Can Tail Risk Predict Asia-Pacific Exchange Rates Out of Sample?

1. Introduction

This study contributes to the Meese–Rogoff (1983) puzzle, which contends that time-series models cannot outperform autoregressive models in exchange rate out-of-sample predictability. On the contrary, the present study shows that information contained in extreme market events, measured by tail risk, can be exploited to predict the exchange rates for Asia-Pacific (AP) markets.^[1] We build on the study of Bouri et al. (2020), who find stronger return spillover among AP currency markets with extreme bands, to situate the contribution of our paper.^[2] Further motivation to study the predictive content of tail risk is based on the baseline results that extreme events, such as the 1997–1998 Asian financial crisis and the 2008–2009 global financial crisis, impact the volatility of the foreign currency markets of the AP region (Ahmad et al., 2012; Darrat et al., 2011; Liu & Yang, 2017; Melvin & Taylor, 2009).^[3]

Following Bali et al. (2009) in capturing conditional volatility, we seek theoretical backing in the intertemporal capital asset pricing model (see Merton, 1973, 1980) to incorporate tail risk as a measure of market risk. We strengthen our argument with the position that mean-based forecasts of exchange rate returns can be grossly inadequate (Bouri et al., 2020). Hence, we quantify tail risk using Engle and Manganelli’s (2004) conditional autoregressive value at risk (CAViaR) method, as well as to forecast AP foreign exchange (forex) market returns. This effort proves worthwhile, since we document strong out-of-sample forecast performances for tail risk across the full sample and advanced countries and emerging countries in the AP region. Following the introduction, next, we present the methodology in Section 2. The discussion of results follows in Section 3, and Section 4 concludes the paper.

2. Methodology

Our analysis has two layers: 1) the specification of the conditional autoregressive quantile models for estimating the AP currency market value at risk and 2) the specification of the predictive model for forecasting AP forex market returns, where we test whether the inclusion of tail risk improves forecast performance over the baseline historical average model.

We adopt the CAViaR (for its computational advantages, see Engle & Manganelli, 2004) in its generic specification and as specified in the adaptive, symmetric absolute value, asymmetric slope, and indirect generalized autoregressive conditional heteroskedasticity (1,1) variants, respectively:^[4]

$$\begin{align} f_{t}(\beta)=&\ \beta_{0}=\sum_{i=1}^{q} \beta_{i} f_{t-i}(\beta)+\sum_{j=1}^{r} \beta_{j} l\left(x_{t-i}\right) \tag{1} \\ f_{t}\left(\beta_{1}\right)=&\ f_{t-1}\left(\beta_{1}\right)\\ &+\beta_{1}\left\{\left[1+\exp \left(G\left[y_{t-1}-f_{t- }\left(\beta_{1}\right)\right]\right)\right]^{-1}-\theta\right\}\tag{2}\\ f_{t}(\beta)=&\ \beta_{1}+\beta_{2} f_{t-1}(\beta)+\beta_{3}\left|y_{t-1}\right| \tag{3}\\ f_{t}(\beta)=&\ \beta_{1}+\beta_{2} f_{t-1}(\beta)+\beta_{3}\left(y_{t-1}\right)^{+}+\beta_{4}\left(y_{t-1}\right)^{-} \tag{4}\\ f_{t}(\beta)=&\ \left(\beta_{1}+\beta_{2} f_{t-1}^{2}(\beta)+\beta_{3} y_{t-1}^{2}\right)^{1 / 2} \tag{5} \end{align}$$

where $f_{t}(\beta)=f_{t}(x_{t-1},\beta_{\theta})$ represents either the 1% or 5% quantile of the distribution of the AP exchange rate returns at time $t$, formed at $t-1$; $\beta_{i} f_{t-i}(\beta), \forall i=1, \ldots, q$ are autoregressive terms; $l$ are lagged observables; and $G$ is constrained to be a positive finite number. We select the optimal model from the four variants of the CAViaR model based on the dynamic quantile (DQ) test and %Hits criteria.

We evaluate the predictive content of the CAViaR series in the return predictability for AP currencies, with, first, a simple time-series specification and, then, a panel specification that accounts for cross-sectional dependence and heterogeneity, amid other salient features (Chudik & Pesaran, 2015; Westerlund & Narayan, 2016), with the following equations, respectively:

$$r_{t}= \alpha+\theta TR_{t}+ e_{t} \tag{6}$$

$$\begin{array}{l}r_{i, t}&=\omega_{i}+r_{i, t-1}+\sum \beta_{i} B_{i, s}+\delta_{i} T R_{i, t-1}+\varepsilon_{i, t}, \varepsilon_{i, t}\\ &=\lambda_{i} f_{t}+v_{i, t} \\ s&=t, \ldots, t-\rho T, i=1,2, \ldots N, t=1,2, \ldots T \end{array} \tag{7}$$

where $r_{t}$ is the exchange rate return, computed as the logarithmic difference, in percent, of the bilateral exchange rates; $TR_{t}$ is the measure of tail risk obtained from the three exchange rate series; $\beta_{i} \neq 0$ is the cross-sectional average; $\omega_{i}$ and $\delta_{i}$ are parameters that differ across the countries; $\varepsilon_{i,t}$ is a two-way error term that captures both factor loadings ($\lambda$ and $f_{t}$); and the remainder error is $v_{i,t}$. We include five lags in Eq. (7) (where $\sum_{1}^{5} \hat{\delta}_{i}>0$) and evaluate the significance of the cumulative parameter using F-tests.

We select eight AP countries’ currencies:^[5] the Australian dollar (AUD), the Chinese yuan (CNY), the Indonesian rupiah (IDR), the Japanese yen (JPY), the Malaysian ringgit (MYR), the New Zealand dollar (NZD), the Philippine peso (PHP), and the Singapore dollar (SGD). For robustness, we use three variants of the exchange rate pairs of domestic currencies against the US dollar (USD), the euro (EUR), and the pound sterling (GBP), obtained at a daily frequency between January 3, 2007, and March 8, 2021.^[6] We split the data with a ratio of 75 to 25 between the in- and out-of-sample forecast evaluations, respectively. We use the forecast evaluation measure of Clark & West (2007) to compare the in- and out-of-sample forecasts for the return predictive model containing tail risk against the baseline historical average model.

3. Results

As in the previous section, the results are two-fold. We obtain tail risk as measures of AP forex rate market risks, designated by Engle & Manganelli (2004) as the CAViaR. We produce the CAViaR for both the 1% and 5% tail distributions across the four specifications (see Eqs. (2) to (5)) and select the optimal tail distributions for each country, based mainly on the statistical nonsignificance of the DQ test (see Table 1).^[7] We then adopt the panel data technique of Chudik & Pesaran (2015) to evaluate the predictive power of the optimal tail risk in the model for the AP forex market returns, with results for advanced and emerging countries, as well as for the full sample. The choice of the panel technique is not driven by the desire to save space, but, rather, by evidence of strong financial integration in the region, especially because of extreme market events (Ahmad et al., 2012; Darrat et al., 2011; Didier et al., 2017; Liu & Yang, 2017).^[8]

The impact analysis results in Table 2, Panel A indicate that market (tail) risk significantly impacts AP forex markets for USD- and GBP-denominated exchange rate returns. In terms of the sign, while the impacts of tail risk are generally positive for USD-denominated exchange rates (and statistically significant for the full sample and advanced countries’ panel), it is negative for GBP-denominated exchange rates across panels. The results for the euro-denominated exchange rate returns are neither significant nor consistent. These findings reveal notable inferences for investors in AP forex markets. The implication is that investors could use USD-denominated exchange rates to hedge against GBP- and EUR-denominated exchange rates, especially in advanced AP markets.

We compare the forecast accuracy of the exchange rate return model containing market risk as a predictor with the baseline using only a constant as the predictor (historical average model).^[9] We evaluate the in- and out-of-sample forecast performance of these models across the full sample and the advanced and emerging countries’ panels, respectively. Hence, we divide the data sample along a 75-to-25 ratio and evaluate the out-of-sample forecast for two out-of-sample horizons (h = 10 and h = 20). The Clark–West statistic proves handy in this direction, and we expect it to be statistically significant, in which case, the extended model is preferred.

The in- and out-of-sample forecast evaluation results are presented in Table 2, Panels B and C, respectively. In Panel B, the three models for the exchange rate returns fulfill the conditions, indicating that the model with tail risk outperforms the baseline for in-sample evaluation across the three panels).^[10] All the coefficients are significant at the 1% level. The major focus of our study is an out-of-sample forecast evaluation that seeks to challenge the position of Meese & Rogoff (1983) with evidence that AP forex market risk can forecast exchange rate returns out of sample better than the historical average (equivalent to a random walk model without differencing). Our preferred model consistently outperforms the baseline in out-of-sample forecast evaluations across the three variants of exchange rate pairs and the 10- and 20-day-ahead forecast horizons (see Panel C). Interestingly, out-of-sample forecast performance does not wane at longer forecast horizons or depending on whether we consider the full sample or the panels for advanced and emerging AP countries.

4. Conclusion

We build on the work of Bouri et al. (2020), who suggest that return and volatility transmission is heightened among AP currency markets in the extreme tails of conditional distributions. We are also informed by the fact that extreme market events influence the financial climate of the region, as shown by Didier et al. (2017) and Liu & Yang (2017), among others. We improve on these ideas to obtain measures of market risk from the CAViaR of Engle & Manganelli (2004). We test the performance of the CAViaR in a predictive model for the exchange rate returns of eight AP countries, following Chudik and Pesaran’s (2015) panel technique. The results clearly show that tail risk matters in predicting exchange rates out of sample, a finding that suggests reconsideration of the Meese–Rogoff puzzle. For investment decisions, we infer that investors in the AP region could obtain hedging benefits in the USD-denominated exchange rate markets of advanced AP countries. In all, there could be a need for a stronger forex buffer (foreign reserves), especially among emerging AP countries, to counter forex market risks.

Figure 1:Exchange rate returns and tail risk

Note: The description is limited to the USD exchange rates given space constraints. The rest are available on request.