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Forecasting the CNH-CNY pricing differential: the role of
investor attention
Liyan Han1, Yang Xu
1, Libo Yin
2,*
(1School of Economics and Management, Beihang University, Beijing, China)
(2School 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) 18801061962
Email: yinlibowsxbb@126.com
Address: No. 39 South College RD., HaiDian DIST., Beijing, 100081, China.
Acknowledgements
This research is financially supported by the National Natural Science Foundation of China
under projects No. 71401193 and No. 71371022, the Program for Innovation Research in the
Central University of Finance and Economics, and the Innovation Foundation of BUAA for PhD
Graduates.
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 2011 to November 2015. 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
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 RMB1, which is mainly attributed to the development of
offshore RMB (CNH) exchange rate market. Since the officially sanction of offshore renminbi
trading in July 2009, issues concerning “one currency, two markets” have attracted increasing
attentions from both policymakers and academics.
Besides the exponential expansion of trading volumes2, 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 2011 to November 2013 then constantly appreciating by around 5% until the
end of 2015. Take one episode for example, while on October 2012 the offshore rate of 6.2640
renminbi to the US dollar was nearly 100 pips below the onshore rate of 6.2735, by December the
gap widened to roughly 400 pips (6.2148 offshore to 6.2566 onshore). As the offshore renminbi
market is the very key component of RMB’s internationalization (Ma and McCauley, 2010),
which could provide fundamental influences on both the country of issuance as well as the global
economy (Maziad and Kang, 2012; Shu et al., 2014)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 2013 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., 2015). In October 2013, 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 12th
currency for international payments in the world (Shu et al., 2014).
2 According to Shu et al. (2014), the daily average volume of inter-dealer transactions in offshore market increased from 0.398 billion in
2007 to 3.903 billion in 2013.
3 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, 2012), thereby improving global risk sharing and managing systemic vulnerability.
potentially influence the pricing spread: those related to capital market liberalization policies (Shu
et al., 2014; Funke et al., 2015); and those related to fundamentals or economic conditions (Shu et
al., 2007; Fratzscher and Mehl, 2011; Subramanian and Kessler, 2012; Ding, et al., 2012; Funke et
al., 2015). 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., 2015). For example, Maziad and Kang (2012) 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. (2014) 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., 2014; Yuan, 2015). 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., 2007; Fratzscher and Mehl, 2011;
Subramanian and Kessler, 2012; Ding et al., 2012; Funke et al., 2015), 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, 2002; Balke et al., 2013). 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., 2002; Killian
and Taylor, 2003). One notable exception in investigating the predictability of exchange rate is Yu
(2013) who shows that investor sentiment helps account for the forward premium puzzle. Another
study closest to ours is by Craig et al. (2013) 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, 2003; Hirshleifer and Teoh, 2003; Peng and Xiong, 2006; Barber
and Odean 2008; Da et al. 2015), 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., 2014; Yuan, 2015). 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 (2013,
2014); 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., 2002; Killian and Taylor,
2003), and microeconomic factors, such as order flow (Evans and Lyons, 2005), we first provide
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. 2015,
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, 2014; Kim et al., 2014), 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., 2015), 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., 2007; Fratzscher and Mehl, 2011; Subramanian and Kessler,
2012; Ding et al., 2012). 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,
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 2, 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.
2. 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,
ttt ADE 1 , (1)
where tA 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,
1111 )( tttttt ADED , (2)
where 1t is unpredictable and unrelated to
tA .
Let tNtt xxx ,,1 ,..., denote an 1N vector of individual investor attention proxies at
period Ttt ,...,1 . We assume that Nix ti ,...,1, has a factor structure,
tititiiti eEAx ,2,1,0,, , Ni ,...,1 . (3)
wheretA is the investor attention that matters for forecasting CNH-CNY pricing differential, 1,i
is the factor loading that summarizes the sensitivity of sentiment proxy tix , to movements in tA ,
tE is the common approximation error component of all the proxies that is irrelevant to the pricing
spread, and tie , is the idiosyncratic noise associated with i only.
The objective is to impose the above factor structure on the proxies to efficiently estimatetA ,
4 We have free access to weekly data from Google Trend since Jan 2004 till the current, and daily data can be
obtained up to the recent 90 days.
the collective contribution to the true investor attention, and at the same time, to eliminatetE ,
their common approximation error, and tie , from the estimation process. Following Wold (1966,
1975) and Kelly and Pruitt (2013, 2014), we apply the partial least squares (PLS) approach to
extracttA and filter out the irrelevant component
tE , while the commonly used principal
component (PC) method cannot by guaranteed to do so. The key idea is that PLS extracts the
investor sentiment,tA 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 proxyix , we run a time-series
regression of 1, tix on a constant and realized CNH-CNY pricing differentialtD ,
1,0,1, titiiti Dx , Tt ,...,1 . (4)
Instrumented by future pricing differentialtD , the loading
i captures the sensitivity of each
attention proxy 1, tix to the attention index1tA . Since the expected component of
tD is driven
by 1tA , 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 period t , we run a cross-sectional regression of tix , on the
corresponding loading i estimated in Eq. (4),
tiittti Acx ,,ˆ , Ni ,...,1 , (5)
wheretA is the estimated investor attention. That is, in Eq. (5), the first-stage loadings become the
independent variables, and the aligned investor attention tA is the regression slope to be
estimated.
In practice, if the true factor loading i was known, we could consistently estimate tA by
simply running cross-sectional regressions of tix , on i period-by-period. Since
i is unknown,
however, the first-stage regression slopes prove a preliminary estimation of how tix , depends on
tA . In other words, PLS uses time t+1 differential to discipline the dimension reduction to extract
tA relevant for forecasting and discards common and idiosyncratic components such as tE and
tie , that are irrelevant for forecasting.
Mathematically, the 1T vector of aligned investor attention index, Tt AAA ,...,1 , can
be expressed as a one-step linear combination of tix , ,
DJDDJXXJJDDJXXJA TTNTTN
1 , (6)
where X denotes the NT matrix of individual investor attention proxies, TxxX ,...,1 ,
and D denotes the 1T vector of CNH-CNY pricing differentials as 12 ,..., TDDD . The
matrices TTTTT
IJ 1
and NNNNN
IJ 1
is entered in the formula because each
regression is run with a constant. TI is a -T dimensional identity matrix and T is a -T vector
of ones. The weight on each individual measure tix , in tA 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. (2011, 2015), we use the public Search Volume Index (SVI) from Google
Trends ( http://www.google.com/trend/) 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.
Vozlyublennaia (2014) 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, 1992; Phylaktis and Ravazzolo, 2005; Hau and Rey, 2006;
Cumperayot et al., 2006), 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.
(2015), 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 2011 until November 20155. 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. (2011,
2015), we work in logarithms of search terms for ease of exposition and notation. Table 2 displays
some summary statistics of the attention terms over full sample, and the statistics are generally
consistent with literature.
3.2 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 2011 until November 2015 and summary
statistics are reported in Pane A, Table 1. The weekly CNH has a mean of 6.2605 with a standard
deviation of 0.1266 and the weekly CNY has a mean of 6.2584 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 28, 2013. To possibly include large sample we employ weekly attention data from the first week of
March 2013.
0.1208. 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 2011 to November 2015. As presented in Table 1, the weekly carry trade has a mean of
1.8355 and a standard deviation of 0.0208, with high autocorrelation. The monthly carry trade has
a mean of 1.8339 and a standard deviation of 0.0189 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 (2009), Wu and Hu (2009), Zwart et al. (2009), Balke et al. (2013), Ince (2014),
Bekiros (2014), 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 2011 to November 2015 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 4.2 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., 2014; Yuan,
2015). 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:
1,,1 titiiit AD , (7)
where 1tD denotes the pricing differentials between CNH and CNY at period 1t , tiA , denotes
the investor attention that is available at period t , and 1, ti is a zero-mean disturbance term. In line
with Inoue and Kilian (2004), who recommend a one-sided alternative hypothesis to increase the
power of in-sample predictability tests, we test 0 : 0iH against : 0A iH 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 tiA , in Eq.(7) with tX , which takes the formulation:
11 ttt XD , (8)
where tX refers to the macroeconomic index at period t , and the denotations of
1tD and
1, ti are defined the same as those in Eq. (7). Similarly, we test 0:0 H against
0: AH using a heteroscedasticity-consistent t-statistic that corresponds to , the OLS
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., 2003). 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 (2013, 2014) 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
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
1t , 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 tA 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 ofi for the attention indices, over the sample period of March 2011 through
December 2013. Overall, attention indicesiA generate small and positive regression slopes
i of
0.0116, 0.0123, and 0.0064 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 2R of 51.66%,
57.35%, and 16.2% 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., 2002; Killian and Taylor, 2003) 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 (2013, 2014). The regression slope is equal to 0.0104, slightly lower than
stock and macro attention index while higher than self attention index, with a significant -t
statistic at 1% significance level. Also, the2R 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
terms of the magnitude of and 2R 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., 2015).
Panel B presents weekly predictive results for the attention indices. Overall, attention indices
iA generate small and positive regression slopesi of 0.0138, 0.0179, and 0.0137 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
iA yield large 2R of 11.93%, 18.62%, 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 2R 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 4.2.
Summarizing Table 1, the aligned investor attention indices iA 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 of2R , suggesting that investor attention may contain sizable
forecasting information beyond what is contained in the macroeconomic predictors.
4.2 Out-of-sample analysis
Although the in-sample analysis provides efficient parameter estimates and thus more precise
pricing differentials forecast, Goyal and Welch (2008), 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, 2002) and the look-ahead bias
concern of the PLS approach (Kelly and Pruitt, 2013, 2014). Hence, it is of interest to investigate
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 1t . Following Goyal and
Welch (2008), Kelly and Pruitt (2013), we run the out-of-sample analysis by estimating the
predictive regression model recursively based on individual investor attention index,
tttt
m
t AD ;11ˆˆˆ
: , (9)
where t and t are the OLS estimates from regressing 1
11
t
s
m
sD on a constant and an
attention index 1
1;1
t
s
k
stA: . 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, 2006). In finance, Rapach et al. (2010) 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 Tppt ,...,2,1 . Hence, there are pTq
out-of-sample evaluation periods. That is, we have q out-of-sample forecasts: 1
1ˆ
T
pt
m
tD . More
specifically, we use the data covers March 2011 through December 2013 as the initial estimation
period so that the forecast evaluation period spans over January 2014 through November 2015.
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 (2008)
1 211
21
112
)(
)ˆ(-1
T
pt
m
tm
t
T
pt
m
t
m
t
OS
DD
DDR , (10)
where m
tD 1 denotes the historical average benchmark corresponding to the constant expected
pricing differentials model ( 11 t
m
tD ),
t
s
m
s
m
t Dt
D1
1
1. (11)
Goyal and Welch (2008) 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 2
OSR statistic lies in the range 1- , . If 02 OSR , it means that the forecast m
tD 1ˆ outperforms
the historical average m
tD 1 in terms of MSFE.
The second statistic we report is Diebold and Mariano (1995) statistic modified by
McCracken (2007), 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 (2007) 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 (2007). 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 0: 2
0 OSRH
against 0: 2 OSA RH . Clark and West (2007) show that the test has an asymptotically standard
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 2
OSR statistic is negative.
[Insert Table 4(a) Here]
Table 4(a) presents monthly results for the out-of-sample period of January 2014 through
November 2015. The first and second columns report the MSFE and MSFE-adjusted statistics; the
forth column presents -p values for the Clark and West (2007) MSFE-adjusted statistic; the third
column presents 2
OSR 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
2
OSR statistics (42.0116%, 16.3614%, and 44.5094%, 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., 2010). The squared bias
(remainder term) is 0.0203‰ (0.0042‰) 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
2
OSR statistic (-0.2706%). 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. (2002), Killian and Taylor (2003), 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., 2014).
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
improving forecast performance with multiple predictors, following Bates and Granger (1969),
Stock and Watson (2004) , Aiolfi and Timmermann (2006), Rapach et al. (2010), 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 2
OSR values are sizable and all significant at 1% level of significance using
the MSFE-adjusted 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 2
OSR value with significance, 48.5608%, 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, 2008). 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 2
OSR value of 42.8586%, while in Panel C the average
2
OSR value drops to 38.4941%, 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 2
OSR reaching
51.3478%. 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
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, 2007).
[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. (2014). 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 2014 through November 2015.
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 2
OSR statistics reaching
38.3716%, 25.9971%, and 10.6620% 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
2
OSR 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 2
OSR value
reaching 37.2768%, which is in accord with the literature that simple average scheme usually
exhibits the best forecast performance than other combination models (Rapach et al., 2010). 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 iA 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
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 tiA , . Following Kandel and Stambaugh (1996),
Campbell and Thompson (2008) and Ferreira and Santa-Clara (2001), 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 period t , the investor optimally allocates
2
1
1
ˆ
ˆ1
t
tt
Dw
, (12)
of the portfolio CNH-CNY pricing differential during period 1t ,where is the risk aversion
coefficient, 1ˆtD is the out-of-sample forecast of the CNH-CNY pricing differential, and
2
1t is
the variance forecast. The investor then allocates tw-1 of the portfolio to risk-free bills, and the
1t realized portfolio return is
f
ttt
p
t RDwR 111ˆ
, (13)
where f
tR 1 is the gross risk-free return. Following Campbell and Thompson (2008), 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 tw 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
2ˆ5.0ˆpppCER , (14)
where p and 2ˆp are the ample mean and variance, respectively, for the investor’s portfolio over
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, 2009). 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 (2009), we use the approach of
Jobson and Korkie (1981) corrected by Memmel (2003) 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 4.7452% for January 2014 through November
2015. 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 2.7252%, 0.5786%, and 2.5652%, respectively. As for the macroeconomic index, while it also
generates a positive CER gain of 1.6094%, 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 1.1152. The macroeconomic index
also delivers a Sharpe ratio of 0.7746 that is higher than that of historical average. The average
turnover is 11.6397% 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
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 2.5508%. The
macroeconomic index yields a net-of-transaction-cost CER of 0.2051% 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 295 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 (3.4602%) or diffusion index model (3.0674%). While after
accounting for transaction costs, the simple average model and discount MSFE model generate
higher gains of 1.7612% and1.7418% than other three models, which are 0.6144%, 0.6146, and
1.6311%, 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, 2015). 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 11.3281% for December 2013
to November 2015. 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 2
OSR statistics in Table 3. The three attention indices produce
hither weekly Sharpe ratios than that of the historical average, with macro attention generating the
highest ratio of 0.7419. The average turnover is 2.3084% for the historical average. Although the
macro attention portfolio turns over roughly 2.5 times more often than the historical average
portfolio, it still improves the net-of-transactions-costs by 922 basis points. Portfolios based on
stock attention self attention terms also provide sizable CER gains of 8.0948% and 7.1096%, with
the Sharpe ratios of 0.6556 and 0.6065, 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 8.0599% and 6.2023%, 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, 2007; Lusting, et al.,
2011). 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, 2013). 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, 2002). As demonstrated
by many studies, carry trade is part of the explanation of foreign exchange rate puzzles
(Brunnermeier et al., 2009). 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.
[Insert Table 5 Here]
Table 5 reports the results of out-of-sample predictive performance of investor attention
indices on CNY carry trades. Similar to section 4.2, we first run the out-of-sample predictive
regression model recursively based on individual investor attention indices, and then employ the
combination forecast models. This exercise is taken twice, based on monthly and weekly data.
Again, we compute three statistics for evaluation, namely2
OSR , MSFE, and MSFE-adjusted
statistics in respective. The monthly results are presented in the second through the fifth columns.
Panel A of Table 5 reports out-of-sample results for bivariate predictive regression forecasts based
on individual attention indices. Only macro attention index provides positive2
OSR statistics
(1.8524%); the other two indices thus fail to outperform the historical average benchmark in terms
of 2
OSR (-17.5652% and -1.5741%) . In accord with the2
OSR statistics, macro attention index
delivers MSFE less than the historical average MSFE while stock and self attention indices
generate MSFEs greater than the historical average MSFE. Nevertheless, the MSFEs for these
three predictors are insignificant at a conventional level according to the MSFE-adjusted statistics
and corresponding P -values. Reminiscent of Goyal and Welch (2008), individual investor
attention indices displays poor monthly out-of-sample predictive ability in Table 5, Panel A. Panel
B, reports the monthly results of combination forecasts. Not surprisingly, all combination models
deliver negative 2
OSR statistics, with the lowest approaching -23.7839% by the Kitchen sink
model, and thus fail to outperform the historical average benchmark in terms of MSFE. Also, their
MSFEs are not significant at a conventional level according to MSFE-adjusted statistics. Overall,
investor attention indices appear to have limited predictive power over monthly CNY carry trades.
The sixth through ninth columns, in Table 5, report the weekly results of out-of-sample
forecast of CNY carry trades. All2
OSR statistics are positive in the eighth column of Panel A; each
of the attention indices thus delivers a lower MSFE than the historical average benchmark. Three
2
OSR statistics exceed 10%, with the highest reaching 67.7609%, and MSFEs for all individual
attention indices are significantly less than the historical average MSFE based on the
MSFE-adjusted statistics. Matching the individual weekly results, combination models also
generate out-of-sample forecasts better than the historical average forecasts. As presented in Panel
B, all combination models provide sizable 2
OSR statistics, with four of them exceeding 50%, and
consequently each delivers a significantly lower MSFE than the benchmark at conventional level.
Overall, investor attention indices appear to have economically and statistically significant
predictability of CNY carry trade at weekly frequency.
5. Conclusion
We investigate the predict power of investor attention on the CNH-CNY pricing differential
in the period of March 2011 through November 2015, by utilizing our aligned attention indices
constructed by applying the partial least squares (PLS) approach following Wold (1966, 1975) and
Kelly and Pruitt (2013, 2014). For interest of comparison, we also compare the forecast
performance of investor attention indices to that of macroeconomic index. Additionally, we
compute the economic value of investor attention through asset allocation. At last, we explore the
forecast ability of investor attention on CNY carry trade.
Our results show that the aligned investor attention indices display strong marginal in-sample
forecast power for the CNH-CNY pricing differentials at both monthly and weekly frequencies,
clearly on par with that of macroeconomic index. Consistent with in-sample results, individual
investor attention indices also exhibits statistically and economically significant out-of-sample
predictive power on both monthly and weekly CNH-CNY pricing spread. In addition, the
employment of combination forecasts effectively improves the out-of-sample forecast of
individual attention indices. In comparison, macroeconomic index has poor out-of-sample
predictability for the monthly pricing spread, and the inclusion of macroeconomic index in
combination forecast does not strengthen the performance. Furthermore, the investor attention
could generate substantial economic values in asset allocation at both monthly and weekly
frequencies. Finally, we find that investor attention indices provide economically and statistically
significant out-of-sample forecast of the CNY carry trade on weekly basis. In economic sense,
these empirical findings directly and indirectly indicate that investor attention contains
information that drives the persistent pricing differential between CNH and CNY, and investor
attention has much stronger influence, especially out-of-sample forecast power, than
macroeconomic variables on the CNH and CNY exchange rates.
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Figure 1 CNH and CNY spot exchange rate differential
Note: The spot exchange rate data for CNH (at Hong Kong SAR) and CNY span March 2011 until November 2015 (via Datastream). Rhs: in basis points. Lhs:
vis-à-vis USD.
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Rhs:Differential
Lhs:CNH
Lhs:CNY
Table 1 Summary statistics of macro variables
Mean Std. dev. Min Max Skewness Kurtosis Jarque-Bera Auto-correlation
Panel A: weekly data
CNY 6.2584 0.1208 6.0589 6.5767 0.5969 2.6900 12.47*** 0.9723
CNH 6.2605 0.1266 6.0188 6.5650 0.4085 2.4682 10.14*** 0.9677
CT_weekly 1.8355 0.0208 1.8000 1.8820 0.3449 2.5719 6.99*** 0.9729
Panel B: monthly data
IR 1.5167 0.2182 1.1314 1.9459 0.0202 2.2508 2.21 -0.3732
M1 4.8465 0.0946 4.6839 4.7158 -0.4244 1.7543 13.74*** 0.1376
M3 5.0159 0.1849 4.6895 5.3171 0.3419 -0.2009 9.74*** 0.0696
CPI 4.7040 0.0312 4.6405 4.7501 -0.2611 1.8224 11.37*** 0.1112
CT_monthly 1.8339 0.0189 1.8088 1.8796 0.5590 2.3107 4.80*** 0.8577
Note: CNY (CNH) refers to the spot exchange rate of onshore (offshore) renminbi, IR refers to 3-month interest rate, M1 (M3) refers to the index of narrow (broad)
money supply, CT_weekly (CT_monthly) refers to weekly (monthly) carry trade payoffs of Chinese yuan. The spread is calculated as the log difference of CNY and
CNH. Eighth column computes the chi-squared value for Jarque-Bera normality test and *** indicates the 1% level of significance. All macro variables are calculated
in log form. The sample period is from March, 2011 to November, 2015.
Table 2 Attention terms from the full sample
Mean Std. dev. Min Max Skewness Kurtosis Jarque-Bera Auto-correlation
Panel A: self attention
CNH 3.8138 0.1543 3.3673 4.2341 0.2745 2.9627 3.20 0.6642
CNY 3.3135 0.2906 2.7726 4.6042 1.0277 5.0571 37.16*** 0.8849
Panel B: macro attention
Exchange rate 2.7398 0.1524 2.3026 3.2958 0.5432 3.7542 13.52*** 0.8890
CPI 1.1471 0.2211 0.6931 2.0794 0.0855 4.5209 10.01*** 0.5980
PPI 2.5020 0.2657 1.7918 3.1780 0.1527 3.4476 3.16 0.8829
M1 3.5629 0.0825 3.4012 3.8712 0.6259 3.9238 16.98*** 0.5450
M2 3.8885 0.3743 3.4012 4.6052 0.6816 1.6704 15.45*** 0.9863
M3 4.0303 0.0743 3.8712 4.3041 0.6299 2.9358 12.74*** 0.8668
Interest Rate 3.6275 0.1185 3.1781 4.0253 -0.4355 5.6813 22.40*** 0.7008
PPP 3.5926 0.0936 3.2188 3.9703 0.3857 5.9868 22.90*** 0.6626
Financial stress 3.0249 0.2681 2.3029 4.6109 -0.1730 2.6435 2.75 0.3295
GLI 4.4098 0.7846 4.0943 4.6051 -1.0368 4.9751 37.00*** 0.7869
VIX 1.9128 0.1901 1.6094 3.0445 0.0361 1.5862 24.65*** 0.6430
ASX 3.7749 0.1461 3.2958 4.4659 0.2133 0.7073 29.72*** 0.8006
SPASX 3.1522 0.3257 2.1972 4.6052 0.6212 5.1009 23.84*** 0.7001
Panel C: stock attention
Gold prices 1.0869 0.3759 0.6931 2.5649 0.9491 4.1356 28.88*** 0.8314
Gold price 2.9575 0.2676 2.5649 4.6052 1.9527 9.6193 26.64*** 0.7690
Depression 1.4216 0.1461 1.0986 1.7918 -0.4108 3.2800 7.43*** 0.6385
Gold 4.0439 0.0958 3.8918 4.6052 2.1794 11.2283 21.16*** 0.6596
Economy 1.6593 0.1455 1.0986 1.9459 -0.9544 3.7523 26.74*** 0.7251
Frugal 0.5185 0.3016 0.0000 0.6931 -1.1422 2.3047 37.89*** 0.5512
GDP 2.2014 0.1525 1.6094 2.5649 -0.9276 4.3605 29.53*** 0.7464
Bankruptcy 2.0778 0.2832 1.3863 2.6391 0.1426 1.7609 55.11*** 0.8902
Unemployment 0.7220 0.1368 0.3266 0.9704 -0.3544 1.9928 35.81*** 0.8806
Bankrupt 3.0113 0.2512 2.4849 4.6052 1.3217 9.2517 65.77*** 0.7198
Car donate 0.6495 0.1984 0.0000 1.0986 -2.4311 9.5862 64.20*** 0.1984
Expense 0.7070 0.1450 0.0000 1.0986 -1.0037 15.3015 69.58*** 0.4352
Donation 1.5229 0.1397 1.3863 2.3979 1.4985 9.8726 73.47*** 0.5508
Default 3.6530 0.0794 3.4657 3.9703 0.8429 4.4669 27.32*** 0.8048
Benefits 4.3988 0.1013 4.0604 4.6052 -0.4450 3.0432 7.53*** 0.8239
Unemployed 0.4029 0.3427 0.0000 0.6931 -0.3296 1.1086 24.60*** 0.7201
Note: Table 2 presents the summary statistics of attention terms, derived from Goolgle Search Volume Index and computed in log form. Eighth column computes the
chi-squared value for Jarque-Bera normality test and *** indicates the 1% level of significance. The sample period is from March, 2011 to November, 2015.
Table 3 In-sample Predictive Regression Estimation Results
Predictor Slope coefficient t statistic %2R
Panel A: monthly estimates
Macro attention 0.0116*** 5.7556 51.66
Stock attention 0.0123*** 6.4562 57.35
Self attention 0.0064*** 2.4481 16.20
Macro variables 0.0104*** 4.8937 43.58
Panel B: weekly estimates
Macro attention 0.0138*** 4.4022 11.93
Stock attention 0.0179*** 5.7207 18.62
Self attention 0.0137*** 4.3064 11.48
Note: Pale A reports estimates from the OLS regressions of monthly differentials on four indices
generated from macro attention terms, stock attention terms, self attention terms, and macro
variables, respectively. Pale B reports estimates from the OLS regressions of weekly spread on
three attention indices. In-sample period is from March, 2011 to December, 2013. *** indicates the
1% level of significance.
Table 4(a) Evaluations for out-of-sample forecast of CNH-CNY differentials (monthly)
MSFE (‰) adjusted
MSFE
-
(%)2
osR
P
-value
)(ann
(%)
Sharpe
ratio
Average
turnover
(%)
)(ann
cost=50bps(%)
2)(e
(‰)
2)(eVar
(‰)
HA 0.0245 4.7452 0.5580 11.6397 4.0251 0.0203 0.0042
Panel A: bivariate predictive regressions
Macro attention 0.0142 2.4030 42.0116 0.0081 2.7252 1.1152 2.9911 1.2708 0.0047 0.0095
Stock attention 0.0205 1.8622 16.3614 0.0313 0.5786 0.6645 1.0021 0.5723 0.0152 0.0053
Self attention 0.0136 3.1767 44.5094 0.0007 2.5652 1.0508 1.0091 2.5508 0.0083 0.0054
Macro variables 0.0246 0.1855 -0.2706 0.4264 1.6094 0.7746 2.9810 0.2051 0.0194 0.0052
Panel B: attention indices combinations
Kitchen sink 0.0126 3.1206 48.5608 0.0009 3.7611 1.2780 2.9842 2.2951 0.0007 0.0119
SIC 0.0141 2.7180 42.3235 0.0033 3.7661 1.2783 2.9948 2.2994 0.0013 0.0128
POOL-AVG 0.0147 2.6304 40.1420 0.0043 2.5652 1.0508 1.0091 2.5508 0.0089 0.0058
POOL-DMSFE 0.0142 2.5948 41.9447 0.0047 2.5050 1.0511 1.0062 2.4885 0.0079 0.0063
Diffusion index 0.0144 2.8094 41.3218 0.0025 2.0298 0.9126 2.9857 0.6058 0.0081 0.0063
Panel C: all indices combinations
Kitchen sink 0.0156 2.7276 36.1917 0.0032 3.4601 1.2507 4.9665 0.6144 0.0004 0.0152
SIC 0.0163 2.4676 33.6179 0.0068 3.4602 1.2507 4.9666 0.6146 0.0019 0.0144
POOL-AVG 0.0163 2.6255 33.7271 0.0043 1.7711 0.9016 1.0063 1.7612 0.0111 0.0051
POOL-DMSFE 0.0153 2.5158 37.5859 0.0059 1.7710 0.9022 1.0034 1.7418 0.0094 0.0059
Diffusion index 0.0119 2.4569 51.3478 0.0070 3.0674 1.0478 2.9894 1.6311 0.0048 0.0071
Note: Panel A reports monthly forecast results of four indices generated from macro attention terms, stock attention terms, self attention terms, and macro variables,
respectively. Panel B reports monthly combination forecast results of three attention indices and Panel C reports monthly combination forecast results of all four
indices. Kitchen sink, SIC, POOL-AVG, POOL-DMSFE, and Diffusion index refer to five combination methods, namely, kitchen sink forecast, combination forecast
based on Bayesian model (Cremers, 2002), simple combination forecast, discount MSFE combination forecast (Rapach et al., 2010), and diffusion indices forecast
(Ludvigson and Ng, 2007; Neely et al., 2012). First row reports the results of historical average as benchmark. Out-of-sample period is from January, 2014 to
November, 2015.
Table 4(b) Evaluations for out-of-sample forecast of CNH-CNY differentials (weekly)
MSFE
(‰) adjusted
MSFE
-
(%)2
osR
P
-value
)(ann
(%)
Sharpe
Ratio
Average
Turnover
(%)
)(ann
cost=50bps(%)
2)(e
(‰)
2)(eVar (‰)
HA 0.0302 11.3281 0.2830 2.3084 10.8880 0.0166 0.0135
Panel A: bivariate predictive regressions
Macro attention 0.0186 3.2686 38.3716 0.0005 11.1133 0.7419 5.1290 9.2266 0.0057 0.0129
Stock attention 0.0223 4.4670 25.9971 0.0000 8.0948 0.6556 1.0490 8.0599 0.0088 0.0135
Self attention 0.0270 2.8400 10.6620 0.0023 7.1096 0.6065 2.9810 6.2023 0.0126 0.0144
Panel B: attention indices combinations
Kitchen sink 0.0206 3.0739 31.6410 0.0011 10.1803 0.7000 4.9367 8.3804 0.0062 0.0145
SIC 0.0189 3.1970 37.2768 0.0007 11.1135 0.7419 5.1288 9.2446 0.0059 0.0131
POOL-AVG 0.0216 3.6250 28.5332 0.0001 9.3167 0.6616 1.0561 9.2782 0.0088 0.0128
POOL-DMSFE 0.0202 3.3068 32.9828 0.0005 9.3415 0.6632 1.0558 9.3045 0.0080 0.0123
Diffusion index 0.0192 3.4904 36.4236 0.0002 10.8231 0.7243 1.0646 10.7799 0.0059 0.0133
Note: Panel A reports weekly forecast results of three indices generated from macro attention terms, stock attention terms, self attention terms, respectively. Panel B
reports weekly combination forecast results of three attention indices. Kitchen sink, SIC, POOL-AVG, POOL-DMSFE, and Diffusion index refer to five combination
methods, namely, kitchen sink forecast, combination forecast based on Bayesian model (Cremers, 2002), simple combination forecast, discount MSFE combination
forecast (Rapach et al., 2010), and diffusion indices forecast (Ludvigson and Ng, 2007; Neely et al., 2012). First row reports the results of historical average as
benchmark. Out-of-sample period is from January, 2014 to November, 2015.
Table 5 Evaluations for out-of-sample forecast of carry trade
Monthly results Weekly results
MSFE
(‰) adjustedMSFE - (%)2
osR P -value MSFE
(‰) adjustedMSFE - (%)2
osR P -value
Historical Average 0.1927 0.0964
Panel A: bivariate predictive regressions
Macro attention 0.1892 0.7955 1.8524 0.2131 0.0854 5.5084 11.3300 0.0000
Stock attention 0.2266 -0.5816 -17.5652 0.7196 0.0714 4.6885 25.8536 0.0000
Self attention 0.1958 -1.1694 -1.5741 0.8789 0.0311 3.9161 67.7069 0.0000
Panel B: attention indices combinations
Kitchen sink 0.2386 -0.4767 -23.7839 0.6832 0.0310 4.0582 67.8270 0.0000
SIC 0.2296 -0.4661 -19.0993 0.6794 0.0311 4.0524 67.7240 0.0000
POOL-AVG 0.2010 -0.5896 -4.2709 0.7223 0.0491 4.4316 49.0868 0.0000
POOL-DMSFE 0.2019 -0.6626 -4.7319 0.7462 0.0396 3.9451 58.8782 0.0000
Diffusion index 0.2054 -0.9309 -6.5895 0.8241 0.0315 4.0993 67.2752 0.0000
Note: Panel A reports monthly (weekly) forecast results of three indices generated from macro attention terms, stock attention terms, self attention terms, respectively.
Panel B reports monthly (weekly) combination forecast results of three attention indices. Kitchen sink, SIC, POOL-AVG, POOL-DMSFE, and Diffusion index refer
to five combination methods, namely, kitchen sink forecast, combination forecast based on Bayesian model (Cremers, 2002), simple combination forecast, discount
MSFE combination forecast (Rapach et al., 2010), and diffusion indices forecast (Ludvigson and Ng, 2007; Neely et al., 2012). First row reports the results of
historical average as benchmark. Out-of-sample period is from January, 2014 to November, 2015.
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