The pricing of unexpected volatility in the currency market

Abstract

Many recent papers have investigated the role played by volatility in determining the cross-section of currency returns. This paper employs two time-varying factor models: a threshold model and a Markov-switching model to price the excess returns from the currency carry trade. We show that the importance of volatility depends on whether the currency markets are unexpectedly volatile. Volatility innovations during relatively tranquil periods are largely unrewarded in the market, whereas during the unexpected volatile period, this risk has a substantial impact on currency returns. The empirical results show that the two time-varying factor models fit the data better and generate a smaller pricing error than the linear model, while the Markov-switching model outperforms the threshold factor models not only by generating lower pricing errors but also distinguishes two regimes endogenously and without any predetermined state variables.

KEYWORDS:

• Carry trade
• asset pricing
• trading strategies
• currency portfolios
• Markov-switching model

JEL classifications::

• F3
• G12
• G15

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Ang, Chen, and Xing (2006), Lettau, Maggiori, and Weber (2014), Atanasov and Nitschka (2014), Dobrynskaya (2014) and Farago and Tédongap (2018) use threshold model to study the downside risk.

2 The correlations between return and market return risk factor do not change significantly when the ‘abnormal state’ is defined in this way.

3 See Appendix A1 for a simple t statistics test result.

4 GMM could be used as an alternative estimator to the Fama–Macbeth two-stage procedure, and the two estimators lead to consistent results as shown in Copeland and Lu (2016). Note that GMM could be used in the threshold model, but not in the Markov-switching model.

5 The portfolios are defined in the data section.

6 The threshold is defined in the empirical results section.

7 Specifically, the first-state initial parameters $\{b_1(s_t=1),b_2(s_t=1),{\sigma }^2(s_t=1)\}$ are taken from the conditional SDF estimates from the periods where volatilities are above the threshold. The second-state initial parameters $\{b_1(s_t=2),b_2(s_t=2),{\sigma }^2(s_t=2)\}$ are likewise taken from the unconditional SDF estimates for the periods where volatilities are below the threshold.

8 This is standard in the carry trade study, as the currency number is small (e.g. 29 currencies in our case). In the literature, Ang, Chen, and Xing (2006) and Menkhoff et al. (2012) sort the currencies into five portfolios, Lettau, Maggiori, and Weber (2014) and Farago and Tédongap (2018) sort the currencies into six portfolios.

9 Copeland and Lu (2016) used 75th percentile of volatility innovation as the threshold, which is very close to the threshold we defined here.

10 See the derivation of the ex-ante probabilities $p_{1,t|t-1}$ in Appendix A2.

11  Note that intercept is not included in Tables 3 and 5. ${\lambda }_1$ in Tables 3 and 5 served as an intercept as ${\hat{b}}_{11}$ is closed to 1 for i=1,2, … ,6.

Additional information

Notes on contributors

Wenna Lu

Wenna Lu, Cardiff School of Management, Cardiff Metropolitan University, Llandaff Campus, Cardiff, CF5 2YB, United Kingdom.

Laurence Copeland

Laurence Copeland, Cardiff Business School, Cardiff University, Colum Drive, Cardiff, CF10 3EU, United Kingdom.

Yongdeng Xu

Yongdeng Xu, Cardiff Business School, Cardiff University, Colum Drive, Cardiff, CF10 3EU, United Kingdom.