The Term Structure of Currency Futures' Risk Premia

• Published date: 01 February 2022
• Author: KERSTIN BERNOTH,JÜRGEN VON HAGEN,CASPER DE VRIES
• Date: 01 February 2022
• DOI: http://doi.org/10.1111/jmcb.12872

DOI: 10.1111/jmcb.12872

KERSTIN BERNOTH

JÜRGEN VON HAGEN

CASPER DE VRIES

The Term Structure of Currency Futures’ Risk

Premia

The use of futures instead of forwards exchange contracts completes the ma-

turity spectrum of the correlation between spot yields and the premium. We

nd that the forward premium puzzle appears to be a precrisis phenomenon

and is only observed for maturities longer than about 1 month. Differences

in the exposure to risk help to explain cross-sectional spreads in currencyex-

cess returns. However, this only applies for medium and longer maturities.

Considering that most studies that test the validity of a risk-based approach

to currency excess returns focus on short maturity securities, this explains

why this approach is so often rejected.

JEL codes: F31, F37, G12, G13, G15

Keywords: forward premium puzzle, uncovered interest parity, futures

rates, price of risk, currency excess returns, capital asset pricing model

A     (EH), for-

ward exchange rates are unbiased predictors of future spot exchange rates. As a con-

sequence, currency excess returns should be zero on average over time and across

The authors thank Milian Bachem for his excellent support in data collection, our two referees for ex-

cellent comments that changed the direction of the paper, and the associate editor handling this paper.

Financial support by the Deutsche Forschungsgemeinschaft (DFG BE 5381/1-1) is gratefully acknowl-

edged.

K B is Deputy Head of Department Macroeconomics, DIW and Hertie School of Gov-

ernance, Berlin (E-mail: kbernoth@diw.de). J  H isa Professor of Economics at the In-

stitute for International Economic Policy,University of Bonn, Germany, and CEPR, London, UK (E-mail:

vonhagen@uni-bonn.de). C  V is a Professor of Economics at Department of Economics

and Tinbergen Institute, Erasmus University Rotterdam, Netherlands, and CEPR, London (E-mail:cde-

vries@ese.eur.nl).

Received August 1, 2018; and accepted in revised form May 19, 2021.

Journal of Money, Credit and Banking, Vol. 54, No. 1 (February 2022)

© 2021 The Authors. Journal of Money, Credit and Banking published by Wiley Periodicals

LLC on behalf of Ohio State University

This is an open access article under the terms of the Creative Commons Attribution-NonCom-

mercial-NoDerivs License, which permits use and distribution in any medium, provided the

original work is properly cited, the use is non-commercial and no modications or adaptations

are made.

6:MONEY,CREDIT AND BANKING

currencies. This hypothesis is an important building block of models of international

macroeconomics and nance. It manifests itself also in the form of the well-known

uncovered interest parity (UIP) condition. However, empirical support is weak at best.

Fama (1984) was the rst to report that, in a regression of foreign exchange returns on

forward premia, the estimated slope coefcient is negative rather than one. This phe-

nomenon is known as the “forward premium puzzle” (FPP). Lustig and Verdelhan

(2007) added that the UIP fails not only in the time series of individual currencies

but also in the cross-section; high-yield currencies tend to produce positive excess

returns, while low-yield currencies generate negative excess returns, which explains

large and sustained carry trade gains.

The rst contribution of our paper is that we close existing gaps in the overall

picture of currency excess returns. More specically, we analyze the time series of

individual currencies and the cross-section of currency excess returns for the entire

available term structure. This is possible due to using futures instead of forward

data. While data for forward contracts are available only for xed maturity horizons,

futures contracts have xed delivery dates. Since futures contracts are traded in

secondary markets, this makes it possible to analyze futures rates from the rst to

the last trading day of a given contract and to construct the full maturity spectrum of

futures premia in daily units. While differences in trading mechanisms, default, or

liquidity premia between forward and futures contracts might somewhat cloud the

comparability of the two, empirical studies suggest that this is not the case.1Only

the early paper by Hodrick and Srivastava (1987) uses data from 3-months futures

contracts to test a hypothesis related to the EH. To the best of our knowledge, no

paper has exploited these data to obtain the estimates at the daily grid level.

We examine the behavior of exchange rates for the United States relative to all

countries for which currency futures have been traded at the Chicago Merchantile

Exchange. These comprise nine developed countries and six emerging market

economies. The time period covered is 1979Q1–2018Q4 and we consider futures

rates with a time to maturity ranging between 1 day and one and a half years.

Focusing rst on time series of individual currencies, we nd that the slope coef-

cient in a regression of the spot exchange rate return on the futures premium (“Fama

regression”) depends signicantly on the maturity horizon of the futures contract and

on the choice of sampling period. For maturities shorter than about a month, it is gen-

erally positive, and the EH is not rejected by the data. For longer maturity horizons,

however,the sign and also size of the slope coefcient depend on the time period cov-

ered. Focusing on the period before the global nancial crisis, the slope coefcient

tends to become negative as the maturity horizon overwhich expectations are formed

increases. This nding is consistent with the often described FPP and indicates that a

currency tends to appreciate when the futures premium would indicate a depreciation

and vice versa. When focusing on the postcrisis period, however, we cannot reject

1. See, for example, Cornell and Reinganum (1981), Hodrick and Srivastava (1987), Chang and

Chang (1990), and Polakoff and Grier (1991).

KERSTIN BERNOTH, JÜRGEN VONHAGEN, AND CASPER DE VRIES :7

the validity of the EH for most currencies and maturities. In the few cases where

there are signicant deviations from the EH, these are upward rather than downward:

A currency whose futures premium predicts an expected appreciation actually

appreciates, but by more than the EH indicates. All in all, we conrm the ndings

by Thornton (2007) and Kim et al. (2017) that violations of the EH or UIP vary

considerably across periods. More specically, we nd that the FPP/UIP viola-

tion in the time series of individual currencies appears to be very much a precrisis

phenomenon for most currencies and is only evident for medium to longer maturities.

Our paper is closely related to a strand of literature, suggesting that maturity

of derivative contracts matters for the validity of the EH. Chaboud and Wright

(2005) and Yang and Shintani (2006) give estimates at very short maturities at the

intraday or overnight horizon. Alexius (2003), Chinn and Meredith (2004), and

Fama and Bliss (1987), and more recently Engel (2016) look at the other end of the

spectrum, even going as far as considering multiyear horizons.2Most papers focus

on intermediate horizons by using monthly forward data starting at 1 month up to

several months. Examples in this category are Froot and Frankel (1989), Backus

et al. (2001), Baillie and Kilic (2006), and Clarida et al. (2009). The summary nding

from these papers is that the EH may hold at the very short term and in the very long

run. But signicant deviations are reported for intermediate periods, mostly negative

and sometimes positive. At intermediate periods, however, the evidence is rather

granular as it contains relative long gaps since monthly data are used, so that only

evidence at the 1 month, 2 month, etc., horizons is available.

In the next step, we analyze the cross-section of currency excess returns over the

entire maturity spectrum. For this, we build similarly to Lustig and Verdelhan (2007),

Menkhoff et al. (2012), and Lustig et al. (2011) portfolios of currencies sorted by

their futures discounts. We nd that on average a U.S. investor generates negative

excess returns on currencies with small futures premia. For currencies with the

largest futures discounts, the excess returns are generally positive, rising to up to 3%

as the maturity increases. Consequently, the zero cost (carry trade) strategy, which

goes long in the portfolio with high futures premia and short in the portfolio with

low futures premia, provides signicant positive returns. Furthermore, these positive

carry trade returns grow monotonically with the maturity of the futures contracts. To

our knowledge, this result has not been described in the literature so far.

A second contribution of the this paper is that we test over the entire maturity

spectrum, whether the observed excess returns on futures contracts reect a fair

compensation for currency risk.3As stressed by Burnside (2011) and Barroso and

Santa-Clara (2015), one criticism of a risk-based explanation is that general proxies

2. It is worth mentioning that Engel (2016) attributes the multiperiod excess return to the one-period

interest rate differentials. Therefore, the maturities of assets and interest rates do not coincide.

3. In a previous paper entitled “Estimating a Latent Risk Premium in Exchange Rate Futures,” we

took a different approach and derived a methodology to correct the bias in the Fama regression caused

by the existence of a latent risk premium. This allowed us to test whether the unbiased Fama coefcient

is actually one and therefore consistent with the EH.