function of, as well as conditional volatilities. Consequently, using observed market returns after invert-

ing the price of risk (Sharpe ratio) results in the UIP coefficients being biased.3While the error between the expected

standard deviation of marketreturns and the observed standard deviation can be made relatively small, the error from

using observed returns as a statistic for expected returns is generally large. By using the conditional expected stock

market returns, our model leads to unbiased coefficient estimates, as well as more efficient estimates (i.e., lower vari-

ancethan those estimates attained from similar models) of the domestic and foreign stock market Sharpe ratios implied

by the currency markets.

To examine the likely sizes of the coefficient biases, when observed stock market return differentials are used

instead of conditional expected stock marketreturn differentials,we simulate our UIP model and relate it to previous

studies (Hau & Rey,2006; Malliaropulos, 1998; Solnik,1987). Our simulations find that using observed returns in the

UIPspecification results in large biases in thecoefficienton stock market return differentials with the coefficients com-

pressed to zero from their theoretical value of one. The biases in the intercept coefficient ( ∼0.01 units), the domestic

Sharpe ratio coefficient ( ∼0.1 units), and the foreign Sharpe ratio coefficient ( ∼0.1 units) tend to be mild. Since Hau

and Rey (2006), Solnik (1987), and Malliaropulos (1998) also relate observed stock market returns to exchangerate

changes, we revisit their models and estimate the likely size of biases in their coefficient estimates. While the coeffi-

cients are all biased in the Malliaropulos (1998) model, the biases are relatively minor ( ∼0 for the intercept,∼0.04

for the marketreturn differential coefficient, and∼0.025 on the real exchange rate change coefficient). For the Solnik

(1987) model, the intercept coefficient, the domestic Sharpe ratio coefficient, and the foreign Sharpe ratio coefficient

are unbiased. However, the use of observedstock market returns induces a large bias in the coefficient on the stock

marketreturn differential ( ∼0.5 units). Finally, we find the correlation between exchange rate changes and stock mar-

ketreturn differentials to be biased toward zero when observed stock market return differentials are used rather than

expected ones. This has implications for inference concerning the degree of risk sharing in the global economy (Hau &

Rey,2006).

Toaccount for the observed market return differentials being noisy estimates of exante expected market return dif-

ferentials, we form conditional expectationsusing a vector autoregression (VAR) model that combines both macroeco-

nomic and microeconomic elements. We accomplish this by using a large data set of tick-by-tick exchangerate quotes

for 16 U.S. dollar currency pairs across emerging and developed economies. Hau and Rey (2006) determine that cur-

rency order flows are a function of expected market return differentials, while Bacchetta and van Wincoop (2006)

find that an exchange rate risk premium emerges due to households’ (exogenous) labor income hedging demands.

We transfer the concepts from these models into a VAR specification to form conditional expectations for market

returns. We find that consistent with the models of Bacchetta and van Wincoop and Hau and Rey, currency order

flows have significant explanatory power for future stock market return differentials in excess of macroeconomic

predictors.

Recently, the UIP puzzle (Campbell, Koedijk,Lothian, & Mahieu, 2009; Fama, 1984) has led to several approaches

to explain and reconcile the theory with the empirical evidence.4Traditional monetary models or open economy

macroeconomic models proved to be inadequate (Frankel & Rose, 1995; Mark, 1995; Taylor, 1995). The second

approach employs market microstructure elements in order to solve the UIP puzzle and has established that market

microstructure-based models are better able to explain high-frequency fluctuations in exchangerates (Evans, 2002).

Our treatment of UIP falls within this class of macro-micro models. The exchange rate disconnect puzzle (Meese

3Frankeland Froot (1987) and Froot and Frankel(1989) demonstrate, using survey data, that forward rates are biased estimates of the markets’ expectations.

4Rogoff (1996) emphasizes the PPP puzzle and the existenceof large, volatile short-term deviations from PPP with an extremely slow convergence of devia-

tionsto PPP in the very long run. Rogoff (1996) concludes that while it may be attributed to the adjustment costs across countries, no satisfactory explanation

hasbeen put forth.