Forecasting the CNH-CNY pricing differential: the role of investor attention

Transcription

1 Forecasting the CNH-CNY pricing differential: the role of investor attention Liyan Han 1, Yang Xu 1, Libo Yin,* ( 1 School of Economics and Management, Beihang University, Beijing, China) ( School of Finance, Central University of Finance and Economics, Beijing, China) First Author: Liyan Han Position: Professor Affiliation: School of Economics and Management, Beihang University, Beijing, China Second Author: Yang Xu Position: Ph.D. candidate Affiliation: School of Economics and Management, Beihang University, Beijing, China Corresponding Author: Libo Yin Position: Associate Professor Affiliation: School of Finance, Central University of Finance and Economics, Beijing, China Tel: (86) yinlibowsxbb@16.com Address: No. 39 South College RD., HaiDian DIST., Beijing, , China. Acknowledgements This research is financially supported by the National Natural Science Foundation of China under projects No and No , the Program for Innovation Research in the Central University of Finance and Economics, and the Innovation Foundation of BUAA for PhD Graduates.

2 Assessing the CNH-CNY pricing differential: Role of investor attention Abstract: As the exponential expansion in the international use of RMB, the issues concerning one currency, two markets have attracted increasing attentions from both policymakers and academics. We investigate the forecast ability of investor attention on the CNH-CNY pricing differential for the period of March 011 to November 015. Our results show that investor attention displays economically and statistically significant in-sample and out-of-sample predictabilities of the CNH-CNY pricing gap at both monthly and weekly frequencies. In addition, investor attention could generate substantial economic values in asset allocation at both monthly and weekly frequencies. Furthermore, we find that investor attention provides economically and statistically significant out-of-sample forecast for the CNY carry trade on weekly basis. Keywords: CNH-CNY pricing differential, investor attention, macroeconomic factors, out-of-sample forecast, carry trade

3 1. Introduction On the heels of China s strong economic performance in the past decades, there is a rapid growth in the international use of RMB 1, which is mainly attributed to the development of offshore RMB (CNH) exchange rate market. Since the officially sanction of offshore renminbi trading in July 009, issues concerning one currency, two markets have attracted increasing attentions from both policymakers and academics. Besides the exponential expansion of trading volumes, one important feature for offshore renminbi market is the persistent deviations existing between the CNH and CNY spot exchange rates. As shown in Figure 1, the CNH spot rate displayed greater volatility in daily movements, even though they both have followed the same broad trend, depreciating by around 10% during the period of March 011 to November 013 then constantly appreciating by around 5% until the end of 015. Take one episode for example, while on October 01 the offshore rate of renminbi to the US dollar was nearly 100 pips below the onshore rate of 6.735, by December the gap widened to roughly 400 pips (6.148 offshore to onshore). As the offshore renminbi market is the very key component of RMB s internationalization (Ma and McCauley, 010), which could provide fundamental influences on both the country of issuance as well as the global economy (Maziad and Kang, 01; Shu et al., 014) 3, the understanding of pricing differential between onshore (CNY) and offshore (CNH) markets will have significant implications for promoting the process of RMB s internationalization. To explain this issue, existing studies extensively concentrate on two sets of factors that can 1 According to the Bank of International Settlement s 013 Triennial Central Bank Survey that renminbi now ranks the ninth most traded currency in the world and the most traded in Asia (Funke et al., 015). In October 013, the RMB surpassed euro and Japanese Yen and became the second most used currency in traditional trade finance covering letters of credit and collections, and was ranked the 1 th currency for international payments in the world (Shu et al., 014). According to Shu et al. (014), the daily average volume of inter-dealer transactions in offshore market increased from billion in 007 to billion in Particularly for the Chinese, it would reduce liquidity and exchange rate risks facing domestic economic agents, and allow both the public and private sectors to finance in domestic currency from the global market, as well as improve the cross-border transactions. Form a global perspective, the internationalizing of RMB could effectively reflect the structure of the global economy based on real economic activities and the growth drivers (Maziad and Kang, 01), thereby improving global risk sharing and managing systemic vulnerability.

4 potentially influence the pricing spread: those related to capital market liberalization policies (Shu et al., 014; Funke et al., 015); and those related to fundamentals or economic conditions (Shu et al., 007; Fratzscher and Mehl, 011; Subramanian and Kessler, 01; Ding, et al., 01; Funke et al., 015). As for the first, the CNY market remains constrained by the central bank s intervention and the stipulation of a daily trade band. By contrast, in the CNH market, central bank shows no presence in the price formation or in setting trading limits. The distinct feature of the onshore (CNY) and offshore (CNH) markets have frequently caused the two exchange rates to diverge from each other. Second, the two markets are likely to have different investor bases and liquidity circumstances (Funke et al., 015). For example, Maziad and Kang (01) find that onshore spot rates have an influence on both spot and forward rates in the offshore market under normal market conditions; while under conditions of financial stress offshore exchange rate movements impact onshore spot rate, and volatility spillovers exist in both directions. Ding et al. (014) find that price discovery differences in the offshore markets stem from the offshore spot tracking onshore interest rates while the offshore forward contracts tracking onshore spot rates. In this paper, we seek to investigate the pricing differentials between offshore (CNH) and onshore (CNY) exchange rates from a new perspective investor attention which is recently popular used in asset pricing and market efficiency (Kim et al., 014; Yuan, 015). Our line of thoughts stem from the following two aspects. First, existing literatures provide empirical evidence supporting the dynamic relationship between fundamental economic factors and the onshore and offshore renminbi exchange rate (Shu et al., 007; Fratzscher and Mehl, 011; Subramanian and Kessler, 01; Ding et al., 01; Funke et al., 015), while little research has been taken from the perspective of investor attention. Only considering information from fundamentals is not sufficient as some literatures, however, note that a puzzling feature of currency is that dramatic exchange rate movements occasionally happen without fundamental news announcements, indicating that many abrupt asset price movements cannot be attributed to fundamental news events (Cutler et al., 1989; Fair, 00; Balke et al., 013). Besides that, macroeconomic factors are frequently claimed to have weak out-of-sample predictability of exchange rates since Messe and Rogoff (1983), and by many others (Cheung et al., 00; Killian and Taylor, 003). One notable exception in investigating the predictability of exchange rate is Yu (013) who shows that investor sentiment helps account for the forward premium puzzle. Another

5 study closest to ours is by Craig et al. (013) who attribute the CNH-CNY pricing differential to onshore investor risk sentiment and capital account liberalization. To our best knowledge, investor attention has been widely proved to be statistically and economically significant for security markets (Merton, 1987; Sims, 003; Hirshleifer and Teoh, 003; Peng and Xiong, 006; Barber and Odean 008; Da et al. 015), inspiring us to take an exploration of investor attention in currency market. Therefore, we would expect similar predictive ability of investor attention for the pricing differential between CNH and CNY. Second, the existence of CNH-CNY pricing differential provides a naturally testing pool for investigating the relationship between investor attention and currency market. For one thing, the CNH market is exposed to more complex global factors and appears to be more informationally integrated than the CNY market. Specifically, compared to the CNY market, the CNH market is a free market, with a more diversified range of products, including spot, forward, swap and options, and participant base, including exporters, importers offshore financial institutions, hedge funds and Hong Kong residents (Kim et al., 014; Yuan, 015). Thus from the global perspective, the study of predictive ability of investor attention for the CNH-CNY pricing differential could provide implications for other international currencies, especially currencies of emerging markets. Furthermore, since the information about economic conditions for both exchange rate markets are from the same source of underlying economic fundamentals, experiments on the CNH-CNY pricing differential is free of issues resulting from identifying different control variables. To fulfill the above objectives, we first construct our own attention indices by applying the partial least squares (PLS) approach following Wold (1966, 1975) and Kelly and Pruitt (013, 014); then investigate the in-sample and out-of-sample predictive ability of investor attention on the CNH-CNY pricing differential; then for interest of comparison, we compare the forecast performance of investor attention with that of macroeconomic variables; we also explore the economic implications of investor attention through asset allocations; and finally we investigate the predict power of investor attention on CNY carry trade. This paper contributes to existing literature in the following four aspects. First, unlike existing literatures about exchange rate which extensively focus on macroeconomic factors, such as inflation, interest rate, output, balance of payment, etc. (Cheung et al., 00; Killian and Taylor, 003), and microeconomic factors, such as order flow (Evans and Lyons, 005), we first provide

6 evidence concerning on the relationship between investor attention and exchange rate. To our best knowledge, it is the first time that investor attention is introduced to currency market. Second, existing literatures mostly investigate the relationship between securities and investor attention by simply applying the number of attention terms (except for Da et al. 015, who use a weighted average attention index), while we construct an aligned attention index through PLS method in order to capture the information that most related to target exchange rate. Additionally, current studies frequently use the attention to index to investigate its relationship with the corresponding index return (Vozlyublennaia, 014; Kim et al., 014), while we consider a much wider set of potential attention terms in order to reflect information from three aspects. In particular, we first consider the attention terms CNH and CNY to represent information contained in currency name and generate the first aligned attention index, self attention:. Then we compile a series of attention terms that are directly linked to real economy to generate the aligned macro attention index. And the last group of attention terms are derived from the terms used in FEARS index (Da et al., 015), to possibly reflect investor attention in financial markets. Additionally, by comparing the forecast performance, we also testify that macro attention captures information different from macro factors. Third, we provide evidence that investor attention has both in-sample and out-of-sample predictability of the CNH-CNY pricing differential, while current studies mostly concentrate on the relationship between the pricing spread and fundamental factors and barely investigate out-of-sample forecast (Shu et al., 007; Fratzscher and Mehl, 011; Subramanian and Kessler, 01; Ding et al., 01). Moreover, we prove economic significance of investor attention by investigating its predictability of carry trade, filling the gap in existing literatures. Lastly, a common problem with existing papers is their reliance on ex-post revised economic data for forecasting analysis. The revisions to macroeconomic data may be substantial and are not available to either policy makers or market participants at the time forecasts made. Instead, we use the actual realized values of investor attention to possibly prevent the revised data from yielding misleading inference of exchange rate forecast. Moreover, the macroeconomic data are usually disclosed at a lower frequency (monthly, quarterly, or annually), while we apply the actual realized values of investor attention whose data can be obtained at a relatively higher frequency (weekly,

7 daily) 4. In that sense, with good feasibility at a higher frequency, the actual realized investor attention may play a significant role in risk management area. The rest of this paper is structured as following: In section, we explain the econometric method to construct aligned attention index. Section 3 describes data. Section 4 analyzes the in-sample and out-of-sample empirical results and Section 5 concludes.. Construction of aligned attention index In this section, we provide the econometric method for constructing our aligned attention indices. We assume that the one-period ahead expected CNH-CNY pricing differential explained by investor attention follows the standard linear equation, E t Dt At 1, (1) where A t is the investor attention that matters for forecasting CNH-CNY pricing differential. The realized differential then equals to its conditional expectation plus an unpredictable shock, D E t 1 t ( Dt 1) t 1 At t 1, () where t 1 is unpredictable and unrelated to Let periodt t 1,..., T A t. x t x1, t,..., xn, t denote an N 1 vector of individual investor attention proxies at. We assume that i 1 N x t i,,..., has a factor structure,, i 1,..., N. (3) x i, t i,0 i,1at i,et ei, t where A t is the investor attention that matters for forecasting CNH-CNY pricing differential, i,1 is the factor loading that summarizes the sensitivity of sentiment proxy x i, t to movements in t A, Et is the common approximation error component of all the proxies that is irrelevant to the pricing spread, and e, is the idiosyncratic noise associated with i t i only. The objective is to impose the above factor structure on the proxies to efficiently estimate A t, 4 We have free access to weekly data from Google Trend since Jan 004 till the current, and daily data can be obtained up to the recent 90 days.

8 the collective contribution to the true investor attention, and at the same time, to eliminate E t, their common approximation error, and e i, t from the estimation process. Following Wold (1966, 1975) and Kelly and Pruitt (013, 014), we apply the partial least squares (PLS) approach to extract A t and filter out the irrelevant component E t, while the commonly used principal component (PC) method cannot by guaranteed to do so. The key idea is that PLS extracts the investor sentiment, A t from the cross-section according to its covariance with future CNH-CNY pricing differentials and forms a linear combination of attention proxies which can provide optimal forecast. In doing so, PLS can be implemented by the following two steps of OLS regressions. In the first-step, for each individual investor attention proxy x i, we run a time-series regression of x i, t 1 on a constant and realized CNH-CNY pricing differential D t, x D, i, t 1 i,0 i t i, t 1 t 1,...,T. (4) Instrumented by future pricing differential D t, the loading i captures the sensitivity of each attention proxy x i, t 1 to the attention index A t 1. Since the expected component of D t is driven by A t 1, attention proxies are related to the expected CNH-CNY pricing differentials and are uncorrelated with the unpredictable spreads. Therefore, the coefficient i in the first-stage time-series regression in Eq. (4) approximately describes how each attention proxy depends on the true investor attention. In the second-step, for each time periodt, we run a cross-sectional regression of x i, t on the corresponding loading ˆi estimated in Eq. (4),, i 1,..., N, (5) x i, t ct A ˆ t i i, t where A t is the estimated investor attention. That is, in Eq. (5), the first-stage loadings become the independent variables, and the aligned investor attention A t is the regression slope to be estimated. In practice, if the true factor loading i was known, we could consistently estimate A t by

9 simply running cross-sectional regressions of x i, t on i period-by-period. Since i is unknown, however, the first-stage regression slopes prove a preliminary estimation of how x i, t depends on A t. In other words, PLS uses time t+1 differential to discipline the dimension reduction to extract A t relevant for forecasting and discards common and idiosyncratic components such as E t and e i, t that are irrelevant for forecasting. Mathematically, the 1 T vector of aligned investor attention index, A A,..., A t 1, can T be expressed as a one-step linear combination of x i, t, A XJ N X J T 1 XJ X J D D J D D D J T N T T, (6) where X denotes the X x,..., x T N matrix of individual investor attention proxies, 1 T, and matrices D denotes the J T I T T 1vector of CNH-CNY pricing differentials as 1 T T and J T regression is run with a constant. N I I T N is a 1 N T - N N D D,..., DT 1. The is entered in the formula because each dimensional identity matrix and T is a T - vector of ones. The weight on each individual measure x i, t in A t is based on its covariance with the CNH-CNY pricing differential to capture the inter-temporal relationship between the aligned investor attention and the expected pricing differentials. 3. Data 3.1 Search terms Following Da et al. (011, 015), we use the public Search Volume Index (SVI) from Google Trends ( as our investor attention proxies. The numbers present search probabilities of a given keyword at a given time. To build a list of attention indices that have explanatory ability toward the CNH-CNY pricing differential, we work on search terms from three sources. The first group of attention terms is based on the name of exchange rate itself.

10 Vozlyublennaia (014) find that the attention to an index has a significant short-term effect on the index return. So we consider the attention terms CNH and CNY to generate the first attention index, and name as self attention. The second group, named macro attention, consists of economic terms that are linked directly to economic fundamentals. The majority of economic terms are well-known factors claimed to have predictabilities on exchange rate by studies, such as money supply, inflation, interest rate, etc., although terms are subjectively chosen. For the last group, considering abundant evidence of dynamic relationship between stock prices and exchange rates (Korajczyk and Viallet, 199; Phylaktis and Ravazzolo, 005; Hau and Rey, 006; Cumperayot et al., 006), we are interested to find out if attention terms that reflect information from financial market can also explain the exchange rate movements. Thus, in line with Da et al. (015), we consider 30 terms which are suggested to be useful for forecasting stock prices in the last group to represent information from financial market. The data covers a weekly period from March 011 until November The empirical analysis is carried out at both monthly and weekly frequency, although we start from weekly search terms. The monthly data is derived by averaging four weeks search amount and the construction of weekly and monthly proxies for investor attention follows the same procedure as discussed above. Following the extant literature of Fama (1988) and especially Da et al. (011, 015), we work in logarithms of search terms for ease of exposition and notation. Table displays some summary statistics of the attention terms over full sample, and the statistics are generally consistent with literature. 3. Other data The CNH-CNY pricing differential is computed as the log difference between the spot exchange rate of offshore and onshore Renminbi. The data of CNY and CNH is obtained from Reuters (via DataStream). The data spans March 011 until November 015 and summary statistics are reported in Pane A, Table 1. The weekly CNH has a mean of with a standard deviation of and the weekly CNY has a mean of with a standard deviation of 5 According to Reuters (via DataStream) the spot exchange rate data for CNH at Hong Kong SAR starts from February 8, 013. To possibly include large sample we employ weekly attention data from the first week of March 013.

11 The monthly CNH-CNY pricing differential is derived by averaging four weeks pricing data and follows the same mathematic process. To investigate the economic value of investor attention, we also examine the forecast ability of our attention indices on currency carry trade. The data for 1 month forward exchange rate versus the USD is obtained from Reuters (via DataStream) and covers the sample period from March 011 to November 015. As presented in Table 1, the weekly carry trade has a mean of and a standard deviation of 0.008, with high autocorrelation. The monthly carry trade has a mean of and a standard deviation of with relatively lower autocorrelation than weekly data. For interest of comparison, we also consider four monthly economic variables that are widely acknowledged as useful predictors of exchange rate in a number of studies such as Molodtsova and Papell (009), Wu and Hu (009), Zwart et al. (009), Balke et al. (013), Ince (014), Bekiros (014), and many others, which are interest rate (IR), the amount of narrow money supply (M1), the amount of broad money supply (M3), and consumer price index (CPI). The data spans March 011 to November 015 and summary statistics, reported in Table 1, are generally consistent with literatures. 4. Empirical Results In this section, we present a number of empirical results. Section 4.1 reports the in-sample estimates of the spread of onshore and offshore Renminbi exchange rates by various attention indices. Section 4. examines the out-of-sample forecast ability of attention indices. Section 4.3 assesses the economic value of predictability via asset allocation and section 4.4 investigates the predictability of the CNY carry trade. 4.1 In-sample analysis To investigate the predictive power of individual attention indices, we employ a simple univariate prediction model. As evident from previous literatures, it is presumed that changes in investor attention should cause changes in security prices and returns (Kim et al., 014; Yuan,

12 015). While this proposition has been examined in the literature primarily for individual securities in stock markets, here we test it in currency market, specifically for the pricing differentials between offshore (CNH) and onshore (CNY) Renminbi. The simple univariate predictive regression is specified as following: D A, (7) t 1 i i i, t i, t 1 where Dt 1 denotes the pricing differentials between CNH and CNY at periodt 1, A i, t denotes the investor attention that is available at period t, and i, t 1 is a zero-mean disturbance term. In line with Inoue and Kilian (004), who recommend a one-sided alternative hypothesis to increase the power of in-sample predictability tests, we test H : 0 0 i against H : 0 A i using a heteroscedasticity-consistent t-statistic corresponding to ˆi in Eq. (7). In addition, to directly compare the predict power of attention indices to that of macroeconomic variables employed in traditional structural models, we generate a monthly index for macroeconomic variables following the same PLS procedure as discussed above and evaluate its performance by replacing A i, t in Eq.(7) with X t, which takes the formulation: D, (8) t 1 X t t 1 where X t refers to the macroeconomic index at period t, and the denotations of D t 1 and i, t 1 are defined the same as those in Eq. (7). Similarly, we test H : 0 0 against H : 0 using a heteroscedasticity-consistent t-statistic that corresponds to, the OLS A estimate of in Eq. (8). Statistically, there are issues that may have adverse impact on the statistical inference about the attention indices. First, there is potentially a spurious regression concern when a predictor is highly persistent (Ferson et al., 003). Second, the first-step regression for the in-sample PLS estimation, Eq. (4), introduces a look-forward bias as it uses future information. Although Kelly and Pruitt (013, 014) show that this bias will vanish as the sample size becomes large, it is still a concern with finite sample here. We employ two strategies to alleviate the above issues. First, we base the inference on

13 empirical p values using a wild bootstrap procedure that accounts for the persistence in predictors, correlations between the differentials and predictor innovations, and general forms of distribution. Second, we construct a look-ahead bias-free PLS forecast. To calculate i at time t 1, we run the first-step time-series regression of Eq. (4) with information up to time t only. Then, the regression slopes are used as independent variables for the second-step regression of Eq. (5), whose slope is therefore the attention indices A t at time t. Repeating this procedure recursively, we obtain a look-ahead bias-free attention index. In this paper, we use the first three year data as the initial training sample when computing recursively the look-ahead bias-free attention indices. [Insert Table 3 Here] Table 3 reports the results of the in-sample predictive regression. Panel A provides monthly estimates of i for the attention indices, over the sample period of March 011 through December 013. Overall, attention indices A i generate small and positive regression slopes i of , 0.013, and for macro attention, stock attention, and self attention, respectively. The t - statistics are large in absolute values, with marginally significance at the 1% level. After elimination of look-ahead information, the look-head bias-free indices yield large R of 51.66%, 57.35%, and 16.% for macro, stock, and self attention respectively. The estimated slope coefficients of the three attention indices appear to be in similar patterns in terms of signs and significance. The macroeconomic index, in comparison, provides a relatively good estimate result as well, indicating that macroeconomic variables which are claimed to have poor predictive performance for exchange rate in traditional structural models (Messe and Rogoff, 1983; Cheung et al., 00; Killian and Taylor, 003) substantially improve predict power by eliminating the common noise component of the proxies, which is made possible with the PLS method developed by Kelly and Pruitt (013, 014). The regression slope is equal to , slightly lower than stock and macro attention index while higher than self attention index, with a significant t - statistic at 1% significance level. Also, the R is slightly lower than those of stock and macro attention indices but greater than that of self attention index. Although macro index has significant in-sample estimates, its influence is still no stronger than macro and stock attention indices, in

14 terms of the magnitude of and R statistics. The results are consistent with existing studies on renminbi that investors based on the onshore and offshore markets may react differently to the same fundamental movements or same macroeconomic news which can trigger the immediate adjustment in exchange rate and thus lead to the gap between CNH and CNY (Funke et al., 015). Panel B presents weekly predictive results for the attention indices. Overall, attention indices A i generate small and positive regression slopes i of , , and for macro attention, stock attention, and self attention, respectively. The t - statistics are large in absolute value, with marginally statistical significance at the 1% level. Also, the weekly attention indices A i yield large R of 11.93%, 18.6%, and 11.48% for macro, stock, and self attention respectively. The estimates of the slope i are positive and remain statistically significant at 1% level, in line with the results reported in Panel A. all of the R s in Panel B are substantially smaller than those in Panel A but are still greater than 10%. Economically, if this level of predictability can be sustained out-of-sample, it will be of substantial economic significance (Kandel and Stambaugh, 1996). This point will be analyzed further in Section 4.. Summarizing Table 1, the aligned investor attention indices A i exhibit statistically and economically significant in-sample predictability of the monthly and weekly CNH-CNY pricing differentials. In addition, two of the attention indices provide better estimations than the macroeconomic index in terms of R, suggesting that investor attention may contain sizable forecasting information beyond what is contained in the macroeconomic predictors. 4. Out-of-sample analysis Although the in-sample analysis provides efficient parameter estimates and thus more precise pricing differentials forecast, Goyal and Welch (008), among others, argue that out-of-sample tests seem more relevant for assessing genuine predictability in real time and avoid the in-sample over-fitting issue. In addition, out-of-sample tests are much less affected by the small-sample size distortions such as the Stambaugh bias (Busetti and Marcucci, 00) and the look-ahead bias concern of the PLS approach (Kelly and Pruitt, 013, 014). Hence, it is of interest to investigate

15 the out-of-sample predictive performance of investor attention. The key requirement for out-of-sample forecasts at time t is that we can only use information available up to t to forecast the pricing differentials at t 1. Following Goyal and Welch (008), Kelly and Pruitt (013), we run the out-of-sample analysis by estimating the predictive regression model recursively based on individual investor attention index, where ˆt and ˆt attention index ˆ ˆ ˆ, (9) m D t 1 t t A1 : t; t are the OLS estimates from regressing k A 1 :t ; s t 1 s 1 m t 1 D s 1 s 1 on a constant and an. Like our in-sample analogues in Table 3, we consider macro, stock, and self attention in both monthly and weekly basis, as well as a monthly macroeconomic index. For interest of comparison, we consider the combination forecast that is widely used in econometric forecasting applications and that often beats sophisticated optimally estimated forecasting weighs (Timmermann, 006). In finance, Rapach et al. (010) show that a simply equal-weighted average of univariate regression forecasts can consistently predict the market risk premium. It is hence of interest to see how well it performs in the context of using the attention proxies. Let p be a fixed number chosen for the initial sample training, so that the future expected pricing differentials can be estimated at time t p 1, p,..., T. Hence, there are q T p out-of-sample evaluation periods. That is, we have D ˆ m T t 1 t p q out-of-sample forecasts: 1. More specifically, we use the data covers March 011 through December 013 as the initial estimation period so that the forecast evaluation period spans over January 014 through November 015. To evaluate out-of-sample forecast performance we compute three statistics as follows. First, we evaluate the out-of-sample forecast based on the widely used Campbell and Thompson (008) OS T t ˆ R, (10) 1 m m ( D 1 1) p t Dt 1- T 1 m m ( D 1 t 1) t p t D where m Dt 1 denotes the historical average benchmark corresponding to the constant expected m pricing differentials model ( Dt 1 t 1 ),

16 D m t 1 1 t t s 1 D m s. (11) Goyal and Welch (008) show that the historical average is a very stringent out-of-sample benchmark, and individual economic variables typically fail to outperform the historical average. The R OS -, 1 statistic lies in the range. If R OS 0, it means that the forecast m Dˆ t 1 outperforms the historical average m Dt 1 in terms of MSFE. The second statistic we report is Diebold and Mariano (1995) statistic modified by McCracken (007), which tests for the equality of the mean squared forecast errors (MSFE) of one forecast relative to another. Our null hypothesis is that the historical average has a MSFE that is less than, or equal to, that of the predictive regression model. Comparing a predictive regression forecast to the historical average entails comparing nested models, as the predictive regression reduces to the historical average under the null hypothesis. McCracken (007) shows that the modified DM-test statistic follows a nonstandard normal distribution when testing nested models, and provides bootstrapped critical values for the nonstandard distribution. The third statistic is the MSFE-adjusted statistic of Clark and West (007). It tests the null hypothesis that the historical average MSFE is less than or equal to the predictive regression forecast MSFE against the one-sided (upper-tail) alternative hypothesis that the historical average MSFE is greater than the predictive regression forecast MSFE, corresponding to H : 0 0 R OS against H : 0. Clark and West (007) show that the test has an asymptotically standard A R OS normal distribution when comparing forecasts form the nested models. Intuitively, under the null hypothesis that the constant expected return model generates the data, the predictive regression model produces a noisier forecast than the historical average benchmark because it estimates slope parameters with zero population values. We thus expect the benchmark model s MSFE to be smaller than the predictive regression model s MSFE under the null. The MSFE-adjusted statistic accounts for the negative expected difference between the historical average MSFE and predictive regression MSFE under the null, so that it can reject the null even if the R OS statistic is negative. [Insert Table 4(a) Here] Table 4(a) presents monthly results for the out-of-sample period of January 014 through

17 November 015. The first and second columns report the MSFE and MSFE-adjusted statistics; the forth column presents p - values for the Clark and West (007) MSFE-adjusted statistic; the third column presents R OS values; and the last two columns report the Theil (1966) MSFE decomposition into the squared forecast bias and a remainder term. The first row of Table 4(a) provides monthly out-of-sample forecast results of historical average as the evaluation benchmark. Panel A of Table 4(a) shows that the macro, stock, and self attention indices generate positive R OS statistics (4.0116%, %, and %, respectively), and thus deliver lower MSFEs than the historical average. Moreover, all three attention indices provide significant MSFE-adjusted statistics at 1% significant level according to their bootstrapped p values. The last two columns report the MSFE decompositions into a squared forecast bias and a forecast error variance. The remainder term depends, among other things, on the forecast volatility, and limiting forecast volatility helps to reduce the remainder term (Rapach et al., 010). The squared bias (remainder term) is (0.004 ) for the historical average forecast. All investor attention indices have squared bias well below that of the historical average while the forecast error variances exceed the benchmark. The results indicate strong out-of-sample predictive ability of investor attention for CNH-CNY pricing differentials. The macroeconomic index, on the contrary, is not statistically significant according to its DM- and CW- test statistics. It also yields a negative R OS statistic (-0.706%). Thus, the macroeconomic index exhibits weak out-of-sample forecast ability of the CNH-CNY pricing gap, confirming the widely acknowledged argument by Meese and Rogoff (1983) Cheung et al. (00), Killian and Taylor (003), and many others that macroeconomic variables have little out-of-sample predictability of exchange rate. Also, this result suggests that, while multiple predictors tend to improve in-sample performance through implementing PLS, but the out-of-sample performance may not be necessarily improved (Huang et al., 014). Panel B of Table 4(a) reports the combination forecast results of all attention indices. Intuitively, the economic sources of predictability of investor attention are supposed to be the same which suggests that they are likely to capture very much similar information towards the same proxies. However, we are still interested in finding their differences in forecasting power and thus implement the forecast combination, which is widely known as viable method for

18 improving forecast performance with multiple predictors, following Bates and Granger (1969), Stock and Watson (004), Aiolfi and Timmermann (006), Rapach et al. (010), and many others. The results in Panel B of Table 4(a) show that combination forecasts based on three attention indices generally perform very well over the out-of-sample period. The third column of Panel B shows that all of the the MSFE-adjusted R OS values are sizable and all significant at 1% level of significance using p values. In addition, all MSFE statistics in the first column are well below that of the historical average. Similar to the results of individual predictive regression, all combination forecasts have squared bias well below that of the historical average while the forecast error variances exceed the benchmark. Surprisingly, we find that the kitchen sink model provides the highest R OS value with significance, %, among five combination approaches. The kitchen sink model usually suffers from a serious over-fitting issue and its out-of-sample-performance is very poor (Goyal and Welch, 008). However, it seems not the case in our study, which maybe mainly attributed to the fact that the number of regressors is as few as three in our combination. To further understand the predict power of investor attention and their economic sources, we also examine the combination forecast of all indices including the macroeconomic index. Results in Panel C of Table 4(a) show that the forecast performances are dragged down, except for the diffusion index model, when macroeconomic index is included in combination. Combination forecasts in Panel B provide an average R OS value of %, while in Panel C the average R OS value drops to %, even though the statistics are sizable and all significant at 1% level of significance using the MSFE-adjusted p values. Additionally, all MSFE statistics in the first column are well below that of the historical average, and all forecasts have squared bias well below benchmark while the forecast error variances exceed that of the historical average. Diffusion index model provides the best performance in Panel C of Table 4(a), with R OS reaching %. Nonetheless, it is still not sufficient to suggest that macroeconomic index has out-of-sample predictability and improve the combination performance since the overall performances are pulled down compared to the results in Panel B. Thus, according to results in Table 4(a), we may conclude that investor attention indices have economically and statistically

19 out-of-sample forecast ability of the CNH-CNY pricing differential with monthly data, while macroeconomic variables barely have predict power of exchange rate over the same sample period which is in line with many literatures (Meese and Rogoff, 1983; Engle and West, 007). [Insert Table 4(b) Here] As suggested by existing literatures that investor attention tends to have short term effect on stock market, while due to the limits of arbitrage, its predictability will be substantially impaired over a long horizon Shu et al. (014). Here we investigate its predictability of the CNH-CNY pricing gap with weekly data. Table 4(b) reports the out-of-sample forecasting results of CNH-CNY pricing differentials over the sample period of January 014 through November 015. Results in Panel A of Table 4(b) demonstrate that macro, stock, and self attention indices individually performs well out-of-sample forecasts, with positive R OS statistics reaching %, %, and % respectively, and thus generates lower MSFE than that of the historical average. Also, all three attention indices deliver significant MSFE-adjusted statistics at 1% significant level according to their bootstrapped p values. As for the decomposition of MSFE presented in the last two columns, all three attention indices have squared forecast biases well below that of historical average and forecast error variance equal to or below the benchmark. Panel B of Table 4(b) presents the weekly results of combination forecast of all attention indices for the CNH-CNY pricing spread. All combination forecasts deliver significant positive R OS statistics with an average over 33% and thus have MSFE values well below that of the historical average. More specifically, the simple average model provides the highest R OS value reaching %, which is in accord with the literature that simple average scheme usually exhibits the best forecast performance than other combination models (Rapach et al., 010). Also, all combination forecasts present squared forecast biases well below that of the historical average and forecast error variance equal to or below the benchmark. In summary, this section shows that aligned investor attention indices Ai display strong marginal out-of-sample forecasting power for the CNH-CNY pricing differentials at both monthly and weekly frequencies, consistent with our previous in-sample results (Table 3). In addition, combination forecasts effectively improve the predictability of individual attention indices. The

20 inclusion of macroeconomic index in combination forecast does not strengthen the performance since it has poor out-of-sample predictability of the CNH-CNY spread. 4.3 Asset allocation implications In this part, we examine the economic value of CNH-CNY pricing differential forecasts based on the aligned investor attention indices A i, t. Following Kandel and Stambaugh (1996), Campbell and Thompson (008) and Ferreira and Santa-Clara (001), we compute the certainty equivalent return (CER) gain and Sharpe Ratio for a mean-variance investor who optimally allocates across assets and the risk-free asset using the out-of-sample predictive regression forecasts. This exercise also contributes to many existing studies of investor attention that fail to incorporate risk aversion into the asset allocation decision. At the end of periodt, the investor optimally allocates w t 1 Dˆ ˆ t 1 t 1, (1) of the portfolio CNH-CNY pricing differential during period t 1,where is the risk aversion coefficient, ˆ 1 D t is the out-of-sample forecast of the CNH-CNY pricing differential, and t 1 is the variance forecast. The investor then allocates t 1 realized portfolio return is 1- w t p f Rt 1 wt Dt 1 Rt 1 ˆ of the portfolio to risk-free bills, and the, (13) where f Rt 1 is the gross risk-free return. Following Campbell and Thompson (008), we assume that the investor uses a six-month moving window of past monthly returns to estimate the variance of the CNH-CNY pricing differential and constrains wt to lie between 0 and 1.5 to exclude short sales and to allow for at most 50% leverage. The CER of the portfolio is CERp ˆ 0.5 p ˆ p, (14) where ˆ p and ˆ p are the ample mean and variance, respectively, for the investor s portfolio over

21 the q forecasting evaluation periods. The CER gain is the difference between the CER for the investor who uses a predictive regression forecast of market return generated by Eq. (9) and the CER for an investor who uses the historical average forecast generated by Eq. (11). We multiply this difference by 4 so that it can be interpreted as the monthly portfolio management fee that an investor would be willing to pay to have access to the predictive regression forecast instead of the historical average forecast. To examine the effect of risk aversion, we consider portfolio rules based on risk aversion coefficients of 5. In addition, we also consider the case of 50bps transaction cost which is generally considered as a relatively high number. For assessing the statistical significance, we test whether the CER gain is indistinguishable from zero by applying the standard asymptotic theory (DeMiguel, Garlappi, and Uppal, 009). In addition, we also calculate the weekly (monthly) Sharpe ratio of the portfolio which is the mean portfolio return in excess of the risk-free rate divided by the standard deviation of the excess portfolio return. Following again DeMiguel, Garlappi, and Uppal (009), we use the approach of Jobson and Korkie (1981) corrected by Memmel (003) to test whether the Sharpe ratio of the portfolio strategy based on predictive regression is statically indifferent from that of the portfolio strategy based on historical average. The fifth through eighth columns of Table 4(a) report the monthly results of the average utility gains for each of the individual predictive regression models, Sharpe ratio, turnover ratio, and utility gains net of transaction cost, respectively. As shown in the first row, the CER for the portfolio based on the historical average forecast is 4.745% for January 014 through November 015. The CER gains are positive for individual attention indices in Panel A, while their gains are lower than the historical average. Specifically, the macro, stock, and self attention yield CER gains of.75%, %, and.565%, respectively. As for the macroeconomic index, while it also generates a positive CER gain of %, the result is lower than that of macro and self attention. The three attention indices produce higher monthly Sharpe ratios than that of the historical average, with macro attention generating the highest ratio of The macroeconomic index also delivers a Sharpe ratio of that is higher than that of historical average. The average turnover is % for the historical average. Portfolio based on attention indices turn over approximately 1/10 to 1/5 times less often than the historical average portfolio and the macroeconomic index portfolio turns over roughly 1/4 times as much. After accounting for

22 transaction cost, the relatively low turnovers for attention indices reduce the CER gains but still remain positive, with self attention index provides the highest CER gains of.5508%. The macroeconomic index yields a net-of-transaction-cost CER of 0.051% which is lower than the counterparts of all three attention indices. The Panel B of Table 4(a) reveals that portfolios based on attention indices combinations generally outperform those based on individual index. All attention indices combinations deliver sizable CER gains in the fifth column, reaching a maximum of 376 basis points. Portfolios based on the combinations turn over approximately 1/5 times less often than the historical average portfolio. Due to this turnover, the net-of-transactions-costs CER gains are positive and as high as 95 basis points for all the attention indices combinations. Panel C of Table 4(a) reports performance measures for combination forecasts based on three attention indices and macroeconomic index together. The CER gains and net-of-transaction-costs CER gains are positive for all combinations. Specifically, the CER gains for simple average model (1.7711%) and discount MSFE model (1.7710%) are relatively less than that of a Kitchen sink model (3.4601%), Bayesian model (3.460%) or diffusion index model (3.0674%). While after accounting for transaction costs, the simple average model and discount MSFE model generate higher gains of 1.761% and1.7418% than other three models, which are %, , and %, respectively. The monthly Sharpe ratios are approximately around 1 compared to that of historical average, while the turn-over ratios are considerably lower than that of historical average. This may be due to the short-lived nature of investor attention (Yuan, 015). Generally, the CER gains and net-of-transaction-cost CER gains are slightly decreased after considering macroeconomic index in combinations compared to those of purely attention indices combinations. The asset allocation exercise in Table 4(a) demonstrates substantial economic value of combining information from macro, stock, and self attention indices. Table 4(b) reports the results of portfolio analysis based on weekly data. As shown in the first row, the CER of the portfolio based on historical average forecast is % for December 013 to November 015. The CER gains are positive for individual attention index in Panel A, with macro attention, stock attention, and self attention providing gains of more than 700 basis points, which are in accord with the sizable R OS statistics in Table 3. The three attention indices produce

23 hither weekly Sharpe ratios than that of the historical average, with macro attention generating the highest ratio of The average turnover is.3084% for the historical average. Although the macro attention portfolio turns over roughly.5 times more often than the historical average portfolio, it still improves the net-of-transactions-costs by 9 basis points. Portfolios based on stock attention self attention terms also provide sizable CER gains of % and %, with the Sharpe ratios of and , higher than that of the historical average portfolio. Due to their moderate turnover ratios, which are equal to or less than that of the historical average, their net-of-transaction-costs CER remain considerably high as % and 6.03%, respectively. The overall level of weekly CER and net-of-transaction-costs CER are positive and considerably higher than those of portfolios based on monthly attention data. The performance of individual investor attention indices not only demonstrates the substantial economic value of weekly attention indices but also indicates that investor attentions provide information more powerful at high frequency. 4.4 Carry trade predictability In this section, we examine the relations between investor attention indices and currency carry trades, constructed by selecting onshore RMB to be bought or sold against the US dollar, based on forward discounts. The currency carry trade, consisting of borrowing in low interest rate currencies and investing in high interest rate currencies, has been well documented for at least 30 years (Hansen and Hodrick, 1980, 1983; Fama, 1984; Lusting and Verdelhan, 007; Lusting, et al., 011). As a popular trading strategy, carry trade forms a profitable investment portfolio, violates UIP and gives rise to the forward premium puzzle (Fama, 1984; Yu, 013). Moreover, one puzzling feature of currencies is that dramatic exchange rate movements occasionally happen without fundamental news announcements, indicating that many abrupt asset price movements cannot be attributed to fundamental news events (Cutler et al., 1989; Fair, 00). As demonstrated by many studies, carry trade is part of the explanation of foreign exchange rate puzzles (Brunnermeier et al., 009). Therefore, by investigating the predictability of CNY carry trade, we seek to identify a driving force that can possibly explain the failure of UIP and the sudden exchange rate movements of CNH and CNY unrelated to news announcements.