Monetary Announcement Premium in China

Rui Guo, Dun Jia, Xi Sun∗

This Draft: April 14, 2019

Abstract

By studying China, this paper examines the stock market returns in an environmentwhen the dates of information supply through public announcements are not pre-fixed.We document that excess returns on Chinese equity market accumulate for three daysbefore its central bank PBOC releases data of monetary aggregates, which may beannounced either early or late in a month. This pre-announcement premium appearssizable, has a longer duration than that of the pre-FOMC premium in the U.S., and isnot driven by potential data leakages or expectation changes. We then present a modelto account for this premium by featuring investors’ information demand given centralbank’s announcements are not pre-scheduled. As investors with limited attention findit optimal to learn about monetary data prior to announcement, increasingly devotedattention drives down market uncertainty and boosts up equity prices. We show theinstitutional details of China render the exact data structure for us to test the keymodel mechanism of uncertainty reduction, which helps rationalize the empirics foundboth for China and the U.S.

JEL codes: E44, E52, G12, G14

Key Words: Equity Premium, Monetary Policy, Announcement, Macro-finance

∗Guo: Hanqing Advanced Institute of Economics and Finance, Renmin University of China. Email:rui.guo@ruc.edu.cn. Jia (Corresponding Author): Hanqing Advanced Institute of Economics and Finance,Renmin University of China. Email: dun.jia@ruc.edu.cn. Sun: Hanqing Advanced Institute of Economicsand Finance, Renmin University of China. Email: xi.sun@ruc.edu.cn. We benefit a lot from discussionswith Hengjie Ai, Tao Zha, Jun Qian ”QJ”, Christopher Polk, Xiaoji Lin, and Shiyang Huang. We thankcomments from seminar participants at Tsinghua University PBC School of Finance, Fudan Fanhai Schoolof Finance, University of Hong Kong, Hong Kong Baptist University. All errors are ours.

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1 Introduction

In this paper, we examine why stock market reacts to the anticipated central bank’s

announcement regarding its monetary policy stance ex-ante. In particular, we study the

equity returns in an environment when the dates of information supply through public an-

nouncements are not pre-fixed. Lucca and Moench (2015) documents a robust pre-drift of

U.S. stock market returns prior to the pre-scheduled dates and time of FOMC statement

releases, and labels this as puzzle for absence of data-consistent theories.1 We demonstrate

that by evaluating the implications of having “randomness” in announcement scheduling, it

helps clarify the mechanism behind equity market’s pre-announcement responses.

Our exploration of the research question is framed within Chinese context. Monetary

aggregates data are published every month by People’s Bank of China (PBOC), the central

bank of China, in a “quasi-scheduled” fashion with some randomness in announcement tim-

ing. That is, entering a month, the market expects monetary statistics will be released on

a day of that month with probability one, but the exact date and time of announcement is

largely unknown. We first document a sizable pre-announcement premium of Chinese equity

market before PBOC’s announcement releases of monetary data, which more than triples the

magnitude of total equity premium in China. Qualitatively, the pre-announcement premium

of China and that of U.S. share similar characteristic features.2 However, quantitatively, we

find the accumulation of excess returns on Chinese equity market kicks off three days before

announcements and exhibits a much longer duration than that of its U.S. counterpart for a

few hours.

We then present a model to study the pre-announcement premium by featuring investors’

information demand decision in spirit of Sims (2003) prior to central bank’s announcements.

1Federal Reserve Board (FRB) pre-schedules the dates of eight FOMC meetings of a year, and informs themarket of those dates ahead of time. On average, eight FOMC statements are issued per year right after theFOMC meetings. An FOMC statement is issued around 2:15 PM EST on the pre-scheduled FOMC meetingday. Though, during unusual times, emergent FOMC meetings could take place and extra statements andannouncements were sporadically issued, for example, irregular issuance of FOMC statements in years of2007-2008 during the financial crisis.

2We put the PBOC’s announcements of monetary aggregates data and the U.S. FOMC announcementsthat publish the Federal Funds rate targets, both as important measures of monetary policy stance, ascomparable central bank’s announcements. The growth rate of M2 is one of the most critical monetarypolicy instruments in China. In mid of interest rate liberalization process in 2010s, various interest ratesincluding the overnight repo rates, short-term government yields, and the Shanghai Interbank Offered Rate(Shibor) rates have developed their importance when gauging the tightness of Chinese monetary policypractice. See Chen et al. (2016) and Liu et al. (2017). However, announcements of interest rate adjustmentsfall beyond the scope of our research focus, which is about the “quasi-scheduled” and perfectly pre-scheduledannouncements. For example, benchmark rates of loans and savings in China are changed and made publicquite unexpectedly. Hence investors can form regular anticipations for announcements of monetary datarather than those of unexpected interest rate adjustments.

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Importantly, our model builds upon an environment such that an announcement may arrive

early or late in a month. In the model, investors are not able to draw very informative signals

about the data to be released when it’s too early to do so. Over time, investors’ forecast

uncertainty about money growth accumulates, which increases the opportunity cost of not

paying attention. Investors would start paying attention to learning about monetary data

only when information demand starts bringing value. That is, when uncertainty has been

excessively accumulated and very informative signals can be drawn. Therefore, the timeliness

of announcement arrival shifts the size of uncertainty reduction driven by investors’ attention

allocation. Our model highlights the importance of having endogenous information demand

to account for the pre-announcement premium.

Our model finds the following. First, we show that regardless of announcement schedul-

ing, if investors with limited attention find it optimal to learn about monetary data prior

to announcement, attentive learning reduces market uncertainty about money growth and

boosts up equity prices. Second, with quasi-scheduled announcements, investors may find

desirable to increasingly devote more attention for a few days until announcement, which

leads to more days of uncertainty reduction and persistent accumulation of excess returns.

Third, market accumulates greater uncertainty in case of more postponed announcements,

which triggers greater intensive learning and larger uncertainty reduction.

We highlight the importance of exploiting the uniqueness of Chinese data because the

institutional details of China render us the exact data structure to test the model. Our

model implications can be very useful for rationalizing empirics for both China and the U.S.

First, we show that uncertainty measures constructed from survey forecasts and stock return

volatility both shrink as it gets closer to PBOC’s announcement of monetary aggregates

data. Also, it takes about the same length of three days for reduction of uncertainty and

accumulation of excess returns to reach their respective stops. Second, we provide direct

evidence that across announcement events, the size of uncertainty reduction is correlated

with the magnitude of pre-announcement premium. Finally, by exploiting variations in

the timeliness of announcement arrivals across events, we are able to show that the pre-

announcement premium in China is mainly driven by the delayed releases of monetary data.

We thus conclude that the pre-announcement uncertainty reduction is causal for gener-

ating ex-ante reactions of stock markets. To shed lights on the U.S. pre-FOMC premium,

our model suggests that only when it gets very close to the pre-scheduled FOMC day, in-

vestors see the possibilities for policy changes. This raises uncertainty and triggers attentive

learning, which leads to a quick reduction of uncertainty and pre-announcement premium

few hours before FOMC statement releases. As for China, the absence of financial market

sophistication gives room to cycles of uncertainty accumulation between PBOC’s announce-

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ments. With announcements not pre-scheduled, it takes mores days for investors to devote

attention, and equity prices keep climbing before announcements.

Important to note that this paper distinguishes itself from the large literature that aims

to identify the impacts of monetary policy shocks on equity market and other dimensions

of the economy.3 Rather, we disentangle the effects of anticipation about monetary policy

stance on stock market returns prior to announcement regardless of the realized nature of

policy shocks. Our results show that our documented pre-announcement premium in China

is not driven by potential data leakages or expectation changes. With this respect, this paper

contributes to the literature by theorizing the information channel through which the stock

market can be affected by uncertainty about monetary policy changes ahead of time.

Related Literature. This paper is related to three strands of literature. First, this pa-

per aligns itself with the stream of works that explores the asset pricing implications of macro

announcements. Savor and Wilson (2013) find that the U.S. equity market exhibits larger

excess returns and Sharpe ratios on days of data releases for inflation, unemployment and

various interest rates. By studying the U.S. stock markets, Lucca and Moench (2015) detect

the pre-announcement premium in response to FOMC statements. They show that the U.S.

stock market kicks off its pre-drift starting from the PM until hours before the FOMC state-

ment releases on the FOMC day. Ai and Bansal (2018) provides a theory that under certain

regularlity conditions, a range of non-expected utility functions with probability distortions

can deliver positive premium on announcement days. Wachter and Zhu (2018) accounts for

the announcement premium using a model that investors learn about disaster probabilities.

Balduzzi and Moneta (2017), Altavilla et al. (2017), and Philippe et al. (2017) locate the

announcement premium in the treasury markets, bond future markets, and foreign exchange

markets respectively. Bernile et al. (2016) and Kurov et al. (2019) explore the high frequency

trading data and find that market moves in the right direction with the data to-be-released

in a few minutes before announcements. They present evidence that various sources of infor-

mation including data leakages, embargoed news delivery, and private information may all

lead to intensive trading prior to announcements. Our paper is the first one that provides

empirical evidence on Chinese equity market’s reactions to a range of macro announcements

of important data releases, and finds that we can study the pre-announcement premium

found for both China and the U.S. within the same analytic framework. Importantly, while

the exiting literature largely takes the pre-scheduled announcements as given, we examine

the asset pricing implications given randomness in announcement scheduling. In addition, we

3For example, to name just a few, Bernanke and Kuttner (2005) considers shocks to the U.S. monetarypolicy on asset prices while Romer and Romer (2004) identifies the non-neutrality of monetary policy forthe macroeconomy.

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carefully ruled out data leakages as the main driver for Chinese pre-announcement premium.

Second, at the firm level, a rich literature dated back to Beaver (1968) has documented

higher excess returns on the announcement day of corporate earnings. In addition, both the

pre-announcement and post-announcement drifts of equity returns are identified around the

day of corporate earning announcements (Barber et al., 2013; Bernard and Thomas, 1989;

Frazzini, 2006). This paper applies a similar event study methodology to uncover reactions

of the aggregate stock market to announcements at the macro level.

Third, this paper is also closely related to the literature that explores implications for

asset pricing and macroeconomic policy given frictions of imperfect information and un-

certainty. Following Sims (2003), Peng and Xiong (2006) and Kacperczyk et al. (2016),

investors with limited attention can endogenously choose whether or not and how much

attention should be paid to learn about a variable of interest due to the fact that informa-

tion processing is costly. In line with Coibion and Gorodnichenko (2015), we also highlight

the importance that information updating among rational agents through attentive learning

has non-negligible impacts. Also, in our paper, uncertainty reduction a few days prior to

announcement is the key to generate pre-announcement premium. We provide additional

asset pricing evidence suggesting that uncertainty variations are important forces that could

shift the equilibrium in line with Bloom (2009, 2014). However, to examine higher fre-

quency uncertainty changes within the announcement window, our measures of uncertainty

are proxied by dispersion of forecast errors and the stock market volatility aggregated from

higher frequency return blocks given no option-based implied volatility index nor text-based

uncertainty proxies as in Baker et al. (2016) is readily available up to daily frequency.

The rest of the paper is structured as follows. We discuss the selection of announcement

events and data sources in Section 2. Section 3 presents the main empirical findings regarding

the equity premium associated with monetary announcements. Section 4 presents a model

that marks uncertainty reduction as the key driver of pre-announcement premium. Section

5 summarizes results of a series of empirical tests of the model predictions and provides

evidence consistent with our model. Section 6 concludes. In Appendix, we further give out

technical details and additional empirical results of a wide range of explorations.

2 Data

In this section, we summarize the data used for identifying the response of China’s eq-

uity market to announcements regularly published by PBOC. In particular, we study and

compare the institutional details of PBOC’s announcements relative to those of a range of

macroeconomic announcements made by other statistical agencies of China and the FOMC

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statements issued by the U.S. Federal Reserve. By announcements, we refer to those public

news which specifically deliver the up-to-date statistics of a macroeconomic variable with reg-

ular publication frequency.4 Eventually, we are also able to examine whether China’s equity

market responds to other macro announcements or the U.S. FOMC statement release.

2.1 Announcement Categories

We first select a range of macroeconomic variables that have data regularly published by

different agencies through public announcements. These macroeconomic statistics, by their

data coverage, can be broadly categorized into four groups: monetary-related statistics,

trade data, real-sector productivity measures, and aggregate price indices. The associated

announcements of these data are grouped correspondingly. The U.S. FOMC statement

issuance, labelled as FOMC announcements, belongs to the fifth category. In the following,

we discuss details of our selected announcements that span the five categories.

1. Monetary-related Statistics Announcements. We are primarily interested in

the announcements made by PBOC for publishing China’s monetary aggregates da-

ta, which are indicative of the stance of China’s monetary policy and overall credit

condition. Data on the monetary aggregates including levels and growths of M0, M1,

M2 are all published by PBOC every month on its website in a single announcement

statement. Besides, other monetary and financial statistics including the outstanding

balance of total loans and deposits, monthly interest rate averages, and balance of in-

terbank loan are all published at the same time in the statement.5 To avoid the abuse

of terminology, we simply label the announcements that publish the most updated

monetary aggregates data and other credit statistics as M2 announcements. 6

4Closely related macro data managed by the same statistical agency in China are routinely published atthe same time through a single announcement. In addition, those news that are ruled out by our researchfocus, for example, are those general discussions or comments on Chinese economy and the financial marketsmade by key figures who are affiliated with the statistical agencies such as government/party officials, staffand scholars etc.

5Since November 2012, these statistics are published around the same time as the announcement ofbalance of Total Social Financing (TSF), even though TSF data is made public via a separate statementissue. TSF data could be online few seconds or hours, before or after the monetary aggregates data releases.

6We also note the quarterly publication of China’s Monetary Policy Report (MPR) by PBOC. Techni-cally, MPR does not square well with our research focus, i.e. announcements that release updated statis-tics. Rather, MPR is a comprehensive collection of PBOC’s assessments of the soundness of credit market,macroeconomic and financial stability, and the necessity for PBOC to further fine tune the monetary policy.Therefore, MPR is not directly comparable to other major central banks’ policy statements that specificallypublish policy instrument targets or articulate the decision of monetary policy moves, i.e., the FOMC state-ment by the U.S. Federal Reserve or European Central Bank (ECB)’s Monetary Policy Accounts. However,for completeness, we examined China’s stock market reactions to these Monetary Policy Report announce-ments. Results are collected in Section B.5 of Appendix and we find somewhat similar pre-announcement

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2. Trade Data Announcements. Statistics regarding total imports and exports of

China are published monthly by the General Administration of Customs of the People’s

Republic of China (GACC) via a single statement on its website. We label these data

release news as TRD announcements.

3. Real-sector Productivity Announcements. We also look into four important da-

ta series measuring the functioning of the production side of Chinese economy: fixed

assets investment excluding rural households (FAI), value added of the industrial en-

terprises above the designated size (VAI), profits of the industrial enterprises above

the designated size (INP), and the manufacturing purchasing managers index (PMI).

Every month, all these statistics are published by the National Bureau of Statistics of

China (NBS).7

4. Aggregate Price Indices Announcements. NBS announcements of three other

statistics of aggregate prices are also considered: the consumer price index along with

the producer price index released together (CPI), and the sales price index of residen-

tial real estate in 70 large and medium-sized cities (RST).8

5. FOMC Announcements. FOMC meetings that discuss the relevance of U.S. mon-

etary policy changes are held regularly eight times a year. Each FOMC statement is

issued right after each meeting.9 It can be very interesting to see if China’s market is

responsive to important announcements originated from other country.

In sum, we examine nine selected announcements with each releasing at least one im-

portant statistics.10 Note that most of the selected Chinese announcements are monthly.

However, an announcement made in month may not publish real-time data point but some

statistics spanning over the previous month. 11

responses.7FAI and VAI numbers are routinely published around the same time of a given announcement day

through separate statements on NBS’s website. Though in separate statements as well, additional importantdata including retail sales of consumer goods, development and sales statistics of national real estate, energyproduction and the private fixed asset investment are all published on the same day about the same time.Quarterly GDP growth rate, however, is announced together with all these aforementioned statistics everythree months. INP numbers are often times released a few days later for that month.

8Since 2009, CPI and PPI data are released at the same time in the same public statement. CPI werepreceded by PPI data releases for one day before 2009.

9Under rare circumstances, more than eight FOMC statements a year can be issued. For example, duringrecession years of 2001, 2007 and 2008, the FOMC Committee had issued more than one statement in agiven month of critical times.

10Table A.1 in the Appendix gives a summary of all these selected announcements with their publishingagencies and the statistics published at the same time in the same statement online.

11Exceptions are that for certain statistics of some unusual periods, the monthly statistics can be publishedby the end of that month. For example, Manufacturing Purchasing Managers Index (PMI) numbers of China

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2.2 Data Sources

Our sample ranges from January, 2010 to June, 2017. We made this choice for three

reasons. First, in the post-2010 period, the routine of publishing up-to-date macro data has

been formalized. Statistics are promptly published on data agency’s website. Such internet

information vendor enables us with good precision to tell on what day and at what time

a data point is initially accessible by the market.12 Second, we abstract from a period of

domestic and international financial market turmoil, economic downturn, and massive policy

interventions during 2007-2009.13 Third, by focusing on recent years, China’s equity market

could have increasingly developed its sophistication through rounds of reforms. The market

may have known better how to react to macro announcements and act upon information.

Therefore, our sample selection helps isolate the effects of macro announcements during a

post-crisis period when China’s financial market is getting more sophisticated and when

market participants are familiarized with the delivery process of important macro data. We

render a section in Section B.1 of Appendix to discuss the empirical results using alternative

sample periods.

To identify the pre-announcement reactions of equity market, we extract a list of dates

and times of all the selected announcement events from the Bloomberg Economic Calendar

(BEC) database.14 Stock return data are constructed based on daily open and close price

series of the Wind A Share Index. This index incorporates A shares of all firms listed

on Shanghai and Shenzhen Stock Market Exchanges, which can be considered the most

comprehensive measure of stock performance of China’s equity market. We also examined

the robustness of our empirical results using Shanghai Stock Market Exchange Composite

(SSE) Index and Shenzhen Stock Exchange Component (SZSE) index. All these market

index series are downloaded from Wind Data Feed Services. In addition, intra-day price

index data for both Shanghai and Shenzhen exchanges are sourced from the RESSET High

Frequency Database, which helps reaffirm our baseline findings.

To compute the excess equity returns, we take the 10-year treasury bond daily yield series

as benchmark risk free rate, obtained from Wind Data Feed Services. One-year bank time

deposit rate is treated as an alternative measure. These risk-free rates are downloaded from

are occasionally made public around 30th of a month.12In China, data releases can take forms such as conference press release, statement directly published on

data agency’s website, or public statement delivered through news media etc.13Many countries including China underwent credit shortage and liquidity distress along with large fiscal

and monetary stimulus, all of which could be of the first order importance to shift the asset value in aturbulent period. For example, China introduced a massive stimulus package of 4 trillion RMB (roughly US$ 586 billion) to its economy and provided liquidity support to its financial markets since 2008.

14When downloading, the timing information of FOMC announcements is chosen to be automaticallyconverted to UTC +8, Beijing Time Zone.

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CSMAR Economic and Financial Database. To examine pre-announcement performances

of other major asset markets, CSI300 A share future index, gold future prices, and RMB

exchange rates against major foreign currencies are sourced from RESSET. Finally, we ex-

ploit the forecasts data from Bloomberg Economic Forecast Survey, and the series of daily

volatility of stock returns aggregated over high frequency price data from RESSET database.

By doing this, we rationalize the pre-announcement equity premium through lens of ex-ante

changes in market forecast uncertainty about economic fundamentals and monetary policy

moves.

2.3 Timing of Announcements

Our sample covers 1819 trading days of China’s equity market, and 697 macro announce-

ment events. We first define the day of an announcement as the first trading day that China’s

financial markets have access to the updated macro statistics. Hence, we give a summary of

announcement days by their day-of-month in Table 1.15

According to the table, 75 % of the monetary aggregates data published by PBOC were

announced between the 8th and 14th day of a month. Only a chance of one quarter, should

we see a monetary announcement was delayed beyond the mid of month. We also do a

histogram plot of the day of month distribution in Figure 1. The vertical distance measures

the percent of M2 announcements that fall into a two-day bin. The solid line approximates

a probability density function of the discrete distribution. The graph also shows that about

50 % of M2 announcements in our sample fall between the 11th and 14th day of a month

and the peak day for PBOC releasing the monetary data is the 11th.16

In sum, we see no such a day of month that is strictly preferred by PBOC for releasing

monetary statistics. However, investors may still be able to figure out a window of days

with greatest probabilities to see PBOC’s data releases, for example, the 11th to 14th of a

month. Note that PBOC does not pre-communicate with the market regarding the exact

day of announcement. Though, market knows that there will be one announcement to be

made every month with probability one, sooner or later, which publishes the up-to-date

monetary aggregates data. Hence, we call this PBOC’s routine of releasing monetary data

as “quasi-scheduled”. Rather, the Fed pre-schedules the dates of eight FOMC meeting of

a year, and informs the market of those dates ahead of time. We delegate later sections to

15Summaries of the announcement days by other classifications are left in Section A.2 of Appendix.16In Section A.2 of Appendix, Table A.4 summarizes the degree of co-released announcements according

to the day of announcements of all our selected data release events in the sample. It shows that our identifiedevents of M2 announcements are largely independent events.

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discuss the implications of announcement scheduling for equity premium.17

As for other non-monetary data, Table 1 indicates that the TRD announcements are

typically out before the 15th day of a month. 75 % of FAI and VAI data were published

in the first half of a month. Three quarters of INP announcements are available by the end

of a month. The PMI announcements are found to be routinely published on the first day

of a month. The CPI announcements are mostly published before the 11th day of a month.

The RST data is made public mostly on the 18th day of a month. The days of month for

FOMC statement releases are evenly distributed across months.

Table 1: Day of Month Distribution of Announcements

M2 TRD FAI VAI INP PMI CPI RST FOMC

Min 8 8 9 9 3 1 8 17 125.Perctl 11 8 11 11 27 1 9 18 14Median 12 10 13 13 27 1 10 18 1975.Perctl 14 10 15 15 27 1 11 18 28Max 18 15 21 21 29 31 21 26 31Mode 11 10 13 13 27 1 9 18 28

No. Events 90 90 82 76 42 91 90 76 60

Notes: Sample: January, 2010 to June, 2017. This table shows the day of month distribu-tion of announcements by their percentile cut-off days of a month. Number i in a cell denotesthe i-th day of a month. Min: the earliest day of a month for an announcement day event;Max: the latest day of month for a data release; Percentiles: percentiles of the day of monthdistribution; Median: 50 % percentile cut-off. Mode: the day of month on which largest num-ber of announcement vents fall. Numbers reported are rounded up in case of decimal ratios.

3 Monetary News: Pre-announcement Premium

In this section, we first document a persistent pre-announcement drift of China’s stock

market returns in response to PBOC’s announcements about monetary aggregates data.

Then, we show that the realized pre-announcement equity premium is large, and is not

driven by potential data leakage or expectation changes.

3.1 Evidence from High Frequency Data

To examine the reactions of China’s stock market to M2 announcements, we compute

and plot the average cumulative equity returns constructed from five-minutes trading blocks

of Shenzhen and Shanghai market index in Figure 2.

17However, GACC and NBS are releasing their managed data in a pre-scheduled way. The market isnotified of the announcement date of trade data ahead of time every month. Statistics about the real-sectorproductivity started being announced by the NBS following a pre-fixed schedule since 2007.

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Figure 1: Day of Month Distribution of M2 Announcements

Notes: Sample: January, 2010 to June, 2017. This figure plots the histogram distribution of day of month across allM2 announcements events in our sample. Each bin spans over two consecutive calendar days. The vertical distance of the boxdenotes the percent (%) of M2 announcement events with the announcement day of month that fall into a two-day bin. Thesolid line approximates the probability density function.

Averaged across all M2 announcements for a period of January, 2010 to December, 2016,

the solid lines denote the mean accrued returns of the two exchanges starting from i days

before (after if i is negative) the announcement.18 The day of M2 announcement is marked

by 0 on the x-axis and shaded with a grey bar. One standard deviation confidence bands are

drawn along the cumulative returns. For comparisons, we draw dashed lines to capture the

average cumulative returns across all “non-announcement” seven-day windows, which has

no announcement falling on any day of the seven days in the window.

Accordingly, this figure suggests that China’s equity returns, regardless of stock mar-

ket exchanges, start accumulating three days prior to an average M2 announcement until

reach a peak on the announcement day. The peak of mean cumulative returns of both

markets is about 70-80 basis points (bps). Conversely, returns stay flat for an average non-

announcement window of the same length and are significantly no different from zero. Hence,

we confirm that China’s stock market exhibits a pre-announcement drift of equity returns

in response to incoming releases of monetary aggregates data.19

18A slight shrinkage of our sample length is due to the fact that RESSET High Frequency Database stopsupdating data beyond the end of 2016.

19We also provide extra evidence to account for the sharp drop of returns near the end of the announcementday and the subsequent rebound and climbs of returns thereafter in later sections.

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Figure 2: Cumulative China’s Stock Market Returns Around M2 Announcements

(a) Shenzhen Stock Exchange (b) Shanghai Stock Exchange

Notes: Sample: January, 2010 to December, 2016. This figure shows the average cumulative returns over five-minutes blocks on the Shenzhen Stock Exchange Component (SZSE) Index and Shanghai Stock Exchange Composite (SSE)Index of a seven-day announcement window. The solid line of a plot captures the average cumulative returns across allseven-day windows. The announcement day, i.e. the first trading day when the market has access to the monetary data, iscentered in the middle and is shaded by a vertical grey bar. The dashed line of a plot denotes the average cumulative returnsof seven-day windows with none of any announcement day falls in between. The shadow areas mark ±1 standard deviationconfidence band around the average cumulative returns.

3.2 Monetary Announcements: Pre-announcement Premium

We further identify the pre-announcement equity premium by estimating a baseline spec-

ification given by:

Exrett = γ +T∑

i=−T

βiItM2−i + βxXt + υt (1)

t corresponds to a trading day. Exrett denotes the daily difference of close-to-close stock

returns constructed from the Wind A Share Market Index and the 10-year treasury daily

yield, thus a measure of excess return. We will show that with open-to-close returns and

using alternative risk-free rates would not affect our baseline results.

Our explanatory variables ItM2−i are dummy variables that equal to one if day t is the

i-th trading day before (after if i is negative) an M2 announcement. With i = 0, ItM2= 1

denotes the first trading day on which an announcement is available to the public, i.e. the

announcement day. In total, we include 2T + 1 day dummies to capture the duration of

announcement window. Ceteris paribus, coefficient βi is interpreted as the mean excess

return on the i-th day prior to announcement relative to the average daily excess return

outside an average non-announcement window. We further include year, month and weekday

fixed effects in vector Xt to control for potential seasonality and calendar effect.

12

Table 2 reports the coefficient estimates of Equation (1). According to results in Column

(1), with T = 5 of a 11-day M2 announcement window, we find that most of coefficient

estimates βi are statistically insignificant except for the ones associated with the three day

dummies prior to announcement, i.e. IM2−1, IM2−2, and IM2−3. These point estimates ranges

from 30 to 40 bps for a given trading day, though the largest and the most statistically

significant daily equity premium is realized on the day right before announcement tM2−1.

Important to note that we don’t find a significant premium on the M2 announcement day

though its magnitude is non-negligible. Therefore, we confirm that China’s equity market

accrues a pre-announcement equity premium before PBOC’s releasing of monetary data.

Our findings thus provide an echoing counterpart of Chinese markets for the U.S. pre-FOMC

drifts of equity returns documented in Lucca and Moench (2015).

Column (2) (3) and (4) respectively shows that findings on the three-day pre-

announcement premium are robust given excess returns are constructed using open-to-close

market index, the risk-free rate is proxied by one-year bank time deposit rate, or the de-

pendent variable is stock market raw returns. Column (5) presents similar estimates of the

three coefficient estimates when seven day dummies of announcement windows are included

such that T = 3. In Table B.2 of Appendix, we demonstrate that directly using Shenzhen or

Shanghai stock exchange index for constructing returns does not alter our baseline results.

Given persistent accumulation of equity returns prior to monetary announcements, we

then run the following regression to quantify the relative size of mean daily excess return in

the pre-announcement window of j days.

Exrett = γ + βjItM2−1,j +T∑i=0

βiItM2+i + βxXt + υt (2)

Dummy variables ItM2−1,j = 1 denote those trading days that fall into a j-day window before

an M2 announcement. βj can be interpreted as the average daily excess return of those days

that fall into the j-day window, relative to daily returns outside these windows. Estimation

results are summarized in Columns (6) and (7) of Table 2. Both columns suggest that relative

to non-announcement window length of j days for j = 2, 3 prior to monetary announcements,

the realized daily excess return, i.e. the relative pre-announcement premium, is about 30

bps per day.

3.3 Pre-announcement Premium vs. Total Equity Premium

We then evaluate how quantitatively important the documented pre-announcement pre-

mium is by examining to what percent this premium accounts for the total risk premium

13

Table 2: Wind A Share Index Returns in Windows of M2 Announcements

(1) (2) (3) (4) (5) (6) (7)VARIABLES Exret Open-Close Bank Rate Raw Returns Exret Exret Exret

ItM2−5 0.16 0.18 0.16 0.16 0.16 0.16(0.18) (0.15) (0.18) (0.18) (0.18) (0.18)

ItM2−4 -0.07 0.09 -0.07 -0.07 -0.07 -0.07(0.20) (0.16) (0.20) (0.20) (0.20) (0.20)

ItM2−3 0.29+ 0.31+ 0.29+ 0.29+ 0.28+ 0.29+

(0.19) (0.20) (0.19) (0.19) (0.19) (0.19)ItM2−2 0.25+ 0.25* 0.25+ 0.25+ 0.24+

(0.17) (0.15) (0.17) (0.17) (0.16)ItM2−1 0.39** 0.42*** 0.39** 0.39** 0.38**

(0.16) (0.16) (0.16) (0.16) (0.16)ItM2−1,2 0.32***

(0.12)ItM2−1,3 0.31***

(0.11)ItM2 0.22 0.13 0.22 0.22 0.21 0.22 0.22

(0.17) (0.16) (0.17) (0.17) (0.16) (0.17) (0.17)ItM2+1 -0.21 -0.13 -0.21 -0.21 -0.22 -0.21 -0.21

(0.17) (0.16) (0.17) (0.17) (0.17) (0.17) (0.17)ItM2+2 0.02 0.03 0.02 0.02 0.02 0.02 0.02

(0.19) (0.18) (0.19) (0.19) (0.19) (0.19) (0.19)ItM2+3 -0.02 -0.06 -0.02 -0.02 -0.03 -0.02 -0.02

(0.18) (0.17) (0.18) (0.18) (0.18) (0.18) (0.18)ItM2+4 0.01 0.02 0.01 0.01 -0.02 0.01

(0.19) (0.16) (0.19) (0.19) (0.18) (0.18)ItM2+5 0.03 0.02 0.03 0.03 0.03 0.03

(0.20) (0.19) (0.20) (0.20) (0.20) (0.20)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes Yes YesConstant -0.28 -0.07 -0.28 -0.27 -0.28 -0.28 -0.28

(0.21) (0.20) (0.21) (0.21) (0.20) (0.21) (0.21)

Observations 1,819 1,819 1,819 1,819 1,819 1,819 1,819R2 0.02 0.02 0.02 0.02 0.02 0.02 0.02

Notes: Sample: January, 2010 to June, 2017. Columns (1) to (5) of this table reports regression results of Equation (1) forvarious specifications. Columns (6) and (7) list estimation results of Equation (2). The dependent variable is the log close-to-close excess return constructed from Wind A Share Index except for Column (4) which directly takes stock market returns asdependent variable. Announcement dummy ItM2−i equals to one if the i-th trading day before (after if i is negative) an M2announcement. Excess return data of the first trading day is aligned to the day on which the stock market first has access tothe monetary news with the dummy variable ItM2 = 1 when i = 0. Dummy variable ItM2−1,j equals to one when a tradingday t falls in a j-trading-day window before an M2 Announcement. ***Significant at 1%, **significant at 5%, *significant at10%, +significant at 15%. Robust standard errors are shown in parentheses.

14

of China’s equity market. Our measure of the magnitude of pre-announcement premium is

the mean daily excess return of a three-day window prior to an average M2 announcement.

Table 3 summarizes the results.

Panel (a) of the table presents the relative size of pre-announcement premium using close-

to-close daily returns of China’s equity market. The first row indicates that the average daily

excess return of Wind A Share Market Index is about one bps, which can be aggregated up

to an annual return of approximately 3 %. By contrast, the daily pre-announcement excess

returns averaged over all three-day pre-announcement windows is about 27 bps, which can

be annualized up to more than 10 % using a factor of 36 (twelve times a year). Therefore,

on annual terms, monetary pre-announcement premium in China scales the total equity

premium of China’s equity market by a multiple of 3.40. In terms of Sharpe Ratio, a

trading strategy of buy-and-hold for the Wind A Share Index for three days prior to the M2

announcements for twelve times a year gives to 1.05.20 This is a huge number which is more

than nine times of the mean Sharpe Ratio of 0.11 derived from the same trading strategies

throughout the year. In sum, our found monetary pre-announcement premium is large in

both absolute and risk-adjusted terms.

Table 3: China’s Equity Premium and Monetary Pre-announcement Premium

(a) Close-to-close Returns (%) (b) Open-to-close Returns (%)

No.Obs Daily average Annualized S.R. Daily average Annualized S.R.

Whole Sample 1819 0.01 2.98 0.11 0.12 35.28 1.25PreAnns Days 270 0.27 10.14 1.05 0.38 14.55 1.51

Scale/Ratio 3.40 9.46 0.41 1.21

Notes: This table presents excess returns of Wind A Share Market Index earned in three-day Pre-M2windows relative to the size of China’s total equity premium. Columns “Annualized” stands for cumu-lative annual excess return, assuming there are 250 trading days in a calendar year. Row label “Pre-Anns Days” presents respective returns earned in three-day pre-M2 trading windows. “Whole Sample”presents respective returns earned in all trading days of the sample range: Jan, 2010 to June, 2017.“S.R.” denotes the annualized Sharpe ratio of pre-M2 window excess returns. Given twelve three-daywindows per year, we calculate the annualized announcement Sharpe ratio as the per day Sharpe ratiotimes

√36. “Scale/Ratio” shows the multiple of returns earned in the three-day pre-M2 trading win-

dows to those earned in all trading days. Panel (A) summarizes results based on close-to-close returns;Panel (b) lists results based on open-to-close returns. All returns shown in this table are in percent.

Panel (b) of Table 3 again confirms the quantitative relevance of this pre-announcement

premium using open-to-close returns. It shows that monetary pre-announcement premium

still accounts for a fraction of 41 % of total equity premium in China. The scale of Sharpe

Ratio is greater than one.21 Hence, our results highlight the great importance to study the

20Technically, since investors are not informed of the date ex-ante when the monetary data will be releasedin a month. This three-day trading strategy is not implementable per se. However, for comparisons purposes,this is a way to compute the relative size of this pre-announcement premium.

21This is due to that total premium of China’s equity market is much larger when returns are based onopen-to-close market prices.

15

strong market reactions to incoming monetary announcements.

3.4 Potential Explanations

In this section, we first offer some potential explanations for the baseline empirical find-

ings, and later rule out them as the main drivers for pre-announcement drift of equity returns

in response to PBOC’s monetary data releases.

First, China’s equity market acts upon to-be-released monetary data a few days prior to

incoming PBOC’s announcement. That is, market well reacts to some pre-leaked data given

that data leakage is somewhat possible. Second, without data leakages, the stock market

well expects the direction of monetary aggregate changes ex-ante. Hence, regardless of

whether market reacts to pre-leaked data or to rational expectation changes, our documented

positive pre-announcement premium should be associated with market-preferred PBOC’s

information only. That is, the to-be-released content of monetary aggregates data should

alleviate aggregate market risk and bump up equity prices. Therefore, we hypothesize that

the monetary pre-announcement premium is related to lax monetary data only.

We first break our M2 announcement events into two groups according to the relative

size of announced year-over-year (YOY) M2 growth data for that month and that of previous

month ∆gM2,m = gM2,m − gM2,m−1. The relative size measures if the up-to-date monetary

data is indicative of PBOC’s more lax monetary policy stance for ∆gM2,m > 0 or monetary

tightening if ∆gM2,m < 0. Then, we augment the exercise done for Figure 2 by plotting

the average cumulative stock market returns around the M2 announcements conditional on

whether ∆gM2,m is positive (dashed line) or negative (solid line).

Figure 3 shows that both Shenzhen and Shanghai markets exhibit cumulative drifting

of returns three days prior to announcement no matter if ex-post the monetary data is

suggestive of lax or tightened policy stance. Also, for both markets, the cumulative returns

of either scenario fall into the one standard deviation confidence band of the other. Hence,

in terms of magnitude, no statistically significant difference can be drawn here regarding the

pre-announcement premium with or without a lax M2 growth number.22 Interestingly, after

the data announcements are made public, the post-announcement market index moves in

two opposite directions. The cumulative returns, conditional on positive ∆gM2,m, keep going

up whereas conditional upon a decrease of M2 growth rate, equity price fluctuates and drops

by the end of the PBOC’s announcement day. This post-announcement market behaviors

22However, we note that the realized mean pre-announcement cumulative returns associated with∆gM2,m > 0 are relatively higher on day tM2 − 1 to the scenario of ∆gM2,m < 0 for the Shanghai Ex-change. We are not completely ruling out possibilities of data leakages, which may help account for suchsubtle differences.

16

further justifies our assumption that monetary data of ∆gM2,m > 0 is market-preferred news.

Figure 3: Cumulative Returns Around M2 Announcements by ∆gM2,t

(a) Shenzhen Stock Exchange (b) Shanghai Stock Exchange

Notes: Sample: January, 2010 to December, 2016. This figure shows the average cumulative returns over five-minutes blocks on the Shenzhen Stock Exchange Component (SZSE) Index and Shanghai Stock Exchange Composite (SSE)Index of a seven-day announcement window. Two panels differ by the announcement groups categorized by ∆gM2,m > 0(dashed line) and ∆gM2,m < 0 (solid line). Average cumulative returns across all seven-day windows are centered on the firsttrading day when the market has access to the M2 announcements as shaded by a vertical grey bar. The dotted line at thebottom denotes the average cumulative returns of seven-day windows of non-announcement days. The shadow areas mark ±1standard deviation confidence bands around average returns conditional on data to-be-released in M2 announcements.

To formally test our hypothesis, we use three different proxies to characterize the content

of an M2 announcement. First, monthly changes in YOY M2 growth rate ∆gM2,m serve

as our baseline measure. Second, we construct the “unexpected” innovations to the stance

of monetary aggregates such that εM2,m = gM2,m − gM2,m, where gM2,m denotes the market

expected M2 growth rate as proxied by the median forecast of Bloomberg Survey. In addition,

we take the difference of Bloomberg Forecast Survey data of the M2 growth rate and the

realized M2 growth of previous month E[∆gM2,m] = gM2,m − gM2,m−1 as the expectation-

based measure of announcement content. In sum, positive (negative) of ∆gM2,m, εM2,m, or

E[∆gM2,m] can be all considered extra ease (tightening) of monetary policy or overall credit

condition.

We then estimate the following specification to test the hypothesis that the pre-

announcement premium is not affected by the content of M2 announcements.

Exrett = γ + β1ItM2−1,j + β2 · ItM2−1,j · ContenttM2+ β3 · ContenttM2

+ βxXt + υt (3)

ItM2−1,j is a dummy variable to denote those days that fall into a j-trading day window

before the M2 announcement day tM2. We take j = 3 by focusing on the return reactions

during the three-day window prior to announcement. ContenttM2on the announcement day

17

of a given month is measured by monthly numbers of ∆gM2,m, εM2,m, or E[∆gM2,m]. The

coefficient associated with the interaction term β2 gives the estimate of additional gain or

loss, if any, due to changes in the announcement content.

We summarize the key estimation results in Columns (2) to (4) of Table 4. Results

suggest that the mean daily pre-announcement premium is not affected by the content of

announcement regardless of how much ex-post the market prefers acting upon such news.

In specific, relative daily excess returns of three-day windows prior to announcement is

consistently around 30 bps. The coefficients of interaction terms are insignificant. Hence, we

rule out the possibilities that potential data leakages or expectation changes are the main

drivers behind the documented pre-announcement equity returns.

In addition, we further explore the possibility that investors’ earned pre-announcement

premium may be driven by the announcement content associated with statistics other than

M2 growth but are co-released in the same statement of monetary aggregates data. According

to Section 2, M1, total outstanding loan balance (Loan), deposit balance (Deposit) are jointly

released. In addition, balance of total social financing (TSF), which is later considered

another key measure of monetary policy stance, is also published some time before or after

the M2 announcement though in a separate statement on the same day. 23 Columns (5) to

(8) of Table 4 present coefficient estimates about the interaction term dummy ItM2−1,3 and

measure of content associated with other data statistics, also measured as monthly difference

of YOY growth rates: ∆gM1,m, ∆gLoan,m, ∆gDeposit,m, and ∆gTSF,m. It shows that none of

these content measures shifts the magnitude of pre-announcement premium.

Our results show that the sizable equity premium prior to M2 announcements is not

simply driven by the to-be-released content of incoming announcements. In the following,

we provide a model to account for the mechanism behind the pre-announcement premium.

4 Model

In this section, we present a model that generates a positive equity premium while the

market is anticipating an incoming announcement made by the central bank regarding mon-

ey growth. The key mechanism is that investors can learn about monetary data prior to

announcement, which helps mitigate their forecast uncertainty about economic fundamen-

tals. This further leads to decreased aggregate risk, which boosts up equity price. In spirit

23However, TSF data are quarterly statistics before 2016. Not until the end of 2016, TSF data startedbeing published monthly and jointly within the same data release statement of monetary aggregates data.We thus have fewer day return observations for the regression that involves TSF data and insignificantcoefficients.

18

Table 4: Announcement Premium: Content of Announcements

VARIABLES (1) (2) (3) (4) (5) (6) (7) (8)

ItM2−1,3 0.30*** 0.31*** 0.32*** 0.32*** 0.30*** 0.31*** 0.30*** 0.28(0.11) (0.11) (0.12) (0.12) (0.11) (0.11) (0.11) (0.26)

ItM2−1,3 · εgM2,m 0.10(0.16)

ItM2−1,3 ·∆gM2,m 0.09(0.12)

ItM2−1,3 · E[∆gM2,m] -0.08(0.15)

ItM2−1,3 ·∆gM1,m -0.01(0.03)

ItM2−1,3 ·∆gLoan,m 0.01(0.12)

ItM2−1,3 ·∆gDeposit,m -0.01(0.09)

ItM2−1,3 ·∆gTSF,m 0.03(0.05)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes Yes Yes YesLevel Term Ctrls Yes Yes Yes Yes Yes Yes Yes YesConstant -0.28 -0.27 −0.35+ -0.28 −0.31+ −0.33+ −0.30+ 3.02

(0.21) (0.21) (0.21) (0.23) (0.21) (0.23) (0.21) (3.69)

Observations 1,819 1,819 1,819 1,819 1,819 1,819 1,819 540R2 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.06

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regression results of Equation (3).The dependent variable is the close-to-close excess returns constructed from Wind A Share Index. Announcement dummyItM2−1,j equals to one if a trading day falls into the j-day window before a particular type of announcement. ***Significantat 1%, **significant at 5%, *significant at 10%, +significant at 15%. Robust standard errors are shown in parentheses.

of Sims (2003), our model features the endogenous choice of information demand made by

investors who have limited attention to learn. By optimizing attention and learning, pre-

announcement equity prices can go up as uncertainty is lowered.

In specific, our model accommodates “quasi-scheduled” public announcements. That is,

even though investors when entering a month do not know the exact day of central bank’s

data release announcement for that month, they are certain that some data will be released,

sooner or later, with probability one. In the model, an announcement with updated data

may arrive early or late in a month, and investors are not able to draw very informative

signals about the data to be released when it’s too early to do so. Investors would pay

attention to learning about monetary data only when information demand starts bringing

value. It follows that size of uncertainty reduction driven by investors’ attention allocation

depends on the timeliness of announcement arrival. Our model highlights the importance of

having information demand to account for the pre-announcement premium.

Ultimately, apart from rationalizing Chinese evidence, this model helps explain the short-

lived pre-FOMC announcement premium though the U.S. market is well informed of the pre-

fixed Fed’s announcement schedule ahead of time. Investors would learn about the potential

changes in federal funds rate target when it gets very close to the FOMC meeting days.

19

Jumps of equity prices thus arise from increased information demand a few hours before

FOMC statement release.

4.1 Environment

The model is discrete-time and each period t corresponds to a day.24 A central bank

closely monitors log changes in the balance of monetary aggregate for the economy on a

daily basis, i.e. daily money growth rate mt. For simplicity, mt is assumed to be evolving

via a stationary AR(1) process

mt = ρmt−1 + (1− ρ)µ+ et (4)

where ρ ∈ (0, 1) governs the persistence of money growth and et ∼ N(0, σ2e) captures the

i.i.d. innovations to the money growth process. µ ≥ 0 denotes the unconditional mean of

daily money growth rate.

We assume that the state of money growth can be perfectly known to the market investors

only through central bank’s monthly announcements, which are “quasi-scheduled” in line

with the publication routine of PBOC’s monetary announcements in China. Suppose each

month i for i = 0, 1, 2, ... has N > 0 days and ti is used to denote the end day of month i

such that ti = i ·N . We then lay out a formal definition of “quasi-scheduled” announcements

in the following.

Definition 1 (Quasi-scheduled Announcements) Monthly announcements are quasi-

scheduled if: (1) every month, an announcement is to be made with probability one. The

announcement day tAi falls on a particular day of month i such that tAi = ti−1 + T with

T ∈ 1, ..., N; (2) T , unknown to investors entering month i until tAi , is identically and

independently drawn from a given distribution with Cumulative Density Function F (T ) ∀month i.

Then we model central bank’s announcements as monthly public signals informing the

investors of the money growth rate realized on the announcement days tAi .25 A signal stAi is

24We don’t differentiate between trading and non-trading days in the model.25In reality, to have data on real money growth, data on GDP deflater and nominal balance of monetary

aggregates are both needed. However, for many countries, these two statistics are routinely managed bydifferent statistical agencies and released through separate announcements. The signal structure in our modelcan be regarded as a composite signal that has already aggregated various sources of statistics relevant forinvestors to compute the real money balance growth. Despite this, given price rigidity, short-run changesin nominal money growth can be largely considered as real changes. In addition, daily growth rate in themodel can be easily converted to lower-frequency growth rate in order to be aligned with the reality ofannouncement routines, by which monthly, quarterly or yearly statistics are often times released.

20

thus given by

stAi = mtAi. (5)

Equation (5) says that on the announcement day, money growth rate is perfectly revealed

to the market.26 For illustration purposes, we draw a time line to recapitulate the baseline

environment of our model.

Figure 4: Time Line of Monetary Announcements

Date t

ti−1

end of month i− 1ti

end of month iti+1

end of month i+ 1

announcment about mtAiannouncement about mtAi+1

tAi tAi+1

Without loss of generalities, suppose investors stand on day t = ti, the end of month

i, and are about to enter month i + 1. By the Bayes’s rule, we can compute investors’

expectation of money growth rate of a day prior to the announcement to be made on tAi+1.

Conditional on the information delivered through previous announcement made on day tAi ,

mt is used to denote investors’ conditional expectation regarding money growth of day t

prior to announcement for t = ti + x and 1 ≤ x < T . Investors’ pre-announcement forecast

of money growth is thus captured by mt. For ease of notations, we define ∆it = t− tAi ≥ 0,

the gap days between future day t of month i + 1 and the announcement day of previous

month i. By the AR(1) structure, the market expected money growth rate follows that

mt = ρ∆itmtAi

+ (1− ρ∆it)µ (6)

Equation (6) suggests that investors’ forecast of money growth of future day t is a weight-

26There are additional complexities associated with how we define an announcement signal. First, an-nouncements can be backward-looking or may publish the real-time statistics. For instance, the U.S. FOMCstatement in the U.S. publishes the most recent federal funds rate target determined at the just convenedFOMC meeting, which reflects the monetary policy moves around the announcement time. By contrast, aPBOC’s announcement publishes some statistics of the previous observation cycle. For example, in May,PBOC announces YOY M2 grow rate of April. Second, data initially released is subject to measurementerrors and rounds of ensuing revisions. Considering all these, in Section C.2 of Appendix, we redefine signalsas backward looking signals with measurement errors. We show that our theoretical results are robust toextra complications.

21

ed average of previously formed belief about mt, the true state revealed through previous

announcement mtAi, and the unconditional mean µ, the a priori mean of money growth. In-

vestors update mtAiover ∆i

t days by assigning weight ρ∆it < 1. As ∆i

t goes larger, investors’

confidence of previously formed belief decays. At the same time, forecast gets increasingly

close to µ as the weight attached to a priori mean 1− ρ∆it gradually climbs up to 1.

Similarly, variance of money growth rate conditional on investors’ forecast follows that

σ2m,t = (1− ρ2∆i

t)σ2e

1− ρ2(7)

σ2m,t naturally measures size of investors’ forecast uncertainty regarding money growth rate

of a future date. By Equation (7), forecast uncertainty up to day t takes a fraction of

1 − ρ2∆it ≤ 1 out of the unconditional variance of money growth, σ2

e

1−ρ2 . As time t evolves,

larger ∆it makes investors’ forecasts about mt become increasingly uncertain over time. As

a result, forecast uncertainty gets closer to the a priori variance of money growth.

Equation (7) implies that investors’ forecast uncertainty about money growth keeps ac-

cumulating until the arrival of next announcement. Given that the new announcement

perfectly reveals mtAi+1, accumulated forecast uncertainty then sharply drops to zero on the

announcement day tAi+1. We thus have the following proposition

Proposition 1 In our baseline environment, for each monthly cycle, investors’ forecast

uncertainty accumulates over time since the previous announcement day tAi , peaks on day

t = tAi+1 − 1, and collapses to zero conditional upon the arrival of next announcement made

on day tAi+1 = ti + T with T ∼ F (T ).

By Proposition 1, the exact announcement day tAi+1 = ti + T differs across months given

the random draw of T for each month. It implies that early or late arrivals of announcement

for different months are associated with different peak sizes of pre-announcement forecast

uncertainty on day tAi+1−1. Hence, investors build up higher uncertainty when it takes more

days for the central bank to release the next signal. For illustration purposes, we plot an

example evolution of forecast uncertainty regarding money growth over months. It shows

that pre-announcement peak of forecast uncertainty varies across months.

We further explore the implications of this announcement environment for equity premi-

um. We work with the fundamental equation regarding the expected excess return of stock

market portfolio in the following

EtRt+1 −Rft+1 = α · σ2

x,t+1 (8)

where EtRt+1 − Rft+1 measures the expected return on stock market portfolio relative to

22

Figure 5: Uncertainty Dynamics and Announcement Cycles

Notes: t corresponds to a day. Each month i is marked by two end points of ti−1 and ti and has a duration of Ndays. tAi indicates the day on which an announcement is made.

risk-free rate Rft+1. Expectation operation is taken upon information available up to day t.

σ2x,t+1 denotes the expected variance of portfolio returns for day t+ 1, i.e. the expected risk

of stock market portfolio. With α > 0, the expected excess return, or, the equity premium

increases in the risk of stock market.27

If the expected market risk increases in the expected variance of money growth∂σ2x,t

∂σ2m,t

> 0

for any given day t, Equation 8 suggests that higher forecast uncertainty raises the expected

equity premium by incorporating larger market risk.

∂[EtRt+1 −Rft+1]

∂σ2m,t+1

= α ·∂σ2

x,t+1

∂σ2m,t+1

> 0 (9)

To evaluate the assumption that uncertainty about future money growth scales up the ag-

gregate market risk∂σ2x,t

∂σ2m,t

> 0, important notes can be addressed here. First, we show in

Section B.7 of Appendix that evidence based on survey of professional forecasts suggests

that forecast uncertainty about money growth is more generally linked to uncertainty about

the broader economic fundamentals in China. In Section C.1 of Appendix, we explicitly

derived an equilibrium condition with a more elaborated model framework such that the

expected excess return increases in the expected variance for future money growth. Second,

27This equation can be derived from various forms of capital market asset pricing models. See Mehraand Prescott (1985) and Fama and MacBeth (1993) and Section C.1 of Appendix for a derivation of thisequation with recursive preference. For example, α can denote investors’ coefficient of relative risk aversionand is positive.

23

with partial derivative expression in Equation (9), we do not rule out the possibilities that

expected uncertainty about other macro variables may also shift up the aggregate market

risk. We show in Section ?? of Appendix that China’s equity market realized excess returns

prior to some non-monetary macro announcements, though PBOC’s announcements that re-

lease monetary aggregates data give the largest and more robust gauge of pre-announcement

premium.

We thus have Proposition 2 governing the relationship between equity premium and

forecast uncertainty about money growth:

Proposition 2 Lowered forecast uncertainty about money growth is associated with lower

aggregate market risk and higher equity prices

Our baseline results so far are derived from an environment that investors have no other

useful information in between announcements to form better forecasts about money growth.

We move on to relax this assumption by having investors optimally choose when and how

much attention is paid to learning about money growth prior to the incoming announce-

ment. We will show that learning during the pre-announcement period drives down forecast

uncertainty over time, which leads to an accumulation of excess equity returns.

4.2 Information Demand and Forecast Uncertainty

In this section, we further enrich the baseline model environment by building in investors’

endogenous choice of acquiring information prior to announcement, which results from in-

vestors weighing the marginal gain of learning against the cost of doing so. In line with

Sims (2003), we employ the framework of rational inattention to endogenize the decision of

information demand. That is, subject to some constraint of information processing capacity,

investors allocate optimal amount of attention paid to learning about money growth rate,

which equivalently pins down the flow of information demand.

In specific, we assume that upon entering day t, money growth mt realizes and investors

see whether or not the central bank made the announcement. Then, in absence of announce-

ment, investors decide how much attention is paid to learn about money growth. By paying

attention, investors may draw an informative signal ft about mt such that

ft = mt + ut. (10)

The noise term ut is orthogonal to the true state of money growth and is i.i.d. draw from

N(0, σ2u,t). Equation (10) suggests that investors’ forecast uncertainty about mt conditional

on exploiting information of ft is given by σ2u,t. It follows that the amount of attention

24

paid can be well proxied by the inverse of noisiness of this optimized informative signal. As

the increased attention aims to enhance the information quality of signal by bringing down

the residual noisiness, variation in the amount of attention allocation over time makes σ2u,t

time-varying.

We further assume that only with probability φt ∈ (0, 1), investors may end up with an

informative signal. This assumption accommodates the scenario with probability 1−φt that

investors might run into a bad luck and have drawn a very noisy signal. We define this noisy

signal as f0,t = mt+ηt with ηt ∼ N(0, σ2η,t). For simplicity, we impose the regularity condition

σ2η,t = σ2

m,t such that the drawn noisy signal adds no extra information value relative to the

forecast variance about mt if no attention is paid, as denoted by σ2m,t.

28

For each day, investors solve the optimal attention allocation problem by minimizing the

expected quadratic loss due to suboptimal belief relative to the true state mt:12φtE[mt −

E(mt|ft)]2 + (1− φt)E[mt −E(mt|f0,t)]2.29 Substituting out the signal structures, investors

choose optimized signal noisiness σ2u,t so as to

minσ2u,t

1

2[φtσ

2u,t + (1− φt)σ2

m,t] (11)

In addition, we assume the optimized informative signal cannot be perfect such that σ2u,t >

0 for all days. This assumption can be rationalized by a constraint that the maximum amount

of information inflow upon learning from optimized informative signal per day is bounded by

an information processing capacity. In models of rational inattention, the entropy measure

H(z) = 12

log2 σ2z gauges the quantity of perceived uncertainty associated with a normally

distributed random variable z. It follows that the amount of information inflow can be

expressed using entropy notations as κt = H(mt) − H(E(mt|ft)) ∈ [0, κ] where κ denotes

the capacity bound. As a result, it gives σ2u,t = 2−2κtσ2

m,t and we see σ2u,t < σ2

m,t as long as

κt > 0. κt is thus interpreted as the actual use of information capacity, i.e. the optimized

degree of attention allocated to learning about mt, which further pins down σ2u,t. Therefore,

endogenously paying attention by exploiting informative signals helps mitigate the forecast

uncertainty relative to that of no attention scenario. In the following, investors’ optimization

28In fact, it is possible that the expected variance of paying attention and drawing signals, φtσ2u,t + (1−

φt)σ2η,t, ends up being larger than that of no learning, σ2

m,t, if σ2η,t > σ2

m,t. For tractability of the model,we abstract from this setup by which learning may generate extra noise. However, in equilibrium, thiscomplication would not affect our baseline results because investors only draw signals when the expectedvariance from paying attention is smaller than that of no learning.

29Quadratic loss minimization can be derived from utility maximization with a second order approxima-tion. We give an example in Section C.3 of Appendix.

25

problem can be summarized as

maxκt− 1

2[φtσ

2m,t2

−2κt + (1− φt)σ2m,t]− vκt (12)

s.t. 0 ≤ κt ≤ κ (13)

By Equation (12), optimizing attention incurs a marginal cost of paying attention v > 0.

This cost may capture the opportunity cost when investors pay attention to learning about

money growth but stay inattentive to other variables of interest, which brings in quadratic

loss. Solving the optimization problem, we then have the following proposition.

Proposition 3 When information demand is endogenous, investors would pay attention to

learn about money growth if (1) the probability of drawing useful information, φt, or (2) the

forecast uncertainty of no learning, σ2m,t, is big enough such that φt · σ2

m,t ≥ v where v = vlog(2)

.

To derive Proposition 3, note that the marginal benefit of paying attention,

φtσ2m,t log(2)2−2κt , decreases in κt. It follows that the maximum marginal benefit at κt = 0,

if dominated by the marginal cost v, makes no value for attentive learning. Hence, learning

is irrelevant when φt · σ2m,t < v. We can thus characterize the optimal degree of attention

allocation in the following using a step function depending on the range of φt given σ2m,t

κ∗t =

κ if φt ∈ [ v

σ2m,t

22κ, 1]

12

log2[φtσ2

m,t

v] if φt ∈ [ v

σ2m,t, vσ2m,t

22κ)

0 if φt ∈ [0, vσ2m,t

)

(14)

Equations (14) suggest that larger φt and σ2m,t call for greater attention input from investors.

In other words, when investors have greater chance to draw precise information and when

forecast uncertainty of no learning would be too large, investors optimally devote more

attention to learn about money growth. Eventually, increased attention devotion will reach

the information processing capacity, which results in constrained learning.

We further map the different types of learning decisions in a two dimensional space of φt

and σ2m,t in Figure 6. It shows that φt and σ2

m,t have to be jointly sizeable in order to trigger

optimized learning. Very intensive learning subject to capacity constraint naturally results

from extremely large probability of drawing informative signals or high level of forecast

uncertainty if learning is not applied.

26

Figure 6: Decision of Attentive Learning over Space of φt, σ2m,t

Notes: Y-axis denotes the forecast variance about mt if no learning is applied. Tickσ2e

1−ρ2 is the upper bound of

forecast variance of money growth rate mt as given by Equation (7). X-axis marks the probability of drawing informativesignals.

Accordingly, after learning decision is incorporated, for all months i, the forecast variance

about money growth of day t can be summarized as follows:

σ2m,t =

(1− φt)σ2

m,t + φtσ2m,t2

−2κ if φt ∈ [ vσ2m,t

22κ, 1] and t 6= tAi

(1− φt)σ2m,t + v if φt ∈ [ v

σ2m,t, vσ2m,t

22κ) and t 6= tAi

σ2m,t if φt ∈ [0, v

σ2m,t

) and t 6= tAi

0 if t = tAi

(15)

where by Equation (4), σ2m,t can be written as function of forecast uncertainty of day t − 1

after learning decision of previous day was taken such that

σ2m,t = ρ2σ2

m,t−1 + σ2e (16)

Importantly, equation systems (15), and (16) fully characterize the dynamics of forecast

uncertainty when information demand via attention allocation is endogenous. In sum, when

investors find it unnecessary to be attentive, they let go the accumulation of forecast variance

over time. Conditional on unconstrained learning as 0 < κ∗t < κ, the optimized noisiness

associated with attentive learning scales down the forecast uncertainty such that (1−φt)σ2m,t+

φtσ2m,t2

−2κ∗t < σ2m,t. Finally, too large of φt or σ2

m,t require the maximum amount of attention

and exploits the full information capacity of the day.

27

For different levels of uncertainty if no attention is paid σ2m,t, we then plot the endogenous

forecast uncertainty as a result of attention allocation against range of φt in Figure 7. The

graph suggests that regardless of how uncertain investors are if no learning is taken, larger

probability of drawing informative signals could result in lower forecast uncertainty σ2m,t

because investors would pay greater attention to learn about money growth. Consistent

with Figure 6, this figure also shows that for the high and medium levels of σ2m,t, investors

would start paying attention to money growth even if φt is still relatively low. In addition,

given extremely high uncertainty if no learning is taken, investors’ attention allocation easily

hits the information processing capacity when φt falls in the middle range. However, for low

levels of σ2m,t, learning may not be optimal even with sizable φt and uncertainty reduction

can be trivial.

Figure 7: Forecast Uncertainty σ2m,t with Endogenous Information Demand

Notes: Y-axis denotes the forecast variance about mt with endogenous information demand. Tick L, M, H respec-tively denotes low, medium, and high level of uncertainty if no learning is applied σ2

m,t. X-axis marks the probability ofdrawing informative signals. Grey dashed line segment denotes the range of forecast uncertainty when learning is not taken.Sold line segment of darker grey captures the range of forecast uncertainty when learning is optimized without being cappedby constraint. Dotted line segment of black color marks the range of forecast uncertainty when learning is constrained by theinformation processing capacity.

4.3 Prediction: Pre-announcement Equity Premium

Our model predicts that high enough uncertainty and increased probability of drawing

informative signals can trigger attentive learning by inducing attention allocation, which

endogenously drives down forecast uncertainty about money growth. By Proposition 2,

aggregate market risk is lower and excess equity returns jumps. To better rationalize the

data in a dynamic setting, we have the following proposition to highlight the key model

mechanism that generates pre-announcement drift of excess returns.

28

Proposition 4 (Uncertainty Reduction and Pre-announcement Premium) When

information demand is endogenous, large enough uncertainty and high probabilities of

drawing informative signals within a few days before announcement lead to continuous

reduction of uncertainty and accumulation of excess returns.

Suppose some initial drop of uncertainty on day t as driven by attentive learning had

pushed down the forecast uncertainty of no learning for next period σ2m,t+1 according to

Equation (16). By Figure 6, to ensure that investors continue devoting attention for next

few days, σ2m,t+1 and φt+1 have to be large enough to confine investors decision of learning

within the area shaded by the upper right corner of the graph. For example, a series of

φt that are trivial at the beginning of a monthly announcement cycle and get larger prior

to announcements can support a path of uncertainty accumulation as followed by days of

uncertainty reduction. To see this, as implied by Figure 7, with high enough φt, high level

of forecast uncertainty (H) can be reduced to a medium level (M) for the next period. A

sizable φt+1 then keeps pushing down forecast uncertainty to even lower level (L). Therefore,

a sequence of declining forecast uncertainty can be obtained.

A critical condition associated with Proposition 4 is that the probability of drawing

informative signals is high for those days prior to announcement. Importantly, φt can be

interpreted as the fraction of useful information outstanding in the market accessible to

investors for forming better forecasts about money growth. Reasonably, as date evolves in

a monthly announcement cycle, more information source could be available for investors

to aggregate and analyze, which necessarily increases the probabilities to draw informative

signals about money growth.

In Figure 8, we plot an example path of forecast variance evolution of month i when

information demand is endogenous and a baseline path of uncertainty dynamics without

learning. In specific, starting from the first day of month i, the black-circled line denotes the

baseline path of forecast uncertainty. This is the case when central bank’s announcements

are the only source of information. On the announcement day tAi , uncertainty drops to zero

and then it kicks off another round of accumulation into the next announcement cycle.

On the other hand, the blue-dashed line captures the path of forecast uncertainty when

information demand is endogenous. To trigger learning, we feed in a series of probabilities of

drawing informative signals which starts at low of and increases at a constant daily rate until

being bounded by one. Upon announcement arrival, φt is again set to be low. Therefore,

as t moves forward, uncertainty undergoes a reduction of forecast uncertainty starting from

the trigger-point day when φt and forecast uncertainty of no learning climb high. A series

of uncertainty reduction hence follows until the announcement day, during which either

unconstrained or constrained learning can be applied depending on parametrization. Once

29

the announcement arrives, forecast uncertainty again collapses to zero. Going forward,

starting with low uncertainty and low probability of drawing useful information, investors

start staying rationally inattentive by letting uncertainty accumulate.

Figure 8: Example Path of Attention-driven Uncertainty Reduction

Notes: Under parameterization of increasing probabilities of drawing an informative signal φt+1 = (1 + g)φt withφ1 = 0.05, g = 0.3 and φtAi +j = 0 for j ≥ 0. The vertical red dotted line marks the day of monetary announcement. The black

solid line dotted with circles captures the initial accumulation and reduction of uncertainty conditional upon the informationdelivered through announcement only. The blue dashed line denotes the path of uncertainty when learning is endogenous.

Tickσ2e

1−ρ2 is the upper bound of forecast variance of money growth rate mt as given by Equation (7).

In sum, a model with investors having choices of information demand may generate

endogenous reductions of forecast uncertainty. Note that our model does not rely on full or

partial disclosure of monetary data in form of data leakage to deliver this premium ex-ante.

4.4 Discussions

In this section, we discuss additional implications derived from our model. These model

predictions will be further tested against the data to establish the empirical relevance of our

model framework. In the end, we discuss the relevance of our model for rationalizing the

characteristic features of pre-announcement premium observed both in China and the U.S.

despite their quantitative differences.

Uncertainty Dynamics Prior to Announcement. Our model highlights the key chan-

nel that attention-driven uncertainty reduction generates pre-announcement drift of equity

returns. We thus test the following two null hypotheses:

30

Hypothesis 1 Measures of forecast uncertainty does not decline before the arrival of P-

BOC’s monetary announcements.

Hypothesis 2 Across announcement events, greater uncertainty reductions are not associ-

ated with larger cumulative excess equity returns.

Hypothesis 1 will be tested against the data using measures of uncertainty constructed

from professional forecasts and China’s stock market volatility. We will test if Hypothesis

2 holds by examining the correlation of size of pre-announcement uncertainty reduction

and the magnitude of accumulated equity excess returns. Rejection of the null hypotheses

listed above provides important evidence in support of the key mechanism behind the pre-

announcement premium.

Early vs. Delayed Arrivals of Announcements. Assumptions that φt and σ2m,t are high

enough prior to announcement are pivotal for Proposition 4 to hold. With quasi-scheduled

monetary announcements, a key model implication is that greater size of daily uncertainty

reduction should be associated with more delayed announcements. To see this, we express

daily changes in uncertainty ∆σ2m,t = σ2

m,t − σ2m,t−1 in the following according to Equations

(15) and (16)

∆σ2m,t =

[1− φt(1− 2−2κ)]σ2

m,t − σ2m,t−1 if φt ∈ [ v

σ2m,t

22κ, 1]

(1− φt)σ2m,t + v − σ2

m,t−1 if φt ∈ [ vσ2m,t, vσ2m,t

22κ)

σ2e − (1− ρ2)σ2

m,t−1 ≥ 0 if φt ∈ [0, vσ2m,t

)

(17)

Equations (17) shows that uncertainty reduction ∆σ2m,t < 0 must be achieved via attentive

learning. The following proposition regarding the size of uncertainty reduction thus holds

Proposition 5 With uncertainty reduction ∆σ2m,t < 0, larger probability of drawing infor-

mative signals φt generate larger uncertainty reduction such that∂|∆σ2

m,t|∂φt

> 0.

In the data, more delayed announcement and investors’ extended time waiting for an-

nouncement gives room for more useful information about money growth to pile up, which

could potentially raise φt. We thus expect to see the size of equity premium and magni-

tude of uncertainty reduction before announcements are more pronounced when PBOC’s

announcements are delayed. Therefore, we test the following null hypothesis

Hypothesis 3 Larger pre-announcement premium is not associated with more delayed an-

nouncement arrival.

31

Then, we test if size of uncertainty reduction is also related to how much an announcement

is delayed:

Hypothesis 4 Across announcement events, greater uncertainty reductions are associated

with even more delayed announcement events.

Quasi-scheduled vs. Pre-scheduled Announcements. Ultimately, our theory quali-

tatively squares well with the pre-announcement premium observed in both China and the

U.S. despite their quantitative differences. The U.S. stock market exhibits very short-lived

pre-FOMC announcement premium, whereas our paper finds that pre-announcement drift

in China takes a few days before reaching its peak. We argue that the institutional dif-

ferences in the routine of announcement scheduling, i.e. quasi-scheduled and pre-scheduled

announcements, and the sophistication of financial markets of the two markets may jointly

account for the characteristic differences, by which dynamics of φt and σ2m,t in our model are

affected.

In particular, as federal funds rate futures and derivatives are actively traded in the

U.S. market, it can be very difficult for uncertainty about monetary policy stance to accu-

mulate between FOMC announcements. In addition, between pre-scheduled FOMC dates,

investors know there is probability zero for the Fed to unexpectedly change federal funds

rate target. Mapping to our model, these institutional backgrounds suggest that prior to

FOMC announcement, φt is high, which implies investors could easily get informative sig-

nals about short term interest rate changes from the sophisticated financial market. Plus,

uncertainty of no learning σ2m,t can be quite low. Therefore, only when it gets very close to

the pre-scheduled FOMC day, investors see the possibilities for policy changes. This raised

uncertainty coupled with good chance of forming precise forecasts triggers learning, which

leads to a quick reduction of uncertainty and pre-announcement premium few hours before

FOMC statement releases.

As for China, absence of financial market sophistication about money growth gives room

to cyclical uncertainty accumulation between PBOC’s announcements. Without knowing

the exact day of announcement, investors with high cumulative uncertainty and informative

signals available would start paying attention to money growth. Endogenously, it takes

a few days to lower uncertainty to the optimum, and equity prices keep climbing before

announcements.

32

5 Empirical Tests of Model Predictions

In this section, we show our model implications are consistent with the data. First, we

demonstrate that uncertainty measures as constructed from forecast data and stock return

volatility decline prior to M2 announcements. Second, we provide evidence showing that

the size of pre-announcement premium is positively correlated with the degree of ex-ante

uncertainty reduction. Finally, our empirical results suggest larger uncertainty reduction

and greater pre-announcement premium are associated with announcement events when

PBOC release monetary data with days of delays.

5.1 Uncertainty Declines Before Announcements

We test Hypotheses 1 by examining if forecast uncertainty about money growth declines

before monetary announcements in the data. We construct two empirical measures to proxy

for investors’ uncertainty about money growth: first, the daily dispersion of Bloomberg

surveyed forecast errors about M2 growth before M2 announcements; second, daily stock

return volatility aggregated over five-minutes returns in announcement windows.

Bloomberg Economic Forecast Survey database records an unbalanced panel of individual

forecasts of various macroeconomic variables. In particular, we examine the dispersion of

forecast errors about M2 growth conditional on how close the surveyed day of forecasts is

from the day of the associated M2 announcement.30 Stock market volatility is conventionally

treated as a measure of aggregate market risk that is not necessarily tied to monetary

policy (Bloom, 2014). However, given that stock market itself is an aggregator of future

macroeconomic news (Beaudry and Portier, 2006), its return volatility when situated within

the window of monetary news can be the best measure among few alternatives. 31

5.1.1 Time Plots

Some suggestive evidence of time plots is first provided. Figure 9 plots the dynamics of

forecasts dispersion measured in the standard deviation of forecast errors over time. Vertical

30We are computing dispersion of forecast errors instead of forecasts because distribution of individualforecasts made on the j-th day before a given announcement do not maintain the same mean, i.e. the truestate of M2 growth under rational expectation assumption, across distributions of different announcementevents. Demeaned dispersion can be achieved by computing spread of forecast errors. Also, in Section B.7 ofAppendix, we show that this forecast-based uncertainty about money growth is correlated with uncertaintymeasures regarding a range of other macro variables. We thus argue that uncertainty about money growthis linked to aggregate market risk, which is more generally about economic fundamentals.

31Important to note that there is no option-based implied volatility index for China’s stock marketexchanges of our sample coverage. Also, text-based uncertainty proxies in spirit of Baker et al. (2016) is notreadily available for China and for the analysis of daily frequency.

33

distance measures the standard deviation of forecast errors. To smooth out dispersion of

forecast errors over days, we respectively take a three-day (dashed line) and five-day (solid

line) centered moving averages of daily standard deviations. These dispersion measures are

computed based on 66 economists’ 1902 forecast points after we delete forecasters who have

made fewer than five forecasts in the sample. Horizontally, we have the number of days

that a given forecast survey day lags an PBOC’s M2 announcement. Since there are few

forecasts made on the day right before an announcement day, we remove these observations

that biased our measure of dispersion.

Figure 9: Dispersion of Forecast Errors Prior to M2 Announcements

Notes: Sample: January, 2010 to June, 2017. This figure dynamics of dispersion of forecast errors before an M2announcement. −j marks the j − th calendar day before the announcement day, which is the first trading day that markethas access to the updated monetary data. The dashed line and the solid line respectively denotes the centered three-day andfive-day moving average of standard deviation of forecast errors regarding the to-be-released M2 growth.

Time plots in Figure 9 clearly suggest that dispersion of forecast errors first climbs, stays

constant if not fluctuating, and eventually start declining a few days before the announcement

arrivals. Therefore, dynamics of forecast uncertainty before announcements is hump shaped.

Qualitatively, the path of this forecast-based uncertainty measures is consistent with our

model predicted uncertainty path when information demand is endogenous as in Figure 8.

Importantly, evidence finds that forecast uncertainty has to accumulate to some higher levels

before uncertainty reduction is triggered.

We then compute the mean daily return volatility aggregated over five-minute trading

34

blocks for an average 11-day window centering the M2 announcement for both Shenzhen

(SZSE) and Shanghai (SSE) market indices. These two volatility series are further normal-

ized as divided by their corresponding unconditional mean of daily volatility for days exclud-

ing all 11-day announcement windows. If the relative volatility falls below one, it implies

that the level of uncertainty on that day is lower than that of an average non-announcement

window.

Figure 10: Stock Return Volatility in Windows of M2 Announcements

Notes: Sample: January, 2010 to December, 2016. This figure shows the average relative daily stock market returnvolatility to non-announcement window averages, which aggregates five-minutes return blocks per day on the Shenzhen StockExchange Component (SZSE) Index and Shanghai Stock Exchange Composite (SSE) Index around an M2 announcement.t = 0 marks the first trading day on which the market has access to the announcement as denoted by a vertical solid line.j captures the relative volatility |j| day after (before if j negative) the announcement. The solid line and the dashed linerespectively denote the relative volatility of the SSE and SZSE stock index.

In Figure 10, we plot the two relative volatility series. It shows that regardless of s-

tock exchanges, across all M2 announcement windows in our sample, there is a clear trend

of uncertainty reduction before announcements. Strikingly, this continuous reduction of

volatility-based uncertainty measure initializes three days before announcement, which co-

moves with the pre-announcement drift of returns for a duration of three days. In addition,

the decays of relative volatility hit the bottom on the day right before announcement. This

significantly lower degree of uncertainty relative to that of non-announcement days squares

well with our findings from Table 2 that the coefficient estimate associated with tM2 − 1

has the most significance. Lastly, it turns out the relative volatility stays flat throughout

35

the post-announcement period, which is aligned with our findings that no significant post-

announcement drift of returns is detected in Chinese markets.

5.1.2 Identifications

At the forecast level, Bloomberg forecast data enables us to directly estimate the size

of forecast-specific uncertainty, as measured by how far a particular forecast point about

M2 growth is from the released statistics, as a function of the number of days when this

forecast is surveyed from the associated M2 announcement day. We run the regression of

the empirical specification in the following:

|FEi| = γ + α ·Distancei + β ·Distance2i + τ ·X + ei (18)

To proxy for the forecast-level uncertainty, the absolute forecast error of a particular forecast

point i surveyed on day t, |FEi| is taken as the dependent variable. Distancei captures the

number of gap days that a survey day of forecast i lags its associated announcement day.

To capture the potential non-linearity, we also have the squared term of day distance in the

regression.

In addition, given that forecasts about an M2 number are routinely spread over dispersed

days before announcements, we are also concerned if forecasts made later than the earlier

ones are naturally more precise regardless of how close a forecast is from the announcement

day. To rule out this potential channel, we measure the degree of relative earliness or lateness

of a forecast in an announcement cycle by constructing a measure called LateDaysi. It takes

the day difference of the date of a forecast i and the end date of previous calender month.

That is, if a forecast about the to-be-released M2 growth number this month is surveyed

after (before) the end of previous month, we label this forecast a relatively late (early) one.

LateDaysi along with its squared term LateDays2i , forecaster fixed effects, and year fixed

effects are all included in the co-variate vector X to ensure robustness of our main results.

Estimation results are collected in Table 5. By including term of Distance2i , the estima-

tion gives a better fit that both the coefficient estimates related to the linear and the squared

terms are significant as shown in Column (2). Considering forecaster fixed effects, results

in Column (3) suggest that one day closer to the announcement day shrinks the forecast-

level uncertainty by 0.035. However, for some very earlier made forecasts relative to the

announcement day, the forecast-level uncertainty can be small as well due to the negative

coefficient of the squared term. In the middle range of distance, forecast-level uncertainty is

higher. Hence, we found exactly a similar hump-shape forecast-level uncertainty as a func-

tion of days from announcement, which is consistent with Figure 8 and Figure 9. Coefficient

36

estimates of terms LateDaysi and LateDays2i are not statistically significant according to

Column (4). It double confirms that the hump-shape uncertainty dynamics is not driven

by the lateness of a forecast relative to other forecasts but by the relative distance from the

arrival of PBOC’s announcements.

Table 5: Hump-shape Dynamics of Forecast-level Uncertainty

(1) (2) (3) (4)VARIABLES Pooled OLS Pooled OLS FE Model FE Model

Distance -0.004 0.049*** 0.035** 0.035**(0.004) (0.017) (0.016) (0.016)

Distance2 -0.003*** -0.002*** -0.002**(0.001) (0.001) (0.001)

LateDays -0.010(0.013)

LateDays2 0.002(0.001)

Analyst FE Yes YesYear Dummies YesConstant 0.665*** 0.456*** 0.515*** 0.773***

(0.038) (0.079) (0.072) (0.257)

Observations 1,902 1,902 1,902 1,902R2 0.001 0.005 0.004 0.045

Notes: Sample: January, 2010 to June, 2017. This table reports the re-gression results of Equation (18). The dependent variable is the absoluteforecast error of a particular forecast point i surveyed on day t, |FEi|. 1902forecast points of 66 forecasters are included in the sample after delete fore-casts of those professional forecasters who have made fewer than five fore-casts are deleted. ***Significant at 1%, **significant at 5%, *significant at10%, +significant at 15%. Standard errors are clustered at the forecasterlevel and are shown in parentheses.

Resorting to the measure of uncertainty as proxied by stock return volatility, we directly

test if return volatility prior to M2 announcement is lower than that of other days outside

the pre-announcement windows. We estimate the following model of dummy regressions

with ItM2−1,j = 1 denoting the day that falls into a pre-announcement window of j days

length for j = 1, 2, 3:

Ret V olt = γ + βjItM2−1,j + βxXt + υt (19)

where the estimate of βj captures the size of daily stock return volatility before an M2

announcement day relative to a mean level of uncertainty for days outside these windows.

Table 6 presents estimation results that are aligned with the key message from Figure 10.

First, volatility-based uncertainty is relatively smaller for a few days before the arrival of M2

announcements. Second, while little difference can be discerned between return volatilities

of Shanghai and Shenzhen stock exchanges, we see across columns that the closer days of a

window to the announcement, lower is the average daily volatility. This precisely suggests

37

that the forecast uncertainty keeps declining from a higher level until reaching the bottom

just one day prior to the announcement.

Table 6: Relatively Low Uncertainty Prior to M2 Announcements

(1) (2) (3) (4) (5) (6)VARIABLES SZSE SZSE SZSE SSE SSE SSE

ItM2−1 -0.22*** -0.16***(0.06) (0.06)

ItM2−1,2 -0.18*** -0.14***(0.05) (0.05)

ItM2−1,3 -0.16*** -0.11***(0.05) (0.04)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes YesConstant 1.60*** 1.60*** 1.60*** 1.22*** 1.23*** 1.23***

(0.09) (0.09) (0.09) (0.08) (0.08) (0.08)

Observations 1,700 1,700 1,700 1,700 1,700 1,700R2 0.25 0.25 0.25 0.30 0.30 0.30

Notes: Sample: January, 2010 to December, 2016. This table reports dummy variable regression results ofEquation (19) for different specifications. The dependent variable is daily stock return volatility. Announce-ment day dummy ItM2−1,j equals to one for the trading days in a j-day window before an M2 Announce-ment. ***Significant at 1%, **significant at 5%, *significant at 10%, +significant at 15%. Robust standarderrors are shown in parentheses.

5.2 Correlations: Uncertainty Reduction and Premium

We have shown that our measures of uncertainty decline before M2 announcements.

Then we test the null of Hypothesis 2 to evaluate if the size of uncertainty reduction is

associated with that of pre-announcement equity premium by exploiting the variation across

announcement events. However, the limited number of forecast observations per an an-

nouncement event is unable to give us the unbiased account of uncertainty reduction for days

right before PBOC’s announcement.32 Thereafter, we stick to the stock-market volatility as

proxy for forecast uncertainty when identifications are done at the cross-event dimension.

In specific, across announcement events, we estimate the partial effects of uncertainty

reduction on excess return accumulated over the same duration of uncertainty declining.

The empirical model is specified below:

Cumretj,q = γ + β∆Ret V olj,q + βxX + eq (20)

where Cumretj,q denotes the cumulative equity excess return throughout the pre-

32On average, about 1902/90 ≈ 21 forecasters are surveyed before the monetary data of that month isreleased. Their forecast dates can be spread over very dispersed days. Therefore, per an announcement, nomeasure may well proxy for variations in uncertainty over days prior to that announcement.

38

announcement window of j days associated with a given announcement q. ∆Ret V olj,q =

Ret V oltM2−1,q − Ret V oltM2−j,q measures the size of uncertainty changes from the j-th day

till the day right before the day of announcement q. In the co-variate vector X, we examine

the robustness of results by controlling for the mean level of uncertainty in the j-day window.

We look into pre-announcement windows of three days and two days and the estimation

results are summarized respectively in Panel A and B of Table 7. Columns of Panel A

all suggest that uncertainty reduction (inversely, uncertainty accumulation) is positively

(negatively) correlated with cumulative excess returns over the three-day interval before

announcements regardless of additional controls and market exchange differences.33 Though

with a shorter pre-announcement window of two days, results of Panel B give comparable

point estimates of coefficient β as in Panel A. That is, as long as the same amount of

uncertainty reduction is achieved, same size of cumulative returns can be realized in any

given duration of declining uncertainty.

Table 7: Uncertainty Reduction and the Size of Pre-announcement Premium

Panel A: Cumret3,q

(1) (2) (3) (4) (5) (6)VARIABLES SZSE SZSE SZSE SSE SSE SSE

∆Ret V ol3,q -1.44** -1.50** -1.60** -2.20** -1.97** -1.98**(0.71) (0.66) (0.80) (1.08) (0.99) (0.98)

Mean Ret V ol3,q 0.34 0.26(1.11) (1.12)

Constant 0.54* 0.20 -0.28 0.40 0.14 -0.16(0.31) (1.07) (1.40) (0.25) (0.87) (1.32)

R2 0.04 0.17 0.17 0.13 0.20 0.20

Panel B: Cumret2,q

(1) (2) (3) (4) (5) (6)VARIABLES SZSE SZSE SZSE SSE SSE SSE

∆Ret V ol2,q -1.48** -1.80** -1.74** -1.52** -1.76** -1.76**(0.74) (0.72) (0.73) (0.72) (0.68) (0.69)

Mean Ret V ol2,q -0.47 -0.51(0.42) (0.58)

Constant 0.38* 0.30 0.96 0.31* 0.31 0.90(0.21) (0.55) (0.83) (0.18) (0.48) (0.84)

R2 0.09 0.20 0.21 0.11 0.19 0.20

Year Dummies Yes Yes Yes YesObservations 84 84 84 84 84 84

Notes: Sample: January, 2010 to December, 2016. This table reports dummyvariable regression results of Equation (20). The dependent variable is the cumu-lative excess equity returns over an interval of j days before M2 announcement.Uncertainty is measured by the stock market return volatility aggregated over five-minute trading blocks for the day of both Shenzhen (SZSE) and Shanghai (SSE)exchange market indices. ***Significant at 1%, **significant at 5%, *significant at10%, +significant at 15%. Robust standard errors are shown in parentheses.

33We note that further controlling for month and weekday fixed effects attenuate the significance ofcoefficient estimates because of the limitation of sample size.

39

5.3 Timeliness of Announcement Arrival and Premium

In this section, we test Hypotheses 3 and 4 by exploring whether the size of announce-

ment premium and that of the associated uncertainty reduction depend on the timeliness of

arrivals of M2 announcements. It is important to delve into these question given that mon-

etary announcements are quasi-scheduled in China and stock markets are very responsive to

PBOC’s data releases.

5.3.1 Premium for More Delayed Announcements

First, we examine if the pre-announcement premium is more pronounced for more delayed

monetary announcements. We first select a number of reference days by which we divide

our announcement events into two groups: announcements made earlier, and those made

on and after. Then we estimate the baseline specifications of Equations (1) and (2) using

day return samples of non-announcement windows and the windows of selected group of

announcements.

Table 8 reports the estimation results. Coefficient estimates except for the pre-

announcement dummies are suppressed for the sake of space. In the upper panel, estimations

are associated with those PBOC’s announcements that are made relatively early in a month.

Results from Columns (1)to (3) suggest that regardless of the length of pre-announcement

windows, when the monetary aggregates data are released too early in a month, no significant

relative excess premium can be obtained for days prior to the announcement. In addition,

per the results in Columns (4) and (5), with announcements made just a bit later than the

12-th included, coefficient estimates turn trivially positive and the magnitudes get larger.

Moving towards to the lower panel, results in Columns (1) to (5) exhibit that for those

announcements made late in a month, the coefficient estimates of pre-announcement excess

returns are significantly greater than zero. More importantly, across all the columns of the

lower panel, we see the magnitudes of estimated one-day and three-day ahead premium

become monotonically larger as data releases are further postponed in a month. Evidence

shows that the size of pre-announcement premium is strikingly dependent on the relatively

timeliness of PBOC’s announcement arrival. Compared to our baseline results shown in Table

2, the daily relative excess return of 30 bps of a three-day window prior to announcement is

then largely driven by the accumulation of returns before those delayed announcements.

40

Table 8: Pre-announcement Premium: Early vs. Late Announcements

(1) (2) (3) (4) (5)VARIABLES Earlier than 10 Earlier than 11 Earlier than 12 Earlier than 13 Earlier than 14

ItM2−1,3 -0.20 -0.01 0.14 0.22* 0.29**(0.24) (0.20) (0.15) (0.12) (0.11)

Constant -0.15 -0.13 -0.25 -0.33 -0.30(0.30) (0.28) (0.25) (0.24) (0.23)

R2 0.04 0.03 0.03 0.02 0.02Observations 893 980 1,259 1,436 1,510

ItM2−1 0.17 0.02 0.13 0.22 0.23(0.42) (0.38) (0.27) (0.20) (0.18)

Constant -0.16 -0.13 -0.21 -0.30 -0.26(0.30) (0.28) (0.25) (0.23) (0.23)

R2 0.04 0.03 0.03 0.02 0.02Observations 893 980 1,259 1,436 1,510

(1) (2) (3) (4) (5)VARIABLES On and after 10 On and after 11 On and after 12 On and after 13 On and after 14

ItM2−1,3 0.34*** 0.37*** 0.47*** 0.48** 0.42*(0.12) (0.12) (0.15) (0.20) (0.24)

Constant −0.31+ −0.34+ -0.23 -0.15 -0.20(0.21) (0.22) (0.23) (0.25) (0.26)

R2 0.02 0.02 0.03 0.03 0.02Observations 1,755 1,668 1,389 1,212 1,138

ItM2−1 0.41** 0.47*** 0.63*** 0.73*** 0.83***(0.17) (0.17) (0.20) (0.26) (0.32)

Constant −0.31+ −0.34+ -0.23 -0.15 -0.19(0.21) (0.22) (0.23) (0.25) (0.26)

R2 0.02 0.02 0.03 0.03 0.02Observations 1,755 1,668 1,389 1,212 1,138

Year / Month / Weekday Dummies Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regression results of Equations (1) and (2). The de-pendent variable is the excess return constructed from the Wind A Share Index. Announcement day dummy ItM2−1,j equals to one forthe trading days in a j-day window before an M2 Announcement. Announcement day dummy ItM2−i equals to one if the i-th tradingday is before (or, after if i is negative) an M2 announcement. We align the return data of the first trading day that the equity markethas access to the news to the dummy variable ItM2 = 1 when i = 0. Each column summarizes estimation results based on a restrictedsample that includes only trading days of non-announcement days and either one-day or three-day pre-announcement windows of thoseselected announcement events that fall into either early or the late group. ***Significant at 1%, **significant at 5%, *significant at 10%,+significant at 15%. Robust standard errors are shown in parentheses.

5.3.2 Uncertainty Reduction for More Delayed Announcements

Our empirical evidence is consistent with the model prediction that more delayed arrivals

of monetary announcement, by triggering larger reduction of uncertainty due to attentive

learning, can generate larger pre-announcement premium. In following, we test if the time-

liness of announcement arrivals indeed affects the size of pre-announcement uncertainty

reduction.

41

In specific, across announcement events, we estimate the following specification

∆Ret V olj,q = γ + α ·DaytM2,q + β ·Day2tM2,q

+ βxX + eq (21)

where ∆Ret V olj,q again measures the uncertainty changes over a j day interval until the day

right before the day of announcement. Equation (21) also involves the linear and squared

term of DaytM2,q, which captures the day of month associated with the date of announcement

q, tM2,q. It thus measures the duration of time lapsed for investors, upon entering a month,

to see the final arrival of a PBOC’s monetary announcement.

Table 9 presents the estimation results for both Shanghai and Shenzhen stock exchanges.

Results of Panel A and B differ by the length of observation window of three days and

five days. Focusing on Columns (2) and (6) of both panels, we find that one more day

of monetary announcement delay shrinks the stock market return volatility by about a

maximum of half standard deviation for a given duration of days. In addition, the statistically

significant coefficient associated with the squared term Day2tM2,q

finds that the magnitude of

uncertainty reduction due to one more day of delay gets smaller as the announcement day

is further postponed. However, this convexity effect is relatively trivial. For example, an

announcement has to be made on the 25-th day of a month so as to completely nullify the

linear effect of delays on size of uncertainty reduction.

42

Table 9: Uncertainty Reduction Across Announcements

(1) (2) (3) (4) (5) (6) (7) (8)VARIABLES SZSE SZSE SZSE SZSE SSE SSE SSE SSE

Panel A: ∆Ret V ol3,q

DaytM2,q -0.03 -0.51*** -0.49** -0.47* -0.04* -0.31* -0.26 -0.21(0.02) (0.19) (0.19) (0.24) (0.02) (0.17) (0.16) (0.21)

Day2tM2,q0.02** 0.02** 0.02* 0.01* 0.01 0.01

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01)Constant 0.25 3.18** 2.97** 2.53* 0.38 2.04* 1.76* 1.09

(0.29) (1.21) (1.25) (1.43) (0.24) (1.05) (1.00) (1.24)R2 0.02 0.06 0.11 0.17 0.03 0.05 0.09 0.18

Panel B: ∆Ret V ol5,q

DaytM2,q -0.03 -0.61** -0.47* -0.48 -0.05 -0.60* -0.37 -0.38(0.03) (0.27) (0.24) (0.37) (0.04) (0.31) (0.25) (0.35)

Day2tM2,q0.02** 0.02* 0.02 0.02* 0.01 0.01

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01)Constant 0.21 3.76** 2.63* 2.38 0.42 3.77* 2.24 1.91

(0.42) (1.66) (1.56) (2.33) (0.45) (1.96) (1.64) (2.22)R2 0.01 0.03 0.08 0.17 0.02 0.03 0.12 0.23

Year Dummies Yes Yes Yes YesMonth / Weekday Dummies Yes YesObservations 84 84 84 84 84 84 84 84

Notes: Sample: January, 2010 to December, 2016. This table reports the dummy variable regression resultsof Equation (21). The dependent variable is the size of uncertainty reduction, which is measured by the jday difference in level regarding the intra-day return volatility constructed from high-frequency return dataof SSE (Shanghai) and SZSE (Shenzhen) market index. ***Significant at 1%, **significant at 5%, *signifi-cant at 10%, +significant at 15%. Robust standard errors are shown in parentheses.

However, across columns, we note that our estimated correlation is more pronounced for

Shenzhen stock exchange. In Section B.8 of Appendix, we delve deeper into this issue by

providing additional evidence in the cross-sectional dimension to show that performance of

large cap stocks are less sensitive to the timeliness of M2 announcements. This helps explain

the relatively weaker evidence regarding stock return volatility of Shanghai exchange that

lists more medium and large cap firms. In addition, including time dummies of months

and weekdays also attenuate our results by injecting greater standard errors associated with

point estimates. This can be potentially due to the fact that delayed announcements may

fall in certain months of a year or on some weekdays. For example, it takes longer for PBOC

to publish its official statistics when it comes to months with national holidays. Nonetheless,

the sign and magnitude of our coefficient estimates regardless of whether we control for

additional time dummies are within the same range.

We thus conclude that more delayed announcements are associated with larger reduction

of uncertainty as well as more pronounced pre-announcement premium. In sum, we provide

a series of evidence in this section to show that our model is well aligned with the data.

43

6 Conclusion

By studying China, this paper examines the stock market returns in an environment

when the dates of information supply through public announcements are not pre-fixed. We

document a “pre-announcement drift” of excess returns on Chinese equity market in response

to its central bank’s monthly announcements of measures of monetary aggregates, which may

arrive early or late in a month. For a period of 2010 to 2017, on average, Chinese A-share

market climbs and realizes an excess return of 30 basis points per day in the three-day window

prior to the day of announcement as followed by a flattening-out after the announcement.

In this paper, we demonstrate that by evaluating the implications of having “randomness”

in announcement scheduling, it helps clarify the common mechanism behind equity market’s

ex-ante reactions found for both China and the U.S.

We propose a theory for investors to endogenously acquire information to learn about

money growth given announcements are not pre-scheduled. Pre-announcement premium is

driven by the endogenous attention-driven information demand such that investors’ learning

helps reduce their forecast uncertainty prior to monetary announcements. We show the

institutional details of China render the exact data structure for us to test the key model

mechanism of uncertainty reduction, which helps rationalize the empirics found both for

China and the U.S.

We then provide comprehensive evidence at both micro and macro level to show data is

consistent with our model predictions. First, measures of uncertainty decline prior to PBOC’s

announcements. Second, more accumulated returns are associated with larger uncertainty

reduction ex-ante. Third, by exploiting the timing variations across announcement events,

we show that pre-announcement premium is more pronounced when the release of monetary

data is more delayed. Our model implications help rationalize the characteristic features of

pre-announcement premium found both in China and the U.S. even though the U.S. FRB

has the FOMC dates pre-fixe whereas PBOC’s announcements are quasi-scheduled.

44

Online Appendix

A Additional Summaries

A.1 List of Selected Announcements

In Table A.1, we list our selected announcements that publish major macroeconomic

statistics on a regular basis. Except for the FOMC announcements, others release critical

data about Chinese economy. For our sample coverage of January 2010 up to June 2017, a

given Chinese announcement may release more than one statistics. Routinely, these statistics

of China are published monthly. However, a subtlety should be noted. In a year, there are

at most eleven announcements for data releases of FAI, FAI and INP. This is because the

March statements release data of both January and February of the year after NBS skips

February for publishing any statistics. This may be due to the fact that Chinese Spring

Festival holidays normally fall within February. In addition, the U.S. FOMC Committee

may issue more than eight statements in recession years under rare circumstances.

Table A.1: List of Selected Announcements

Announcement Label Publishing Agency Released Statistics No. of Routine Issues Per Year

M2 PBOC M0/M1/M2 Level and Growth 12Loan and Savings Balance: Level and GrowthInterbank Loan: Interest Rate and Balance

TRD GACC Import/Export Level and Growth 12FAI NBS Fixed Assets Investment 11VAI NBS Value Added of Industrial Enterprises 11INP NBS Profits of Industrial Enterprises 11PMI NBS Manufacturing/Non-manufacturing PMI 12CPI NBS CPI & PPI 12RST NBS Price Indices of Residential Buildings 12FOMC U.S. FRB FOMC Statement 8

A.2 Summaries of Announcement Timing

Table A.2 gives a summary of announcement days by looking into the day of week dis-

tribution for all announcements. It shows that M2 announcements are often time made

public on weekdays and 33% of them fall on Fridays. While most of the announcements

have greater chance to be public around Thursdays and Fridays, announcements of TRD

and PMI are more evenly distributed within a week.

45

Table A.2: Day of Week Distribution of Announcements

M2 TRD FAI VAI INP PMI CPI RST FOMC

Mon .10 .16 .11 .12 .12 .13 .09 .18Tue .17 .12 .17 .17 .14 .14 .17 .13Wed .13 .16 .18 .18 .07 .15 .12 .14 .13Thu .19 .17 .15 .14 .17 .13 .22 .12 .83Fri .32 .14 .23 .24 .24 .16 .23 .21 .03Sat .03 .13 .11 .09 .10 .12 .10 .12Sun .06 .12 .05 .05 .17 .15 .07 .09

No. Events 90 90 82 76 42 91 90 76 60

Notes: Sample: January, 2010 to June, 2017. This table shows the percentage of announce-ments (in decimals) made on each day of week for a given announcement. Due to rounding,column numbers may not add up precisely to one.

Table A.3 summarizes the distribution of announcement days by the point of time for

data release across events. In general, except for FOMC announcements that always fall

on weekdays before the trading hours of Beijing Local Time, the rest of announcements are

made public on either weekdays or weekends regardless of whether it’s within, before or

after the trading hours. About one third of all times in the sample, monetary aggregates

data (M2 announcements) are published after trading hours on weekdays. Also, another

one third fall between weeks, i.e. post-trading hours on Fridays till the end of Sundays.

Announcements about international trade data, real-sector statistics, and the price indices

are routinely made available within trading hours, though sometimes data may be released

during weekends. As for the PMI data, data are sharply public at 9:00 AM though the

announcement day can be any day of weekdays or weekends.

Table A.3: Timing Distribution of Announcements

M2 TRD FAI VAI INP PMI CPI RST FOMC

Weekday beforetrading hours

No. Anns. 3 66 60Avg. Time 8:40 9:00 2:07

Weekday withintrading hours

No. Anns. 26 66 68 64 31 75 60Avg. Time 10:30 10:38 11:08 11:02 9:41 9:39 9:32

Mon-Thur aftertrading hours

No. Anns. 30 1 1 1Avg. Time 15:58 15:34 15:40 15:40

Betweenweeks

No. Anns. 31 23 13 11 11 25 15 16Avg. Time 15:19 10:40 12:55 12:49 9:43 9:00 9:34 9:33

Total 90 90 82 76 42 91 90 76 60

Notes: This table reports the number of announcement events by categorized groups of announcement timingand the averaged point of time for data releases within each group. Four groups are: (1) announcements releasedbefore trading hours on weekdays; (2) announcements released within trading hours (announcements with datareleased between morning session and afternoon session are included); (3) announcements released after tradinghours from Monday to Thursday; (4) announcements released between market closure on Friday till midnight ofSunday. Shanghai and Shenzhen Stock Exchanges are normally open for trading from Monday to Friday, withcall auction from 9:15 to 9:25, and continuous auction in 9:30 - 11:30 and 13:00 - 15:00. Intent orders for blocktrades are accepted between 9:30 and 11:30 and again between 13:00 and 15:30, while execution orders and fixed-price orders for block trades are accepted from 15:00 to 15:30. Special block trade sessions are held on an ad-hocbasis between 15:00 and 17:00.

46

By comparing M2 and FOMC announcements, we address a few notes here. PBOC’s

announcements are made public on any day of a week, whereas the FOMC statement releas-

es predominantly fall on early mornings of Thursdays in Beijing time (Wednesdays P.M. in

the U.S. Eastern Time). In addition, a greater fraction of M2 announcements are publicly

available during off-trading sessions including post-trading hours and between-weeks. How-

ever, the FOMC statements are issued routinely within trading hours around 2:15 PM of

U.S. Eastern time. Accounting for China-U.S. time difference, this FOMC news are initially

accessible by the Chinese market around 2:15 to 3:15 AM of Thursdays of Beijing Time,

depending on whether the U.S. Daylight Saving Time applies.

A.3 Summary of Co-released Announcements

Table A.4 summarizes the number of a labeled announcement that is made public on a

day when some other selected announcements are also published on that day, i.e. co-released

announcements. Out of the 90 M2 announcements, about 20 times, monetary data are

co-released with FAI, VAI and CPI data. Also, FAI and VAI statistics are routinely released

together.

Table A.4: Co-released Announcements

M2 TRD FAI VAI INP PMI CPI RST FOMC

M2 90 7 20 19 18 2TRD 90 1 1FAI 82 76 31 3 1VAI 76 29 3 1INP 42PMI 91 2CPI 90 1RST 76 4FOMC 60

Notes: Sample: January, 2010 to June, 2017. Number in a cell indicates the numberof row announcement events that overlaps with the column announcement events. Anoverlap is counted if both types of labelled announcements fall on the same day. Notethat the sum of row or column numbers does not have to be equal to the total numberof announcement events of a given announcement label.

B Additional Empirical Results

B.1 Return Responses: Alternative Sample Periods

In this section, we examine China’s stock market’s reactions to M2 announcements when

other periods of time are considered. According to Columns (1)(2)(4) and (5) of Table B.1,

the estimation results suggest that the pre-announcement premium is robust regardless of

47

whether sample starts one year earlier or later than 2010, our baseline starting point. The

relative excess return is consistently around 30 bps per day of a three-day window before

announcement. However, when we exclusively focus on a sample period of pre-2010 years,

little evidence can be detected to argue for the existence of pre-announcement premium no

matter how long the pre-announcement window is. This can be explained by the fact that

the stock market was far from sophistication back then when incorporating macroeconomic

news, let alone the irregularity when PBOC started releasing monetary aggregates data in

those years.

Table B.1: Alternative Samples and Reactions to M2 Announcements

(1) (2) (3) (4) (5) (6)VARIABLES 2011-2017 2009-2017 2002-2010 2011-2017 2009-2017 2002-2010

ItM2−1 0.44** 0.31** −0.25+

(0.18) (0.15) (0.17)ItM2−1,3 0.34*** 0.24** -0.14

(0.12) (0.11) (0.13)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes YesConstant -0.28 0.08 -0.03 -0.28 0.08 -0.03

(0.22) (0.22) (0.25) (0.22) (0.22) (0.25)

Observations 1,577 2,063 1,928 1,577 2,063 1,928R2 0.02 0.02 0.03 0.02 0.02 0.03

Notes: This table reports the dummy variable regression results of Equations (1) and (2) for different sample periods.The dependent variable is the close-to-close excess return constructed from the Wind A Share Index. We align the returndata of the first trading day on which the equity market has access to the monetary aggregates data to the dummy variableItM2 = 1 when i = 0. Announcement dummy ItM2−1 equals to one for the day that is one day before an M2 Announcement.Announcement dummy ItM2−1,3 equals to one for the trading days in a 3-trading-day window before an M2 Announcemen-t. ”Other Anns Window Ctrls”: whether or not controls for the remaining day dummies of the announcement window oflength of 2T + 1 as T = 5. ”Year/Month/Weekday Dummies”: the year, month and weekday dummy controls. ***Signifi-cant at 1%, **significant at 5%, *significant at 10%, +significant at 15%. Robust standard errors are shown in parentheses.

B.2 Return Responses: Alternative Market Indices

We discuss the robustness of our baseline results when returns are constructed from other

market indices of Shenzhen (SZSE Index) and Shanghai (SSE Index) stock exchanges. We

run regressions of baseline specification of Equation (1). In Table B.2, our results show that

even if we have removed potential seasonality of equity premium by controlling for year,

month and weekday dummies, coefficients associated with the first, second, and third day

prior to announcement are all positive and large in size, whereas those of post-announcement

dummies are trivial. Returns accumulation of consecutively three days are most noted

when the Wind A share market index is considered per Column (4). However, jumps in

excess returns are statistically significant on the day right before the announcements when

a particular stock exchange is examined according to Columns (5) and (6). In addition, we

see the size of pre-announcement premium is more pronounced for Shenzhen stock exchange

48

relative to that of Shanghai. We offer explanations to account for all these subtle differences

when we discuss the cross-sectional evidence in Section B.8.

Table B.2: Alternative Market Index: Returns in Windows of M2 Announcements

(1) (2) (3) (4) (5) (6)VARIABLES Wind A SZSE Index SSE Index Wind A SZSE Index SSE Index

ItM2−5 0.16 0.15 0.11 0.16 0.15 0.11(0.18) (0.19) (0.15) (0.18) (0.19) (0.15)

ItM2−4 -0.04 -0.09 -0.04 -0.07 -0.12 -0.06(0.19) (0.17) (0.17) (0.20) (0.17) (0.17)

ItM2−3 0.30+ 0.19 0.20 0.29+ 0.17 0.18(0.19) (0.19) (0.16) (0.19) (0.19) (0.16)

ItM2−2 0.23 0.16 0.14 0.25+ 0.19 0.16(0.17) (0.16) (0.14) (0.17) (0.16) (0.14)

ItM2−1 0.41*** 0.34** 0.25** 0.39** 0.32* 0.23*(0.16) (0.16) (0.13) (0.16) (0.17) (0.13)

ItM2 0.21 0.14 0.18 0.22 0.16 0.18(0.16) (0.18) (0.14) (0.17) (0.18) (0.14)

ItM2+1 -0.19 −0.26+ -0.17 -0.21 −0.29+ -0.19(0.17) (0.18) (0.14) (0.17) (0.18) (0.14)

ItM2+2 0.04 -0.11 -0.04 0.02 -0.12 -0.05(0.19) (0.20) (0.18) (0.19) (0.20) (0.18)

ItM2+3 -0.04 -0.09 -0.08 -0.02 -0.07 -0.06(0.18) (0.19) (0.15) (0.18) (0.19) (0.15)

ItM2+4 0.03 -0.02 -0.04 0.01 -0.04 -0.07(0.19) (0.21) (0.17) (0.19) (0.21) (0.17)

ItM2+5 0.02 -0.04 -0.06 0.03 -0.02 -0.05(0.19) (0.19) (0.16) (0.20) (0.19) (0.16)

Year / Month / Weekday Dummies Yes Yes YesConstant -0.04 -0.04 -0.03 -0.28 -0.24 -0.26

(0.06) (0.06) (0.05) (0.21) (0.22) (0.19)

Observations 1,819 1,819 1,819 1,819 1,819 1,819R2 0.01 0.01 0.01 0.02 0.02 0.02

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regression results of Equation (1).The dependent variable is the excess equity return constructed from a different market index. Announcement dummyItM2−i is equal to one if the i-th trading day before (after if i is negative) an M2 announcement. We align the returndata of the first trading day that the equity market has access to the news to the dummy variable ItM2 = 1 when i = 0.***Significant at 1%, **significant at 5%, *significant at 10%, +significant at 15%. Robust standard errors are shownin parentheses.

B.3 Return Responses: Non-monetary Announcements

We examine if the pre-announcement premium associated with releases of monetary ag-

gregates data carries over to other non-monetary macro announcements. Table B.3 reports

the results based on our baseline dummy regression of Equation (1) by looking into win-

dows of other announcement events. Importantly, focusing on a window length of five days

before announcements, we find that China’s stock market also exhibits statistically and sig-

nificant reactions to announcements of VAI, FAI, and CPI. In specific, similar positive

pre-announcement premium can be found. We regard this as key evidence in support of

the channel of uncertainty reduction. Given that aggregate market risk can be shifted by a

range of macro statistics beyond monetary aggregates data, pre-announcement learning of

49

these data helps reduce market risk, which can push up equity prices ex-ante.

We also discuss additional findings of interest in the following. First, for the coefficient

estimate of post-announcement day tAnns+3 regarding to the INP news about industrial

production data, the partial effect is significantly different from zero. Also, in response to

the TRD announcements releasing China’s trade statistics, stock market reacts with a large

40 bps in excess returns relative to no announcement daily returns. However, we should not

confuse these coefficients with those suggest for a pre-announcement premium. Rather, these

evidence suggests that market is simply reacting to these updated statistics conditional on

the release of data. Also, we note that the equity market exhibits trivial or even negative

excess returns in response to incoming announcements of PMI and RST.

Table B.3: Returns in Windows of Other Macro Announcements

(1) (2) (3) (4) (5) (6) (7) (8)VARIABLES M2 TRD VAI FAI INP PMI CPI RST

ItAnns−5 0.16 0.20 0.00 0.01 -0.29+ -0.31 0.02 -0.06(0.18) (0.17) (0.21) (0.20) (0.19) (0.22) (0.20) (0.20)

ItAnns−4 -0.07 0.28 0.40** 0.39** 0.11 -0.20 0.39** 0.13(0.20) (0.20) (0.20) (0.19) (0.24) (0.18) (0.19) (0.17)

ItAnns−3 0.29+ 0.21 0.38* 0.25 -0.22 -0.23 0.17 -0.38**(0.19) (0.18) (0.20) (0.20) (0.20) (0.21) (0.14) (0.19)

ItAnns−2 0.25+ 0.25 0.28 0.23 -0.15 -0.22 -0.06 0.00(0.17) (0.19) (0.20) (0.19) (0.18) (0.20) (0.19) (0.21)

ItAnns−1 0.39** 0.24 -0.02 -0.01 -0.23 0.12 -0.05 -0.01(0.16) (0.18) (0.18) (0.17) (0.18) (0.16) (0.19) (0.21)

ItAnns 0.22 0.37** 0.10 0.14 -0.00 0.21 0.09 -0.35*(0.17) (0.18) (0.21) (0.20) (0.22) (0.20) (0.20) (0.21)

ItAnns+1 -0.21 0.08 -0.02 -0.05 0.06 0.23 0.07 0.03(0.17) (0.17) (0.19) (0.18) (0.19) (0.19) (0.17) (0.21)

ItAnns+2 0.02 0.03 -0.07 -0.03 -0.21 0.19 -0.01 0.01(0.19) (0.19) (0.22) (0.21) (0.21) (0.17) (0.19) (0.18)

ItAnns+3 -0.02 0.17 0.08 0.10 0.51*** 0.06 0.03 -0.15(0.18) (0.14) (0.18) (0.18) (0.16) (0.16) (0.17) (0.20)

ItAnns+4 0.01 0.02 0.10 0.13 -0.01 0.03 0.12 -0.21(0.19) (0.19) (0.21) (0.20) (0.18) (0.16) (0.19) (0.22)

ItAnns+5 0.03 0.06 -0.03 0.00 0.19 -0.05 -0.10 -0.42+(0.20) (0.19) (0.20) (0.19) (0.18) (0.20) (0.19) (0.27)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes Yes Yes YesConstant -0.28 -0.35* −0.32+ −0.31+ -0.26 -0.23 -0.29 -0.28

(0.21) (0.20) (0.21) (0.20) (0.20) (0.20) (0.20) (0.20)

Observations 1,819 1,819 1,819 1,819 1,819 1,860 1,819 1,819R2 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regression results of Equation (1)for announcement windows associated with both monetary and non-monetary data releases. The dependent variable isthe close-to-close excess return constructed from Wind A Share Index. Announcement dummy ItAnns−i equals to oneif the i-th trading day is before (or after if i is negative) a particular type of announcement. We align the return dataof the first trading day that the equity market has access to the news to the dummy variable ItAnns = 1 when i = 0.***Significant at 1%, **significant at 5%, *significant at 10%, +significant at 15%. Robust standard errors are shownin parentheses.

50

B.4 Return Responses: FOMC Statements

We further evaluate if China’s stock market reacts to the U.S. FOMC statement re-

leases. Table B.4 summarizes the key results. Columns (1) and (4) list the coefficients of

pre-announcement dummies of Equations (1) and (2), which suggests that pre-announcment

premium exists when PBOC is about to release the monetary aggregates data. However, by

Columns (2) and (5), we find no evidence that China’s equity market reacts to FOMC state-

ment releases ex-ante. That is, for all lag and lead terms relative to FOMC announcement

days, no daily excess return that is statistically different from zero. This finding differs from

the evidence documented in Lucca and Moench (2015) that the stock markets of a number

of more advanced economies exhibit positive pre-drifts of returns in response to incoming

FOMC announcements.

Importantly, we note the sample difference of our paper, years of 2010-2017 vs. a pre-

2011 period in Lucca and Moench (2015). Hence, our sample captures a period when most

of times the U.S. Federal Funds rate is near a zero lower bound since the end of 2008.It is

possible the U.S. FRB guided the expectations of domestic and international market investors

by minimizing the potential changes in U.S. monetary policy (Yellen, 2015). Market thus

responds little because the aggregate market risk of China assumes little risk from U.S.

monetary policy. Therefore, the implication is that for a sample with more volatile interest

rate changes like pre-2011, we should see Chinese markets react to FOMC news.

However, estimation results using sample years of 2002-2009 do not provide sufficient

evidence to support the claim that China’s equity market significantly responded to FOMC

announcements per Column (6). Though, by Column (3), we see very marginal positive

and negative coefficient estimates associated with daily excess returns two and three days

before the FOMC statement release. Some excess return drops are observed for days after

the statement with a significance level of 10 % according to Columns (3) and (6).

Therefore, it is safe to conclude that China’s equity market does not price in the risk of

the incoming U.S. monetary policy changes as delivered through FOMC statements. Plus, a

constant close-to-zero U.S. Federal Funds rate indicating limited U.S. monetary policy risk

does not help explain the muted reaction of Chinese equity market to FMOC announcements.

In general, non-sophistication of Chinese markets, limited participation of Chinese investors

into foreign capital markets, along with actively managed exchange rate, capital accounts

and trade flows could all isolate China from being affected by market risk that is originated

outside China.

51

Table B.4: China’s Stock Market Responses to FOMC Announcements

(1) (2) (3) (4) (5) (6)VARIABLES M2 FOMC FOMC M2 FOMC FOMC

2010-2017 2010-2017 2002-2009 2010-2017 2010-2017 2002-2009

ItAnns−5 0.16 -0.04 -0.06 0.16 -0.05 -0.05(0.18) (0.18) (0.28) (0.18) (0.18) (0.28)

ItAnns−4 -0.07 -0.14 0.01 -0.07 -0.14 0.02(0.20) (0.21) (0.22) (0.20) (0.21) (0.22)

ItAnns−3 0.29 -0.30 -0.59*(0.19) (0.29) (0.33)

ItAnns−2 0.25 -0.27 0.44*(0.17) (0.26) (0.23)

ItAnns−1 0.39** 0.06 -0.27(0.16) (0.20) (0.28)

ItAnns−1,3 0.31*** -0.17 -0.14(0.11) (0.15) (0.17)

ItAnns 0.22 -0.09 -0.15 0.22 -0.10 -0.14(0.17) (0.22) (0.24) (0.17) (0.22) (0.24)

ItAnns+1 -0.21 0.00 -0.39* -0.21 0.00 -0.38*(0.17) (0.22) (0.22) (0.17) (0.22) (0.22)

ItAnns+2 0.02 -0.09 0.14 0.02 -0.07 0.15(0.19) (0.23) (0.32) (0.19) (0.23) (0.32)

ItAnns+3 -0.02 0.16 -0.36 -0.02 0.16 -0.38*(0.18) (0.19) (0.23) (0.18) (0.19) (0.23)

ItAnns+4 0.01 -0.11 -0.16 0.01 -0.13 -0.16(0.19) (0.19) (0.24) (0.19) (0.19) (0.24)

ItAnns+5 0.03 -0.20 0.22 0.03 -0.21 0.22Year / Month / Weekday Dummies Yes Yes Yes Yes Yes YesConstant -0.28 -0.22 -0.04 -0.28 -0.23 -0.01

(0.21) (0.20) (0.24) (0.21) (0.21) (0.24)

Observations 1,819 1,819 2,037 1,819 1,819 2,037R2 0.02 0.01 0.03 0.02 0.01 0.03

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regression results for specification-s of Equation (1) and Equation (2). The dependent variable is the close-to-close excess return constructed from theWind A Share Index. We align the return data of the first trading day on which the equity market has access to theFOMC news to the dummy variable ItAnns = 1 when i = 0. Announcement dummy ItAnns−i equals to one if the i-thtrading day is before (or after if i is negative) an FOMC Announcement. Announcement dummy ItAnns−1,3 equalsto one for the trading days in a 3-trading-day window before an FOMC Announcement. ”Other Anns Window Ctrl-s”: whether or not controls for the remaining day dummies of the announcement window of length of 2T + 1 as T = 5.”Year/Month/Weekday Dummies”: the year, month and weekday dummy controls. ***Significant at 1%, **significantat 5%, *significant at 10%, +significant at 15%. Robust standard errors are shown in parentheses.

B.5 Return Responses: Monetary Policy Reports

Besides the monthly announcements of monetary aggregates data, Monetary Policy Re-

port is issued every quarter by PBOC, i.e. MPR announcements. We check if the stock

market similarly reacts to the issuance of this policy report. Table B.5 summarizes the

key findings. According to Column (2), the relative excess return per day for a three-day

pre-announcement window is 28 bps, which is positive and statistically significant at the 10

%. Column (4) presents the estimated coefficient of a one-day daily relative premium of 31

bps, which is however not distinguishable from zero in spite of a comparable magnitude to

the number in Column (1) of Table 2. We conclude that the equity market does respond

to issuance of Monetary Policy Reports ex-ante though the estimated size of positive pre-

mium contains larger standard errors. In addition, results of Columns (3) and (6) show the

estimates of the pre-announcement coefficients when all events of M2 and MPR announce-

52

ments are considered. Numbers in these columns suggest that given the similar magnitude,

it is the anticipation of announcements of monetary aggregates data, not the incoming policy

reports, that predominantly drives the pre-announcement premium.

However, greater noises associated with the estimation of pre-announcement premium

in case of MPR announcements may be due to the following facts. First, China’s mone-

tary policy report, though covering statistics about the conducts of Chinese monetary policy,

delivers much more complex information and assessment with little focus on releasing the up-

dated data. Second, monetary aggregates data are published with monthly frequency, which

could be more useful for investors to draw real-time investment implications, as compared

to an encyclopedia style of quarterly issues of Monetary Policy Report.

Table B.5: Returns in Windows Prior to MPR Announcements

(1) (2) (3) (4) (5) (6)VARIABLES M2 Ann. MPR Ann. M2 and MPR Ann. M2 Ann. MPR Ann. M2 and MPR Ann.

ItAnns−1,3 0.31*** 0.28* 0.34***(0.11) (0.17) (0.10)

ItAnns−1 0.39** 0.31 0.37***(0.16) (0.27) (0.14)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes YesConstant -0.28 -0.27 -0.32 -0.28 -0.27 -0.32

(0.21) (0.20) (0.21) (0.21) (0.20) (0.21)

Observations 1,819 1,819 1,819 1,819 1,819 1,819R2 0.02 0.02 0.02 0.02 0.02 0.02

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regression results for specifications of Equation (1)and Equation (2). The dependent variable is the close-to-close excess return constructed from the Wind A Share Index. We align thereturn data of the first trading day on which the equity market has access to the MPR reports to the dummy variable ItAnns = 1 wheni = 0. Announcement dummy ItAnns−1 equals to one for the day that is one day before an MPR Announcement. Announcement dummyItAnns−1,3 equals to one for the trading days in a 3-trading-day window before an MPR Announcement. ”Other Anns Window Ctrls”:whether or not controls for the remaining day dummies of the announcement window of length of 2T + 1 as T = 5. ”Year/Month/WeekdayDummies”: the year, month and weekday dummy controls. ***Significant at 1%, **significant at 5%, *significant at 10%, +significant at15%. Robust standard errors are shown in parentheses.

B.6 Return Responses: Other Markets

We further explore the responses of other asset markets of China to PBOC’s announce-

ments of monetary aggregates data. As response variables, we take the daily returns of 10

year government bond yields, i.e. risk-free rates, and the daily excess returns for Chinese

A share futures of 300 big stocks, gold futures, along with exchange rates of RMB against

major currencies including the U.S. dollar, Japanese Yen, and Euro. According to Table B.6,

we find no excess returns for most asset markets relative to no announcement windows ex-

cept for the stock futures despite of a 10% significance level. This piece of evidence confirms

our main findings that the excess return of stock market portfolios, regardless of whether

it’s computed based on spot or future prices, are particularly responsive to monetary data

releases.

53

Table B.6: Other Markets’ Reactions to M2 Announcements

(1) (2) (3) (4) (5) (6)VARIABLES R10Y,bond FurtureCSI300 FurtureGold EXUSD EXJPY EXEUR

ItM2−1,3 0.12 0.18* 0.04 -0.00 -0.01 -0.03(0.20) (0.11) (0.07) (0.01) (0.05) (0.04)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes YesConstant 0.18 -0.29 0.20* -0.03** 0.14* -0.04

(0.30) (0.24) (0.11) (0.01) (0.07) (0.07)

Observations 1,819 1,750 1,819 1,819 1,817 1,818

Notes: Sample: January, 2010 to June, 2017 (Series of FurtureCSI300 starts from April, 2010). This table reportsdummy variable regression results of Equation (1) different dependent variables. Announcement dummy ItM2−1,3 equalsto one for the trading days in a 3-trading-day window before an M2 Announcement. ”Other Anns Window Ctrls”:whether or not controls for the remaining day dummies of the announcement window of length of 2T + 1 as T = 5.”Year/Month/Weekday Dummies”: the year, month and weekday dummy controls. ***Significant at 1%, **significant at5%, *significant at 10%, +significant at 15%. Robust standard errors are shown in parentheses.

B.7 Forecast Uncertainty: M2 Growth and the Broader Economy

What exactly our empirical measure of uncertainty, the standard deviation of forecast

errors about M2 growth, are measuring for? Does it simply proxy for uncertainty about

monetary policy changes? We show in this section that our forecast-based measure of un-

certainty is more broadly related to the market uncertainty about the general economy, i.e.

aggregate market risk.

We explore these questions by first computing the standard deviation of forecast errors

across all available forecasts per month for a range of macro variables recorded in Bloomberg

Survey Database. Macro series being forecast are YOY growth rates of M1, exports, im-

ports, CPI, PPI, GDP, VAI, and PMI besides the M2 growth. Then, we compute pair-wise

correlation coefficients of monthly forecast error dispersion across variables of forecast. Re-

sults are tabulated in Table B.7. Accordingly, by looking at the first row, it shows that

the forecast error dispersion of M2 growth forecasts is positively correlated with all the rest

of the dispersion measures of other macro variables of forecast except for the series of M1

growth. In particular, correlation coefficients are all statistically significant at the level of 5

%.

54

Table B.7: Correlations: Monthly Dispersion of Forecast Errors

M2 M1 Export Import CPI PPI GDP VAI PMI

M2 1.00 -0.05 0.27 0.40 0.28 0.23 0.81 0.24 0.42(0.63) (0.01) (< 0.01) (0.01) (0.03) (< 0.01) (0.03) (< 0.01)

M1 1.00 0.66 0.55 0.27 -0.04 -0.08 0.12 -0.03(< 0.01) (< 0.01) (0.01) (0.71) (0.7) (0.33) (0.76)

Export 1.00 0.74 0.50 0.15 0.35 0.68 0.30(< 0.01) (< 0.01) (0.17) (0.06) (< 0.01) (< 0.01)

Import 1.00 0.46 0.30 0.54 0.63 0.39(< 0.01) (< 0.01) (< 0.01) (< 0.01) (< 0.01)

CPI 1.00 0.04 0.70 0.62 0.43(0.69) (< 0.01) (< 0.01) (< 0.01)

PPI 1.00 0.45 0.14 0.38(0.01) (0.23) (< 0.01)

GDP 1.00 0.76 0.77(< 0.01) (< 0.01)

VAI 1.00 0.44(< 0.01)

PMI 1.00

Notes: Sample: January, 2010 to June, 2017. This table shows the pearson correlation matrix of stan-dard deviation of forecast errors regarding a series of macroeconomic variables. P-values are reported in theparentheses.

Further, at the forecaster level, we estimate the following specification to disentangle the

associations between the size of forecast error about a macro variable and that regarding M2

growth.

|FEij,m| = α + γi|FEM2

j,m |+ βi,xXm + υij,m (B.1)

In Equation (B.1), |FEij,m| denotes the absolute value of forecaster j’s forecast error regarding

a given macro variable i of month m. Absolute value proxies the magnitude of making errors

relative to the true state of variable. i = M2 captures the absolute forecast error for M2

growth. We control for year and forecaster dummies in covariates vector Xm.

Regression results are collected in Table B.8. Panel A presents the regression results

regarding the correlations of absolute values of forecast errors at the forecaster level. Columns

(1)(3)(4) suggest that a forecaster’s uncertainty about M1 growth, imports growth, and

growth of value added are all positively correlated with the uncertainty about M2 growth with

statistical and economic significance. For robustness, we also take the standard deviation of

forecast errors about M2 growth as regressor, i.e. our measure of uncertainty at the aggregate

level. We examine if individual’s size of forecast errors about other macro variables are at

least correlated with that of a “representative” forecaster about M2 growth at the aggregate

level. Estimation results are shown in Panel B. Across columns, we see that uncertainty

about growths of M1, VAI, GDP, PMI and CPI are all correlated with uncertainty about

M2 growth.

55

Table B.8: Forecast-level Regressions: Forecast Errors Across Macro Variables

Panel A : Baseline

(1) (2) (3) (4) (5) (6) (7)VARIABLES M1 Export Import VAI GDP PMI CPI

|FEM2j,m| 0.27* 0.42 1.12*** 0.09** 0.07 0.01 0.01

(0.15) (0.38) (0.39) (0.05) (0.05) (0.03) (0.01)Year / Forecaster Control Yes Yes Yes Yes Yes Yes YesConstant 0.51+ 12.73*** 26.80*** 2.06*** 0.35** 0.53*** 0.57***

(0.34) (2.71) (3.73) (0.34) (0.14) (0.07) (0.09)

Observations 588 1,781 1,774 1,412 542 1,119 1,638R2 0.12 0.09 0.22 0.16 0.39 0.32 0.13

Panel B : Alternatives

(1) (2) (3) (4) (5) (6) (7)VARIABLES M1 Export Import VAI GDP PMI CPI

S.D. of FEM2j,m 0.68*** 0.21 1.25 0.30*** 0.12** -0.07 0.06**

(0.21) (0.39) (0.92) (0.07) (0.06) (0.06) (0.02)Year / Forecaster Control Yes Yes Yes Yes Yes Yes YesConstant -0.25 12.79*** 26.66*** 1.53*** 0.32*** 1.06*** 0.48***

(0.21) (2.47) (2.94) (0.31) (0.10) (0.20) (0.07)

Observations 963 1,896 1,884 1,576 686 1,666 1,827R2 0.11 0.09 0.21 0.16 0.41 0.31 0.13

Notes: Sample: January, 2010 to June, 2017. The table displays the regression results regarding coefficientestimates of βi per Equation (B.1) for i refers to YOY growth rate of M1, Export, Import, VAI, GDP, PMI,and CPI. |FEij,m| denotes the absolute value of forecaster j’s forecast error regarding a given macro variable

i of month m. i = M2 captures the absolute forecast error for M2 growth. ***Significant at 1%, **signifi-cant at 5%, *significant at 10%. Standard errors are clustered at forecaster level and shown in parentheses.

In sum, both the correlation analysis and the regression results suggest that our mea-

sure of uncertainty about M2 growth represents a general uncertainty about the broader

economy. As shown in Figure 9, uncertainty declining before M2 announcements reflects

that learning among investors that reduces uncertainty about M2 growth also helps resolve

market uncertainty about a range of other macroeconomic variables and thus the aggregate

market risk.

B.8 Cross-sectional Heterogeneities

In this section, we explore the potential heterogeneities in stock reactions to the M2

announcements. By sorting stocks into portfolios by market value and book-to-market ratio,

we show that the magnitude of premium varies across portfolios. We note that our docu-

mented heterogeneities in China’s stock market are absent from the U.S. market (Lucca and

Moench, 2015). Importantly, we find that the heterogeneities are not driven by differences

in firm ownership, i.e. State-Owned-Enterprises (SOE) vs. Non-SOEs, which is a critical

dimension in studies of Chinese economy and its financial market (Song et al., 2011). In

56

addition, shares of institutional holdings do not help explain the heterogeneities in return

responses.

We first sort the A-share stocks into five portfolios by the market value of firm’s total

equity, i.e. Size Portfolios. Then we run estimations according to the specification of E-

quation (2) for each portfolio. Panel A of Table B.9 summarizes the key estimation results.

It shows that portfolios of small and medium-sized stocks exhibit positive and large pre-

announcement premium in response to monetary news. Relative jumps in excess returns

can be as high as about 54 bps per day of a three-day pre-announcement window across

the four smaller size portfolios. However, the portfolio that is consisted of large-cap stocks

displays a coefficient that is about one third of that of other portfolios, not to mention its

marginal significance at the level of 10%. We thus conclude that larger stocks exhibit limited

reactions prior to PBOC’s monetary announcements. Per Column (7) of Table 2, we say

that at the aggregate level, the relative daily excess return of around 30 bps in a three-day

pre-announcement window is mainly driven by ex-ante reactions of small and medium-cap

stocks.

Further, we are concerned that the return heterogeneities across size portfolios may be

explained by differences in SOE shares of firm ownership. In Panels B and C, we present ad-

ditional evidence regarding estimations for five sorted size portfolios of two separate groups:

SOE and non-SOE firms. Results of the two panels confirm that small and medium-cap

stocks exhibit sizeable pre-announcement premium regardless of whether the firm is SOE

or non-SOE. Comparatively, the largest portfolio of non-SOE stocks exhibit larger premium

than that of SOE stock portfolios of the same size. This may be explained by the fact that

the market value of non-SOE firms’ total equity from the largest size portfolio is relatively

smaller than that of SOE firms’ stocks of large caps.

57

Table B.9: Size Portfolios

Portfolio Small 2 3 4 Large

Panel A: Size Portfolio

ItM2−1,3 0.54*** 0.53*** 0.52*** 0.49*** 0.18*(0.14) (0.14) (0.14) (0.14) (0.10)

Panel B: SOE Sample

ItM2−1,3 0.54*** 0.52*** 0.50*** 0.46*** 0.16*(0.14) (0.14) (0.14) (0.13) (0.10)

Panel C: Non SOE Sample

ItM2−1,3 0.55*** 0.54*** 0.54*** 0.50*** 0.24**(0.14) (0.14) (0.14) (0.14) (0.11)

Year / Month / Weekday Dummies Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes YesObservations 1,819 1,819 1,819 1,819 1,819

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regres-sion results of Equation (2) for size portfolios. The dependent variable is the value weightedaverage excess return of each size portfolio. Portfolios are sorted by market value of firms’total equity. The breakpoint is re-calculated every year and is based on market value quin-tiles. Announcement dummy ItM2−1,3 equals to one if it is in the three-trading-day windowbefore an M2 announcement. ***Significant at 1%, **significant at 5%, *significant at 10%,+significant at 15%. Robust standard errors are shown in parentheses.

Secondly, we regroup A-share stocks into five portfolios according to the listing firm’s

book-to-market ratio, i.e. BM Portfolios. Similarly, with and without a further breakdown

by firm’s ownership, we look for difference in size of pre-announcement premium across

portfolios. Regression results per Equation (2) are collected in Table B.10. Results in Panel

A find that only the portfolio of firms with smallest Book-to-Market ratio, i.e. the growth

stocks exhibit sizable pre-announcement premium that roughly doubles that of other four

portfolios. Panels B and C display portfolio-based estimation results by firm ownership. We

see that non-SOE firm portfolios that cover stocks of medium and large BM ratios exhibit

relatively larger pre-announcement reactions.

58

Table B.10: BM Portfolios

Portfolio Low 2 3 4 High

Panel A: BM Portfolio

ItM2−1,3 0.46*** 0.25** 0.25** 0.21* 0.26**(0.13) (0.10) (0.10) (0.11) (0.11)

Panel B: SOE Sample

ItM2−1,3 0.43*** 0.14 0.19** 0.18* 0.28**(0.13) (0.09) (0.09) (0.10) (0.11)

Panel C: Non SOE Sample

ItM2−1,3 0.50*** 0.48*** 0.44*** 0.30** 0.23**(0.13) (0.13) (0.13) (0.12) (0.11)

Year / Month / Weekday Dummies Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes YesObservations 1,819 1,819 1,819 1,819 1,819

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regres-sion results of Equation (2) for size portfolios. The dependent variable is the value weightedaverage excess return of each BM portfolio. Portfolios are sorted by firms’ book-to-marketratio. The breakpoint is re-calculated every year and is based on BM ratio quintiles. An-nouncement dummy ItM2−1,3 equals to one if it is in the three-trading-day window beforean M2 announcement. ***Significant at 1%, **significant at 5%, *significant at 10%, +sig-nificant at 15%. Robust standard errors are shown in parentheses.

Given that both dimensions of size and BM ratio may drive the heterogeneities and the

pre-announcement premium of BM portfolios are sensitive to firm ownership differences, we

further apply a two-way sort of stocks to clear up the findings. The two-way sorting of stocks

by size and BM ratio gives us nine portfolios. Relevant regression coefficients regarding the

day tM2−1,3 relative excess returns are similarly organized in Table B.11. Key findings can

be summarized in the following.

First and foremost, focusing on Panel A, it shows that the size of market value of equity

is the dominant dimension by which the size of pre-announcement premium is affected. In

specific, we see within portfolios of small and medium cap stocks, differences in BM ratio

generates no extra heterogeneities across portfolios. Second, we move towards Panel B and

consider firm ownership differences. We find that stock portfolios of largest stocks of SOE

firms exhibit little pre-announcement premium, whereas stocks of largest non-SOE firms are

more responsive to monetary announcements. This is because the market value of largest

SOE firms is much higher than that of the largest cap stocks of non-SOE firms.

59

Table B.11: Size and BM Two-way Sorted Portfolios

(1) (2) (3) (4) (5) (6) (7) (8) (9)Portfolio (S, L) (S, M) (S, H) (M, L) (M, M) (M, H) (B, L) (B, M) (B, H)

Panel A: Size & BM Portfolio

ItM2−1,3 0.55*** 0.55*** 0.54*** 0.54*** 0.53*** 0.49*** 0.27*** 0.16* 0.22**(0.14) (0.14) (0.14) (0.14) (0.14) (0.14) (0.10) (0.10) (0.11)

Panel B: SOE vs. non-SOE

SOE sample:ItM2−1,3 0.57*** 0.53*** 0.54*** 0.49*** 0.51*** 0.48*** 0.18* 0.12 0.24**

(0.14) (0.14) (0.14) (0.14) (0.14) (0.14) (0.09) (0.09) (0.11)

non-SOE sample:ItM2−1,3 0.55*** 0.57*** 0.55*** 0.57*** 0.55*** 0.48*** 0.45*** 0.32*** 0.16

(0.14) (0.14) (0.14) (0.15) (0.14) (0.14) (0.13) (0.12) (0.11)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes Yes Yes Yes YesObservations 1,819 1,819 1,819 1,819 1,819 1,819 1,819 1,819 1,819

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regression results of Equation (2) forsize-BM portfolios. The dependent variable is the value weighted average excess return of each size-BM portfolio. For a ∈Small(S),Medium(M), Big(B) and b ∈ Low(L),Medium(M), High(H), (a, b) indexes the portfolio of size of a and BM ratio ofb. For example, (S, L) denotes the portfolio of stocks with the smallest market value and lowest book-to-market ratio. Portfolios aretwo-way sorted by firms’ size and book-to-market ratio. The breakpoint is re-calculated every year. Announcement dummy ItM2−1,3

equals to one if it is in the three-trading-day window before an M2 announcement. ***Significant at 1%, **significant at 5%, *signifi-cant at 10%, +significant at 15%. Robust standard errors are shown in parentheses.

In sum, we document the heterogeneities in stock return reactions to M2 announcements

across size portfolios. Small and medium-cap stocks in China are particular responsive to

releases of monetary aggregates data. This holds true regardless of SOE and non-SOE

firm ownership differences. In the following, we examine why these portfolios exhibit large

sensitivities to PBOC’s announcements of monetary data.

It is worth noting that the ease of credit in China, as proxied by money growth, may

directly affect the market liquidity and trading of small and medium cap stocks. We thus

explore if the shares of institutional holdings, which reflects the intensity of institutional

trading, help generate a “trading premium”, which serves the basis for the pre-announcement

premium exhibited among small and medium-cap stock portfolios. We first do a two-way

sort of the stocks by size of firms’ equity and shares of institutional holdings and group

them into nine portfolios. We run similar regressions of Equation (2) and report the results

in Table B.12. Accordingly, results suggest that size of total equity is still the key factor

that drives the heterogeneities whereas trading behaviors of institutions affect little the pre-

announcement premium.

Our model framework, however, helps rationalize why size matters so much for the varia-

tions in the magnitude of pre-announcement premium across portfolios. Our model suggests

that investors of portfolios of small and medium cap stocks could be particularly sensitive

to the loss due to inadequate attention paid to learning about money growth. Therefore,

attentive learning helps reduce forecast uncertainty, which delivers extra returns to investors

of these portfolios prior to announcement. We make the following notes to elaborate this

60

point.

In terms of both the availability of total credit and the financing cost, portfolios of these

stocks could have exposed themselves with extra sensitivity to the numbers behind PBOC’s

monetary announcements. First, credit misallocation is a key concern for small and medium-

sized firms, especially when non-SOE firms are even smaller. Conversely, larger firms and

SOE firms in general have better access to formal credits.34 Hence, increased money growth

and credit expansion means that smaller and non-SOE firms are faced with a greater pool

of extended credits. Second, small and medium-sized firms are more likely to be financially

constrained. They are thus very responsive to changes to the cost of borrowing that are

indirectly affected by money growth.

Table B.12: Size and Shares of Institutional Holdings Two-way Sorted Regressions

(1) (2) (3) (4) (5) (6) (7) (8) (9)Portfolio (S, L) (S, M) (S, H) (M, L) (M, M) (M, H) (B, L) (B, M) (B, H)

ItM2−1,3 0.54*** 0.56*** 0.54*** 0.52*** 0.52*** 0.52*** 0.24** 0.29** 0.12(0.14) (0.14) (0.14) (0.14) (0.14) (0.14) (0.11) (0.12) (0.09)

Year/Month/Weekday Dummies Yes Yes Yes Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes Yes Yes Yes YesObservations 1,819 1,819 1,819 1,819 1,819 1,819 1,819 1,819 1,819

Notes: Sample: January, 2010 to June, 2017. This table reports dummy variable regression results of Equation (2) for size-Sharesof Institutional Holdings (SIH) portfolios. The dependent variable is the value weighted average excess return of each size-SIHportfolio. For a ∈ Small(S),Medium(M), Big(B) and b ∈ Low(L),Medium(M), High(H), (a, b) indexes the portfolio of sizeof a and SIH of b. For example, (S, L) denotes the portfolio of stocks with the smallest market value and lowest share of equitiesheld by institutions. Portfolios are two-way sorted by firms’ size and SIH ratio. The breakpoint is re-calculated every quarter. An-nouncement dummy ItM2−1,3 equals to one if it is in the three-trading-day window before an M2 announcement. ***Significantat 1%, **significant at 5%, *significant at 10%, +significant at 15%. Robust standard errors are shown in parentheses.

C Alternative Model with Recursive Preference

C.1 Expected Return and Uncertainty about Money Growth

Alternatively, we work with a more elaborated model when investors have recursive pref-

erence in form of Kreps-Porteus and Epstein-Zin utilities. An explicit relationship between

the expected excess return of stock market portfolio and the risk-aversion weighted forecast

uncertainty about money growth can be derived.

This model is discrete-time and each period t corresponds to a day. A representative

household maximizes its life-time utility Vt(ct, zt) for day t, which is defined over real con-

sumption ct and the certainty equivalent of day t expected continuation value zt such that

Vt(ct, zt) = maxct,xt,bt∞t=0

[(1− β)c1−ξt + β(EtV 1−α

t+1 )1−ξ1−α ]

11−ξ . (C.1)

34See Song et al. (2011) and Chen et al. (2016)

61

where zt = (EtV 1−αt+1 )

11−α . ξ and α respectively indexes the inverse of household’s elasticity

of inter-temporal substitution and the coefficient of relative risk aversion. We work with

parameter values of α > 1 > ξ such that household prefers early resolution of uncertainty.

Household chooses consumption ct, equity holding xt, and holding of risk-free bond bt

that pays one unit of consumption good in period t+ 1. β ∈ (0, 1) is the subjective discount

factor. Utility maximization is subject to a daily budget constraint

ct + qtxt +bt

Rft+1

= (qt + yt)xt−1 + bt−1 (C.2)

where qt is the per share equity price. yt is the per share dividend payout. The gross rate of

risk-free bond return is given by Rft+1 known as of day t. By definition, the rate of return

from risky equity investment is Rt = qt+ytqt−1

. A portfolio investment with share of holdings φt

invested in equity and 1− φt in the riskless bond on day t gives an aggregate market rate of

return for tomorrow RW,t+1 = Rft+1+φt(Rt+1−Rf

t+1). With the beginning-of-day total wealth

Wt = (qt + yt)xt−1 + bt−1, budget constraint is equivalently given by Wt+1 = (Wt− ct)RW,t+1.

In addition, we impose the constraint of cash-in-advance that necessarily binds in equi-

librium such that the total consumption is financed by holding of real balance of monetary

aggregate Mt with ct = ψMt.35 Given household’s dividend income is consumed every period

yt = ct, it follows that yt = ψMt. Now define mt as the growth rate of real money balance

in log, mt = log(Mt) − log(Mt−1). We thus have ct+1

ct= emt+1 . Also, in equilibrium, the

aggregate holding of risk-free bond bt has to be zero with φt = 1 and thus RW,t+1 = Rt+1.

Imposing constant equity price-dividend ratio χ = qtyt

for simplicity, we derive the first

order condition which gives the key asset pricing equation in the following

1 = Et[βθe−ξθmt+1Rθt+1] (C.3)

where related terms can be factored into a stochastic discount factor Ωt|t+1 = βθe−ξθmt+1Rθ−1t+1

such that 1 = Et[Ωt|t+1Rt+1] and θ = 1−α1−ξ . This equation says that by affecting the stochastic

discount factor, investors’ forecast of money growth mt+1 can shift the expected equity

returns.

We show that the expected excess equity return in log EXt+1|t is determined by the risk-

aversion α weighted investors’ forecast uncertainty about future money growth as of day t,

35Alternatively, we can reinterpret this equilibrium condition as quantity theorem of money. Constantψ > 0 thus measures the velocity of money.

62

σ2m,t+1.

EXt+1|t = log(EtRt+1)− log(Rft+1) = α · σ2

m,t+1 (C.4)

Equation (C.4) suggests that forecast uncertainty about money growth amounts to total

aggregate market risk, which determines the size of equity premium. Larger uncertainty

raises the expected excess return.

Note that Equation (C.4) holds regardless of whether we are working with a recursive

utility or not. For example, α = ξ renders the recursive preference to be time-separable,

which gives to investors’ optimization over conventional expected utility. Therefore, the

expected excess return of stock market portfolio increases in aggregate market risk which is

shifted by investors’ uncertainty about future money growth. Necessarily, lowered forecast

uncertainty reduces the expected risk premium by raising current stock prices and current

returns.

C.2 Signal is Backward-looking and Imperfect

In this section, we consider a more complex structure of central bank’s signals. That is,

money growth is announced with time lags and measurement errors. In specific, the central

bank makes an announcement on day tAi of month i about the money growth realized in the

end of previous month i− 1 such that

stAi = mti−1+ ηtAi (C.5)

where ηtAi ∼ N(0, σ2η) captures the innovations to measurement errors of the signal. This

signal structure sharply differs from the real-time signal modelled in the main section, by

which the announcement releases data about the realization on the announcement day tAi .

We start with a scenario in which investors’ learning is not endogenous. It follows that

only the arrivals of central bank’s announcements affect investors’ conditional expectation

and forecast variance about money growth. Upon the arrival of announcement on day

tAi+1 = ti + T , investors’ forecast of mti+j for j ≥ T with new information incorporated is

given by

mti+j|tAi+1= ρjmti|tAi+1

+ (1− ρj)µ (C.6)

Note the new announcement would directly revise the back-cast of mti by updating mti|tAiwith mti|tAi+1

. According to Equation (C.6), it shows again that forecast of mti+j is some

63

weighted average of prior belief and unconditional mean of money growth. By the same

token, the expected variance of money growth is given by

σ2m,ti+j|tAi+1

= ρ2jσ2m,ti|tAi+1

+ (1− ρ2j)σ2e

1− ρ2(C.7)

Consistent with implications suggested by Equations (6) and (7), the mean forecast and

forecast uncertainty further in the future get increasingly closer to the unconditional moments

of µ and σ2e

1−ρ2 as j goes up.

Now we look at how mti|tAi is updated to mti|tAi+1. Applying the Bayes’s rule, the updated

forecast linearly combines the forecast that is carried over and the announcement signal

weighted by their relative informativeness. It yields that

mti|tAi+1= (1− κ)mti|tAi + κstAi+1

(C.8)

where κ =1/σ2

η

1/σ2η+1/σ2

m,ti|tAi

captures the Kalman gain of information, which measures how

much the updated forecast should be weighted towards the new signal. It shows that more

precise signal of smaller σ2η or a rough forecast of greater σ2

m,ti|tAiraises the Kalman gain.

Consequently, the updated forecast uncertainty must satisfy the following

1

σ2m,ti|tAi+1

=1

σ2m,ti|tAi

+1

σ2η

(C.9)

Equation (C.9) implies that given more informative signal of smaller ση, forecast uncertainty

about money growth in the end of previous month is further reduced.

Hence, uncertainty about money growth up to day tAi+1 = ti + T is consequently lower

conditional on arrivals of announcement. The size of uncertainty reduction ∆σ2m,tAi+1

can be

derived:

∆σ2m,tAi+1

= ρ2T [σ2m,ti|tAi

− σ2m,ti|tAi+1

]

= ρ2Tσ2m,ti|tAi

σ2m,ti|tAi+1

σ2η

(C.10)

The second equality directly comes from Equation (C.9). Important to note that given

perfect signals as if we are in the baseline model environment such that ση → 0, uncertainty

reduction is infinity, which leads to ex-post uncertainty of σ2m,tAi+1

→ 0.

Then, considering endogenous learning, similar attention allocation rules of equation sys-

tem (14) apply. The associated forecast uncertainty dynamics can be similarly summarized

64

by equation systems (C.11), and (C.12)

σ2m,t =

(1− φt)σ2m,t + φtσ

2m,t2

−2κ if φt ∈ [ vσ2m,t

22κ, 1] and t 6= tAi

(1− φt)σ2m,t + v if φt ∈ [ v

σ2m,t, vσ2m,t

22κ) and t 6= tAi

σ2m,t if φt ∈ [0, v

σ2m,t

) and t 6= tAi

min 1σ−2m,t+σ

−2η, (1− φt)σ2

m,t + φtσ2m,t2

−2κ∗ if t = tAi

(C.11)

where σ2m,t can be written as function of forecast uncertainty of day t − 1 after learning

decision of previous day was taken.

σ2m,t = ρ2σ2

m,t−1 + σ2e (C.12)

Note that contrary to the equation system (15), on announcement days, the forecast un-

certainty would not be zero but get updated according to Equation (C.9) given imperfect

signals. In addition, depending on the parametrization, there is some possibility such that

endogenous learning paid that is before investors knowing about if an announcement is made

may generate even lower forecast uncertainty.

In sum, regardless of whether we have simple or more complex signal structure, learning

can trigger uncertainty reduction, which leads to reduced expected risk premium and higher

current returns.

C.3 Derivation of the Loss Function of Learning for Investors

In this section, with recursive preference, we explicitly derive an objective function of

quadratic form for investors’ optimization of attention allocation. Investors’ value function

at optimum Vt(ct, zt) is Homogeneous of Degree One in arguments ct and zt. Conditional on

optimized consumption of previous period ct−1 > 0, it yields that

Vt(ct, zt) = ct−1Vt(ctct−1

,ztct−1

) = ct−1Vt(ect , ezt)

where ct = log[ ctct−1

] and zt = log[ ztct−1

]. Up to a second-order Taylor expansion of Vt(ct, zt)

around any arbitrary couplet point of (ct, zt), we have

Vt(ect , ezt) = Vt(e

ct , ezt) + Vt,1ect(ct − ct) + Vt,2e

zt(zt − zt)

+Vt,11

2ect(ct − ct)2 +

Vt,22

2ezt(zt − zt)2 + Vt,12e

ctezt(ct − ct)(zt − zt) (C.13)

65

where Vt,1 and Vt,2 are partial derivatives of Vt with respect to the first and second arguments

evaluated at the centering couplet (ct, zt). Vt,11, Vt,22, and Vt,12 are the associated second order

partials and cross-partials. Given Equation (C.13), optimization over current consumption

ct gives the first order condition:

Vt,1 + Vt,11(ct − ct) + Vt,12ezt(zt − zt) = 0

Hence, the following identity holds that ct and zt are linearly related at optimum:

ct = a+ bzt (C.14)

where a = ct − Vt,1Vt,11

+ Vt,12ezt ztVt,11

, b = −Vt,12Vt,11

ezt > 0.

Therefore, when evaluating Vt(ect , ezt) up to the second order around the real optimum

couplets (c∗t , z∗t ), it yields:

Vt(ect , ezt) = Vt(e

c∗t , ez∗t )− φt,c(ct − c∗t )2 − φt,z(zt − z∗t )2 + φt,cz(ct − c∗t )(zt − z∗t )

Note that first order conditions about ct and zt hold at optimum such that the first order

terms cancel out to zeros due to the fact that V ∗t,1 = 0 and V ∗t,2 = 0 . Other partials and

cross-partials evaluated at the optimum couplets are absorbed into terms φt,c = −ec∗t V∗t,11

2> 0,

φt,z = −ez∗t V∗t,22

2> 0, and φt,cz = V ∗t,12e

c∗t ez∗t > 0.

Define loss function L(ct, zt) = ct−1L(ct, zt) where

L(ct, zt) = Vt(c∗t , z∗t )− Vt(ct, zt)

=λt2

(ct − c∗t )2

The second equality directly follows from the fact that investors choose ct and zt according

to Equation (C.14) for any chosen couplets. Hence, after substituting out zt and z∗t , we have

λt = 2(φt,c + φt,zb2− φt,cz

b) ≥ 0 as some time-varying constant depending on the true states,

which makes the loss non-negative. Imposing the equilibrium condition of ct = ψMt yields

that log[ ctct−1

] = log(Mt) − log(Mt−1) = mt, we are able to express the loss function in form

of volatility of money growth rate due to suboptimal beliefs.

That is, abstracting from constant λt which is independent of investors’ beliefs, investors

thus optimize the attention allocation in order to minimize the expected gap of real state

66

and all perceived states of mt such that

1

2E(mt −m∗t )2

D Proofs

D.1 Proof of Equation (C.3)

For ease of notations, we first define mct and mVt+1 in the following:

mct =∂Vt∂ct

= (1− β)V ξt c−ξt

mVt+1 =∂Vt∂Vt+1

= βV ξt (EV 1−α

t+1 )α−ξ1−αV −αt+1

By the fact that V (ct, zt) is Homogeneous of Degree One in ct and zt, we can show that the

following equation hold at the optimum.

Vt = mct · ct + E[mVt+1 · Vt+1]

Define Wt = Vtmct

, it follows that

Wt = ct + E[mVt+1 ·mct+1

mct· Wt+1]

Rearranging, we have

1 = E[mVt+1 ·mct+1

mct· Wt+1

Wt − ct]

In the following, we show the stochastic discount factor can be defined as Ωt|t+1 = mVt+1·mct+1

mct

and RW,t+1 = Wt+1

Wt−ct such that Wt = Wt at optimum. Maximizing equation (C.1) subject to

Equation (C.2) when expressed in function of beginning-of-day wealth Wt, it yields that the

first order condition regarding optimal wealth level of t+ 1 is given by

E[mVt+1 ·∂Vt+1

∂Wt+1

·RW,t+1] = mct

67

with marginal value of wealth at t given by ∂Vt∂Wt

= mct according to the Envelope Theorem.

It hence gives

1 = E[mVt+1 ·mct+1

mct·RW,t+1]

and we have Wt = Wt = Vtmct

at optimum. The stochastic discount factor is thus

Ωt|t+1 =βV ξ

t (EV 1−αt+1 )

α−ξ1−αV −αt+1(1− β)V ξ

t+1c−ξt+1

(1− β)V ξt c−ξt

=β[ct+1

ct]−ξ[

Vt+1

[EV 1−αt+1 ]

11−α

]ξ−α

The equilibrium return of the market portfolio RW,t+1 can be expressed as

RW,t+1 =Wt+1

Wt − ct

=Vt+1/[(1− β)V ξ

t+1c−ξt+j]

Vt/[(1− β)V ξt c−ξt ]− ct

= β[ct+1

ct]−ξ[

Vt+1

[EV 1−αt+1 ]

11−α

]ξ−1−1

Now substitute out the ratio of future value relative to the certainty equivalence Vt+1

[EV 1−αt+1 ]

11−α

as function RW,t+1 from the stochastic discount factor, we have the following holds for all

states

Ωt|t+1 = β[ct+1

ct]−ξ[R−1

W,t+1/(β[ct+1

ct]−ξ)]

ξ−αξ−1

= βθ[ct+1

ct]−ξθRθ−1

W,t+1

where θ = 1−α1−ξ .

Hence, in equilibrium, stock market portfolio return satisfies Rt+1 = Rw,t+1 such that

1 = E[mVt+1 ·mct+1

mct·Rt+1]

Similarly, following holds for the risk free rate Rft+1.

1 = E[Ωt|t+1 ·Rft+1] (D.1)

68

D.2 Proof of Equation (C.4)

By Equation (C.3), we exploit the assumption that price-dividend ratio is constant χ.

1 = E[(β(1 + χ)

χ)θ · e(1−α)mt+1 ]

Given that the AR(1) process governing the real money growth has the lognormal structure,

we have the following

log[1 + χ

χ] = −[log β + (1− ξ)mt+1 +

(1− ξ)(1− α)

2σ2m,t+1]

By Equation (D.1), it follows that

1 = E[βθe−ξθmt+1(1− χχ

emt+1)θ−1 ·Rft+1]

Rft+1 can be solved as

log(Rf ) = − log β + ξmt+1 +ξ − α− αξ

2σ2m,t+1)

Per the fact that Rt+1 = 1+χχ

ct+1

ct, the expected equity return follows

ERt+1 = E((1 + χ)

χemt+1)

It solves that

log(ERt+1) = − log β + ξmt+1 +ξ + α− αξ

2σ2m,t+1

Hence, EXt+1|t = log(ERt+1)− log(Rft+1) follows.

69

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