The conditional volatility premium on currency portfolios

https://doi.org/10.1016/j.intfin.2021.101415Get rights and content

Highlights

  • We examine conditional risk-return relations in a number of currency investment strategies.

  • We identify a time-varying relationship between returns and volatility risk.

  • The positive relationship for the value portfolio is associated with “flight to quality” periods.

Abstract

Our paper examines conditional risk-return relations in a number of currency investment strategies, while modeling economic states using a large number of underlying risk factors. We identify a time-varying relationship between currency returns and volatility risk for most currency portfolios. In particular, value and momentum portfolios present risk-return relationships which switch sign, depending upon economic states. The positive relationship for the value portfolio is associated with “flight to quality” periods and the mean reversion for nominal exchange rates during financial crises. The positive relationship for the momentum portfolio is linked to the US and global business cycles and investors require positive compensation for risk in recessions.

Introduction

Central to asset pricing research is testing the empirical relationship between systematic risk and return, given that investors require compensation if risk is priced. When risk is modeled by volatility and assumed to have a time invariant relationship to excess return, Sharpe ratios are state independent. This state independence assumption is open to question. In addition and despite its centrality to asset pricing, the literature has not converged on a consensus on the nature of the link between returns and risk factors, such as volatility. For stock market returns, French et al. (1987), Merton (1987), Scruggs (1998), Ghysels et al. (2005), and Guo and Whitelaw (2006) present positive risk-return relations for example, while Campbell (1987), Glosten et al. (1993) and Ang et al. (2006) report a negative empirical relationship between returns and risk, in the form of return volatility. The former studies indicate investors require a risk premium for additional volatility, while the latter indicates that agents are not averse to additional asset price variability.1

Our work extends the risk-return trade-off test to the under explored area of currency portfolios. Early asset pricing studies focused upon U.S. stock market returns (e.g. Ang et al., 2006, Guo and Whitelaw, 2006). Testing the risk and return nexus using alternative asset classes provides illuminating results, especially since a burgeoning literature has recently implemented portfolio approaches for the currency market. The influential work of Asness et al. (2013) moreover reveals that value and momentum effects are observed in many asset classes. A value strategy in the stock market exploits information on book-to-market ratios and buys higher book-to-market stocks (e.g. Fama and French, 1992, Fama and French, 1993). A currency value strategy can exploit mean reversion to purchasing power parity, therefore using variation in real exchange rates (e.g. Taylor, 2002, Imbs et al., 2005, Boudoukh et al., 2016, Menkhoff et al., 2017). A cross-sectional momentum strategy goes long in high past return assets and goes short in low past return assets, which can be employed in both stock and currency markets. Likewise for currencies, Koijen et al. (2018) highlight that carry strategies are applicable across assets. A currency carry trade focuses upon differentials between spot and forward rates, buying high and selling low forward premium currencies. See for example Lustig and Verdelhan (2007), Lustig et al. (2011) and Menkhoff et al. (2012a). In the stock market, Koijen et al. (2018) show that the carry is determined by the expected dividend yield minus the risk-free rate and a scaling factor.2

The currency portfolio literature has mainly focused upon currency carry trades and investigated systematic risk exposure to market and macroeconomic uncertainty in the cross-sectional context.3 One prominent exception is Bakshi and Panayotov (2013) who use time series to investigate the relationship between FX market risk and currency carry portfolios. The exact ways in which FX market risk is associated with currency momentum and value portfolios using time series methods remains an open question.4 Our study’s first contribution is that we conduct a comprehensive intertemporal analysis of the link between risk and currency portfolio returns. We generalize and therefore extend the study of Bakshi and Panayotov (2013) to a wider array of currency portfolios, considering not only the currency carry but also value and momentum portfolios. In addition we investigate four new currency portfolios: dollar carry trade (Lustig et al., 2014), global imbalances ((Della Corte et al., 2016b), “good” carry trade (Bekaert and Panayotov, 2020), and correlation risk in the FX market (Mueller et al., 2017). Each strategy is based upon a different mechanism and the previous literature focuses upon a risk premium in the cross-sectional context. Hence, there is an open question as to whether FX market risk influences these new currency portfolios in the time-series context. A comprehensive investigation is required, because the mechanisms that create positive payoffs are heterogeneous and combining different currency strategies leads to diversification of portfolio risk (Kroencke et al., 2014, Barroso and Santa-Clara, 2015). Our study is different from Bali and Yilmaz (2009), who focus upon the time series relationship between risk and a single currency return, since currency specific risk components are averaged out in the currency portfolios (Lustig et al., 2011).

The standard approach in asset pricing studies is to examine risk and return in portfolios using unconditional methods. The second contribution we make therefore, is to take into account a time-varying relation between conditional volatility and expected returns. A theoretical asset pricing model conditional upon economic states, was proposed by Backus and Gregory (1993). In contrast to unconditional models, conditional models employ information up to the current time and reflect changes in economic states (Jagannathan and Wang, 1996, Cochrane, 1996, Lettau and Ludvigson, 2001). The advantage of the conditional models is that it allows a time-varying relationship between asset returns and risk. Risk-return trade-offs have been widely investigated using the conditional models in the stock market literature (e.g. Whitelaw, 2000, Rossi and Timmermann, 2010, Ghysels et al., 2014, Adrian et al., 2019).5 Whitelaw (2000) builds a general equilibrium model with a regime-switching consumption process and generates a time-varying and non-linear relation between volatility and expected returns in the stock market. Rossi and Timmermann (2010) find a non-monotonic relation between conditional volatility and expected returns in the stock market, and Ghysels et al. (2014) present work indicating that the positive risk-return relation is not observed in a “flight-to-quality” regime. In recent work, Adrian et al. (2019) find that expected returns on stock and bond markets depend upon the level of VIX and the relationships are nonlinear. To investigate the time-varying relationship between returns and risk, our study adopts a time-varying conditional factor model proposed by Ang and Kristensen (2012), which allows for smooth changes in coefficients. In the FX market, Baillie and Kim (2015) and Sakemoto (2019) observe that utilizing macro indicators results in smooth changes in risk.

The third contribution of our work on the volatility risk premium is to employ an empirical factor model to summarize more broadly macroeconomic and financial market information. This is important since economic states affect the relationship between conditional volatility and expected returns, see Backus and Gregory (1993), and Backus et al. (2001). Such a model is set out in the appendix to this paper. To capture economic states, we focus upon the common component of macro and financial information since it is non-diversifiable and linked to the business cycle (Jurado et al., 2015), while idiosyncratic information can be diversified. Furthermore, narrow macro indicators like consumption may suffer from measurement errors, with an unknown relationship between macro indicators and asset returns. Investors also extract macro-finance information broadly when implementing their investment strategies. Ludvigson and Ng (2007) construct several empirical factors that summarize macro indicators and uncover a positive risk-return relation for U.S. stocks. This factor model is also useful in predicting currency carry returns (Filippou and Taylor, 2017). In contrast to the previous literature, our study predicts conditional FX market volatility by a factor model, not currency portfolio returns. Moreover, our aim is to examine the risk-return relationship with currency portfolios, rather than predict FX volatility.

To preview our results, we find that the relationship between conditional volatility and expected returns is time-varying for most currency portfolios. This time variation is particularly strong for currency momentum and value portfolios. Importantly, we do not find formal statistical evidence of a link between returns and risk on the currency momentum and value portfolios with constant parameter models. When we reflect changes in economic states and adopt the time-varying model, we observe that the risk-return parameters occasionally change signs. This positive and negative risk-return relationship for the value portfolio is associated with flight to quality periods and we observe the positive risk-return relationship during financial crisis periods. This is related to the mean reversion for nominal exchange rates. This result is consistent with evidence from the Treasury market (Adrian et al., 2019) but less consistent with evidence from the stock market (Ghysels et al., 2014). Time variation in the risk-return nexus for the momentum portfolio is linked to business cycles: agents require positive compensation for risk in recessions.

The paper is organized as follows: Section 2 describes the currency volatility and currency portfolios. Section 3 then lays out the econometric methods implemented in our paper, and Section 4 describes the data. Section 5 presents empirical results, Section 6 conducts further analysis and Section 7 concludes.

Section snippets

Currency portfolios and volatility

This section describes the currency volatility data and portfolios used in our study. To examine risk-return trade-offs for a wide range of currency investment strategies, we construct several currency portfolios. These currency portfolios include, carry, momentum, value, “good” carry, dollar carry trade, global imbalances, and global correlation risk.

Empirical methodology

This section describes the econometrics methods used to test risk-return trade-offs in FX markets, and to identify the time varying parameter for variance risk. We employ a factor model to summarize a large information set based upon many macroeconomic indicators. Regressing FX volatility onto common factors, we obtain predicted FX volatility. Furthermore, we use a conditional factor model that allows for a change in risk-return relationship.

Currency data

This study uses daily spot and one-month forward rates against the U.S. dollar, obtained from Datastream. Following Kroencke et al. (2014) and Bakshi and Panayotov (2013), we employ the most liquid 10 currencies which are widely used in currency investment strategies.13

Empirical results

To assess relationships between risk and return, we present empirical evidence in this section. First, we report the summary statistics of the currency portfolios in Section 5.1. and the result of the unconditional model that employs actual FX volatility as risk in Section 5.2. Second, we estimate FX volatility using a large number of macroeconomic indicators in Section 5.3. Third, we investigate the risk-return relationship using the estimated FX volatility in Section 5.4. Finally, we present

Further analysis and discussion

The results obtained in the previous section demonstrate the importance of introducing time variation when examining a variety of currency investment strategies. In this section we provide further analysis. First, we use a rolling regression approach that is widely employed to obtain time-varying coefficients. Second, we formally test whether time-varying risk-return relations are associated with business cycles. Third, we discuss the relationship between our results and related studies.

Conclusion

We explore intertemporal risk-return relationships for currency investment strategies. It is well known that the carry strategy has negative risk-return relationship because it takes exposure to FX volatility and downside stock market risk (Menkhoff et al., 2012a, Bakshi and Panayotov, 2013, Dobrynskaya, 2014, Lettau et al., 2014). Recently, many new currency investment strategies are proposed in the literature and the risk exposure is actively explored in the cross-sectional context. However,

CRediT authorship contribution statement

Joseph P. Byrne: Conceptualization, Methodology, Data curation, Writing, Investigation, Editing. Ryuta Sakemoto: Conceptualization, Methodology, Software, Data curation, Writing, Visualization, Investigation, Editing.

Acknowledgment

We have benefited from five anonymous reviewers and discussion with Jun Nagayasu. We also would like to thank Takahiro Obata for his research support. All errors belong to the authors. This work was supported by KAKENHI (20K22092).

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