Market
Expectations
System
Information up to June 2016
Frequently Asked Questions Series
1
“Frequently Asked Questions” Series
Central Bank of Brazil
1.
Interest Rates and Bank Spreads
3.
Monetary Policy Committee (Copom)
2.
4.
Price Indices in Brazil
Fiscal Data
5.
Regulated Prices
7.
Brazilian Payments System
6.
8.
Public Securities and Public Debt Management
External Accounts
9.
Country Risk
11.
Functions of the Central Bank of Brazil
10.
12.
Inflation Targeting Regime in Brazil
Reserve Requirements
13. Market Expectations System
14.
Monetary Policy, Open Market Operations and FX Swap
15.
Economic Indicators
17.
Gross Domestic Product (GDP)
16.
Banking Credit in Brazil
Economic Policy Deputy Governor
Carlos Viana de Carvalho
Team
Coordinator
André Barbosa Coutinho Marques
Renato Jansson Rosek
Carolina Freitas Pereira Mayrink
Henrique de Godoy Moreira e Costa
Luciana Valle Rosa Roppa
Luiza Betina Petroll Rodrigues
Authoring and publishing
Manuela Moreira de Souza
Investor Relations and Special Studies Department (Gerin)
Maria Cláudia Gomes P. S. Gutierrez
Brasília-DF
Márcio Magalhães Janot
This publishing is part of the Financial Education Program of the Central Bank of Brazil (BCB).
2
Market Expectations System
This paper is part of the Banco Central do Brasil’s “Frequently Asked Questions”
series (FAQ). This series, which is produced by the BCB’s Investor Relations and
Special Studies Department (Gerin), provides information on economic topics of
interest to investors and the general public.
The Banco Central do Brasil (BCB) is producing this series as part of its ongoing
efforts to enhance the transparency of the Brazilian economic policy and the
effectiveness in communicating its actions.
3
Contents
General View ............................................................................................................................................ 6
1.
What is the information collected by the Market Expectations System? .......................................................... 6
2.
What is the importance of market expectations? .................................................................................................. 6
Expectations collection ........................................................................................................................... 7
3.
When was the Market Expectations System implemented? ............................................................................... 7
4.
Who can provide information (expectations) to the System? .............................................................................. 7
5.
How many institutions participate as information providers? ............................................................................ 8
6.
How is the market information collected? .............................................................................................................. 8
7.
Which expectations are collected, and in which format are they informed? ..................................................... 8
8.
What is the validity of the data recorded in the System? ................................................................................... 10
9.
Are the participants obliged to provide information? ......................................................................................... 11
10.
What happens when an institution ceases to inform its projections? ......................................................... 11
Disclosed information ...........................................................................................................................11
11.
What are the main products published? ........................................................................................................... 11
12.
What information does the Focus - Market Report provide? ........................................................................ 12
13.
Are changes in the median of an indicator always caused by changes in the surveyed participants’
expectations? ...................................................................................................................................................................... 12
14.
How is the expectation for the inflation accumulated over the next-12 months calculated? ................. 13
15.
How is the expectation for the inflation accumulated over the next 12 months, smoothed, calculated?
15
16.
How can I obtain daily time series of market expectations collected by the Market Expectations
System? ............................................................................................................................................................................... 19
17.
Is it possible to query individual information? ................................................................................................. 19
Top Five ...................................................................................................................................................20
18.
What is the incentive for the institutions to maintain the expectations updated? .................................... 20
19.
What are reference dates? .................................................................................................................................. 20
20.
How are the Top 5 institutions classified, for which variables and in which horizons? ............................ 20
21.
Is there any precondition for the institutions to participate in the Top 5? .................................................. 22
22.
Which is the formula used for the calculation of the Short Run Top 5 monthly rankings? ...................... 23
23.
Which is the formula used for the calculation of the Medium-Run Top 5 rankings? ................................ 24
24.
Which is the formula used for the calculation of the Long-Run Top 5 rankings, annually released? ..... 25
4
25.
What are the formulas used for the calculation of the Annual Top 5 Rankings (Short Run and Medium
rankings)? ............................................................................................................................................................................ 25
5
Market Expectations System
General View
1. What is the information collected by the Market Expectations System?
They are projections prepared by institutions operating in the financial market, such as banks,
asset managers and consultants and, in some cases, companies of the real sector that have
specialized teams who produce estimates for the main macroeconomic variables, in order to
assist the decision making by professionals of the institution itself as well as by its external
customers. The projections, in many cases with the help of econometric modeling, are
performed for variables related to economic activity, interest rates and exchange rates, the
variation of price indices, the balance of payments and the fiscal sector of the Brazilian economy.
Expectations can be collected in several ways, such as conducting surveys with market
professionals or consumers, or from information extracted from financial assets such as
inflation-linked bonds. The Market Expectations System, developed by the Central Bank of Brazil
(BCB), is a system for the collection of market economists’ macroeconomic projections.
2. What is the importance of market expectations?
The market expectations are important inputs to the monetary policy decisions. Moreover,
the availability of their statistics to the general public, through the BCB's website, enables
enterprises and citizens to be aware about what the market agents are projecting, thereby
constituting an important tool for planning their actions in the short, medium and long term.
6
Expectations collection
3. When was the Market Expectations System implemented?
The market expectations survey started in May 1999. During this period, the BCB's economic
area developed studies and econometric models for the projection of inflation and other
macroeconomic variables, in order to provide the necessary technical tools for the formal
implementation in June 1999 of the inflation targeting regime. The market expectations for
inflation showed, then, strong disparity due to the uncertain backdrop that followed the collapse
of the exchange rate anchor.
Initially, about fifty financial institutions and consultancies were contacted and informed to
the BCB by phone, fax or email of the annual projections for the main price indices (IGP-DI, IGPM and IPA), besides the GDP growth. Subsequently, the survey on market expectations became
more sophisticated, due to the larger number of participants, the incorporation of new variables
(other indicators on inflation, exchange rate, interest rate, fiscal data and the Balance of
Payments variables) and the monthly or quarterly data, in addition to the annual data.
With the growing importance of monitoring expectations for the monetary policy, in
November 2001 the Market Expectations System's webpage was created. It has as main
objectives:
 to ensure the greater speed and safety in the collection process and
 to minimize the occurrence of information errors.
The data started to be provided online, at any time, by institutions previously accredited,
which received from the BCB a specific password for the access to the IT platform.
In 2010, a new set of improvements enhanced the integrity to the system, as the existing
modules were integrated on a single IT platform, with unique processing, thus increasing the
processing agility and maintaining the reliability of their routines and statistics.
4. Who can provide information (expectations) to the System?
The Market Expectations System is an online tool, developed for the web environment, which
can be accessed through the link http://www.bcb.gov.br/expectativas, restricted to the Investor
Relations and Special Studies Department (Gerin) of the BCB and previously accredited
institutions.
New institutions can only be included in the survey by the System administrators after the
applicant informs the respective registration data and of the assignment of specific login and
password. In principle, any entity (banks and other financial institutions, nonfinancial companies,
consultancies, class associations, universities, etc.) may request participation in the research, as
long as they have a specialized team on macroeconomic projections and update their projections
regularly.
7
5. How many institutions participate as information providers?
Currently, about 130 logins are enabled, mostly banks, asset managers, dealers and brokers,
as well as consulting and other non-financial companies. In the universe of qualified institutions,
most of them update their expectations weekly.
6. How is the market information collected?
Gerin is the department responsible for the administration of the Market Expectations
System, a web interface, where financial institutions, consulting firms and companies of the
non-financial sector, previously authorized, inform their expectations for various macroeconomic
variables.
The access can be done at any time, with no pre-set schedule for updates. However, data
reported after 5:00 pm only impact the statistics produced by the System on the following
business day. This happens because every business day at 5:00 pm, the information is
consolidated and several statistics are generated - averages, medians, standard deviations,
coefficients of variation, minimum and maximum values of the expectations recorded by the
participants.
The System also has checks for the consistency and robustness of the data. Certain variables
can be entered directly or calculated from other variables. For example, the expectation for the
trade balance may be informed or calculated by the System based on the expectations for
exports and imports in the same period. If such data have previously been entered, the System
calculates the trade balance and blocks the projection of this variable, to ensure consistency of
information.
7. Which expectations are collected, and in which format are they
informed?
Table 1 shows the 24 variables whose expectations are collected by the Market Expectations
System. As shown in the table, the System receives daily a limited number of monthly, quarterly
and annual expectations for each variable. In addition, the type of information inserted in the
System varies.
8
Table 1– Variables with Expectations Collected by the Market Expectations System
Number of projections
Variable
type
Variable to be forecasted
collected by the System
Monthly
IGP-DI, IGP-M, IPA-M, IPA-DI, IPCA,
FX Rate
18
0
5 [a] y/y % [c]
y/y % [c]
0
6
5 [a]
y/y % [c]
18 [d]
0
5 [e]
[e]
0
0
5
Annual average
18 [d] [f]
0
5 [e]
[e]
GDP or Service GDP
Ptax- annual average
Target for
Selic Target - end-of-period
Annually
0
GDP, Agriculture GDP, Manufacture
(R$/US$)
Quarterly/
0
Industrial Production
Ptax- end-of-period
terly
Annually Monthly
0
Regulated Prices
activity
Quar-
in the System
18
Price index IPCA-15 or INPC
Economic
Type of projection inserted
5 [a] m/m % [b] y/y % [c]
5
y/y % [c]
Selic rate
Selic Target – annual average
0
0
5
Annual average
External
Exports and Imports
0
0
5
Sector
Value in US$
Trade Balance
0
0
5 [g]
Balance of
Current Account Result
0
0
5
Direct Investment Liabilities [h]
0
0
5
0
0
5
0
0
5
0
0
5
payment
Primary Result of the Consolidated
Public Sector
Fiscal
Nominal Result of the Consolidated
Public Sector
Net Public Sector Debt
billions
Value in US$
billions
% of GDP
[a] As part of the solutions for checking the internal consistency of data, the field on the annual projection for the current year is calculated
automatically if there are monthly/quarterly information for every month/quarter of the year. In this case, the System will calculate the annual
figure, considering the effective results already released and the monthly/quarterly projections informed. If some of the monthly/quarterly
projections is missing, the System allows the participant to inform its annual projection.
[b] m/m % = change in comparison to the previous month, without seasonal adjustment.
[c] y/y % = change in comparison to the [same period of the] previous year, without seasonal adjustment.
[d] Monthly information related to December (or the last month in which there is a Copom meeting, in the case of Selic) is automatically assigned
to the end of the annual period, and vice versa, and the annual average is calculated in case all relevant monthly expectations are informed.
[e] Value in the last day of the period.
[f] From the moment the Copom calendar for following year is known, projections for the Selic rate for the months with no meetings cannot be
registered in the system.
[g] The input of exports and imports data eliminates the need of information on the trade balance.
[h] Up to March 2015, the collected variable was "Foreign Direct Investment". Click here for more details on the methodological change (in
Portuguese).
Note: Statistics for the annual inflation may differ from the monthly inflation statistics, accumulated in the year, since the samples may be
different, given that a few institutions inform only annual projections, others only the monthly ones, and there is no obligation to inform every
month. Thus, the samples of institutions that inform each monthly projection and each annual projection are different. Furthermore, the
accumulation of the monthly medians would not necessarily be equal to the respective annual median, even if the samples were the same.
Source: BCB.
Price Indices
The inflation indicators IGP-DI, IGP-M, IPA-DI, IPA-M, IPCA, IPCA-15, INPC and IPC-Fipe
follow the same rules, as shown in Table 1.
9
As part of the solutions for checking the internal consistency of data, the annual expectation
field is calculated automatically if there are monthly information for all the months of the year. In
this case, the System will calculate the cumulative inflation in the year, considering the effective
results already released and the monthly projections informed, recording the annual projection
of the participant. If some of the monthly projections is missing, the System allows the
participant to inform its annual expectation.
Is worth mentioning that the statistics for the annual inflation may differ from the monthly
inflation statistics, accumulated in the year, since the samples may be different, given that a few
institutions inform only annual projections, others only the monthly ones, and there is no
obligation to inform every month. Thus, the samples of institutions that inform each monthly
projection and each annual projection are different. Furthermore, the accumulation of the
monthly medians would not necessarily be equal to the respective annual median, even if the
samples were the same.
Economic Activity
Similar to what happens to price indices, for GDP (and industrial production), the projection for
the current year is automatically calculated, if all quarterly (monthly) expectations have been
informed. Otherwise, the institution may inform the projection for the current year. As soon as
the effective quarterly (monthly) data are released, they are incorporated to the annual result
calculation for the respective year. For both variables, projections are informed as percentage
growth over the same period of the previous year.
Exchange Rate and Selic Target Rate
For these indicators, monthly information related to December (or the last month in which
there is a Copom meeting, in the case of Selic target rate) is automatically assigned to the end of
the annual period, and vice versa, and the annual average is calculated in case all relevant
monthly expectations are informed. From the moment the Copom calendar for following year is
known, projections for the Selic target rate for the months with no meetings cannot be
registered in the System.
8. What is the validity of the data recorded in the System?
The System only considers the data reported in the last thirty days. That is, if an institution
does not inform their expectations again within thirty days, the System automatically saves the
value in the data base, but it will stop considering it in the calculation of the statistics. The aim of
the 30 days limit is to prevent the statistics from loading outdated projections. So even if
expectations have not undergone any modification, the qualified institution must confirm the
data within a range of thirty days to keep it active in the statistics calculation.
10
After thirty days without update, expectations remain in the system, with access through
historical series for Gerin and the participating institution, but are not included in the calculation
anymore.
9. Are the participants obliged to provide information?
There is no mandatory provision of information. There are participating institutions that
specialize in forecasting some variables and do not provide projections for the others.
10. What happens when an institution ceases to inform its projections?
Gerin periodically checks whether the information provided by the System participants is
updated or not, and blocks the input of those which have been for at least six months without
any activity. Thus, the participant's occasional return to the system will depend on a specific
contact requesting the reinstatement of the previous status.
Disclosed information
11. What are the main products published?
From the data collected, the System can calculate in real time the sample statistics,
generating daily reports to the Board. In addition, it generates weekly the "Focus - Market
Report" ("Market Readout"), available to the public at the BCB's internet website, in Portuguese
and English.
The statistics produced by the system and released by the the BCB include the median, mean,
standard deviation, coefficient of variation, maximum and minimum for all variables collected,
including those of the Top 5 institutions group for the possible horizons - up to 18 months, 6
semesters or five years ahead, as the case may be. Because it is less subject to swings of the
extremes, the median expectation is the statistic more closely monitored and disclosed
(including the recent graphical evolution) in the "Focus - Market Report" every Monday regularly
at 8:30 am, with the data collected until the previous Friday. The historical series of statistics are
available since January 2000 in the BCB's website on the internet also updated weekly on
Mondays, along with disclosure of "Focus - Market Report".
Besides the Focus - Market Readout, other reports are published at the BCB's website, such
as the Top 5 ranking (on a monthly and annual basis), and the Focus - Frequency Distributions
(this one just in Portuguese), which compares in three recent moments the shape of the
frequency distributions relative to the projections for the annual IPCA and for the Selic rate
twelve months ahead.
Other reports, used by the BCB Board, are generated periodically.
11
12. What information does the Focus - Market Report provide?
The Market Report provides the following information, together with the graphical evolution
of the indicators and of their weekly behavior:
 The median market expectations for the inflation over the next 12 months, smoothed, for
the IPCA, IGP-DI, IGP-M and IPC -Fipe;
 The median market expectations for the next month for which IPCA and IGP-DI have not
yet been published and for the subsequent month (IPCA, IGP-DI, IGP-M, IPC-Fipe,
exchange rate at period-end and Selic target rate at period-end);
 The median expectations for the next year for which IPCA and IGP-DI have not yet been
published and for the subsequent year (IPCA, IGP-DI, IGP-M, IPC-Fipe, exchange rates
average and at period-end, Selic target rate average and at period-end, net public sector
debt/GDP, real GDP growth, industrial production growth, current account of the Balance
of Payments, Trade Balance, Direct Investment Liabilities and % change in administered
prices);
 The mean and the median expectations of the Top 5 institutions of short and medium term
for the next month for which IPCA and IGP-DI have not yet been published and the
subsequent month (IPCA, IGP-DI, IGP-M, exchange rate at period-end and Selic target rate
at period-end);
 The mean and the median expectations of the Top 5 institutions of short and medium term
for the next year for which IPCA and IGP-DI have not yet been published and for the
subsequent year (IPCA, IGP-DI, IGP-M, exchange rate at year-end and Selic target rate at
period-end).
It is important to highlight that the Focus Report does not present BCB projections, but
consolidated expectations from the market agents that participate on the Market Expectations
System. Besides, the emphasis on the medians, and not on the averages, is based on the fact
that the median is less influenced by extreme values. The historical series of every statistics
calculated by the System may be accessed here.
13. Are changes in the median of an indicator always caused by changes
in the surveyed participants’ expectations?
No. When a monthly or quarterly indicator is released, the Market Expectations System
includes this value in the calculation of the annual indicator since the day of its release, for each
participant, thus affecting statistics of that day. Therefore, even with no changes provided by the
participants in their monthly expectations on the day of the release of the monthly indicator, the
annual indicator changes individually and automatically, proportionally to the difference between
the released value for the monthly indicator and its respective expectation. This occurs for every
participant that has all monthly expectations for the remaining months of that year, and the
annual statistics consequently changes.
12
Let’s suppose, for example, that on a certain day when a monthly IPCA is to be released a
participant has a monthly expectation of 0.5% for the previous month (the one the IPCA to be
released refers to), this institution has projections for all the remaining months of the current
year, and its projection for the annual IPCA is 5%, calculated by the System as a result of the so
far released monthly IPCA changes and the expectations of this institution for the remaining
months of the current year. Let’s also suppose that the monthly IPCA is effectively 1.5%, and not
0.5% as projected by the institution. At the end of the same day the System recalculates the
projection of this institution for the annual IPCA replacing the monthly projection of 0.5% by the
effective 1.5%, and the result is higher than the previous one, even with no changes provided by
the institution in any monthly projection for the remaining months of the current year. The same
happens for every institution having monthly projections for all the remaining months of the
current year. Therefore, averages, medians and other annual statistics will change. Then, when
there is a surprise in a monthly indicator, such as price indices and industrial production, the
respective expected annual indicator may change in a proportion as big as this surprise, even
though no individual change has been provided in the monthly expectations of the participants,
regarding the remaining months of the year. The same occurs for quarterly variables such as
GDP growth. Besides that, a similar behavior occurs for the projected annual average of
exchange and Selic target rates, and for inflation for the next 12 months, regarding price indices.
14. How is the expectation for the inflation accumulated over the next-12
months calculated?
The expectation for the inflation accumulated over the next 12-months is calculated daily for
each institution which have expectations for all twelve months of the period considered. The
calculation is done by accumulating expectations for monthly inflation.
Figure 1 shows the steps followed by the System to calculate the expectation for inflation
accumulated over the next 12-months and their descriptive statistics.
Figure 1 – Expectation for the Inflation Accumulated Over the Next 12 months – Calculation
Steps for a Given Price Index
Step 1: make a list of registered institutions and their monthly expectations for the given price index, valid on the
day of the calculus (day “d”).
Result for day “d”: a list with ”n” institutions registered in the Market Expectations System: institution 1,
institution 2, ..., institution n.
13
Step 2: separate the institutions which have 12 consecutive monthly expectations valid, the first of which being
the next month (the first not-yet-released value for inflation)
Result for day “d”: a list with “z” institutions and their respective expectations for monthly inflation

z≤n

each institution has 12 monthly expectations which will be used in the calculus: e1, e2, e3, ..., e12
Step 3: calculate, for each of the z institutions, the inflation accumulated over the next 12 months
For each institution, the System calculates:
[(1 +
𝑒1
100
) ∗ (1 +
𝑒2
100
) ∗ … ∗ (1 +
𝑒12
100
) − 1] ∗ 100 = E = institution’s expectation for the inflation accumulated over
the next 12 months, measured for a given price index, on the day “d”

Table 2 illustrates the calculation made in this step

Repeat this calculation “z” times (once for each institution)

Result for day “d”: “z” expectations for inflation accumulated over the next 12 months (one for each
institution)

Step 4: calculate the descriptive statistics
The System calculates mean, median, maximum, minimum, standard deviation and coefficient of variation of the
"z" expectations calculated in Step 3.

Total after the calculation: 6 descriptive statistics of expectations valid on day “d”

This step is identical for all variables collected by the Market Expectation System
Source: Gerin. These steps are the same for the calculation of inflation measured by any of the price indices collected. These steps are followed
daily by the System.
The descriptive statistics for the inflation accumulated over the next 12 months, measured by
a given price index, may change daily, for the following three reasons:
 The number of institutions with valid expectations changes when:
> New institutions are registered in the System and start to inform their expectations;
> Some institutions cease to have valid monthly expectations (see Question 7);
 Expectations change: some institutions log in the System and change their monthly
expectations;
 The months considered change: when a monthly inflation figure is released (by IBGE, FGV
or Fipe), the 12-month-interval taken into account for the calculation changes, and
therefore the expectation for the inflation accumulated over the next 12 months may also
change.
Taking the IPCA as example, suppose:
 we are in July 2016,
 the latest information released by the IBGE was the the index in June 2016, published on
July 8th,
14
 the next IPCA release, the July index, is scheduled to be released on August 10th,
 a given institution (“X”) has, in July 15th, the monthly expectations for IPCA shown in Table
2, all in percentages.
The expectation of institution “X” for the accumulated inflation for the next twelve months, in
July 15th, would be the multiplicand of these variations, in decimal format (1 +
𝑒𝑥𝑝𝑒𝑐𝑡𝑎𝑡𝑖𝑜𝑛
up to 0.35 (12 months ahead) which results 5.2397%.
100
) of 0.77
Table 2 – Expectation for Inflation Accumulated Over the Next 12 months – Example for
Institution “X”
Month to
which the
expectation
refers to
Institution ”X”’s expectations
(valid on July 15th) for the
Expectation (on July 15th) for inflation
(1+ expectation/100)
monthly IPCA inflation
accumulated over the next 12 months
(multiplicand of the previous column):
from July/16 to June/17
jul/16
0.77
1.0077 (1.0077)*(1.0089)
ago/16
0.89
1.0089
set/16
0.31
1.0031 *(1.0031) *(1.0030)
out/16
0.30
1.0030
nov/16
0.40
1.0040 *(1.0040) *(1.0040)
dez/16
0.40
1.0040
jan/17
0.40
1.0040 *(1.0040) *(1.0035)
fev/17
0.35
1.0035
mar/17
0.30
1.0030 *(1.0030) *(1.0030)
abr/17
0.30
1.0030
mai/17
0.35
1.0035 *(1.0035) *(1.0035) - 1
jun/17
0.35
1.0035
= 5.2397%
Source: Gerin. Expectations shown in this table are hypothetical.
To know more about price indices, see FAQ 2- Price Indices in Brazil.
15. How is the expectation for the inflation accumulated over the next 12
months, smoothed, calculated?
Expectation for the inflation accumulated over the next 12 months, smoothed, of each
institution registered in the System is calculated from the expectations for the inflation
accumulated over the next 12 months (calculated according to the steps shown in Question 14).
At each publication of a price index1, the twelve-month period (used for the calculation of
inflation accumulated over the next 12 months) changes. The monthly inflation data just
released ceases to compose the original set of twelve months. This value is replaced by the
expectation following the 12th month of the original period (which would thus be the 13th month
with respect to the original period).
1
IGP-DI, IGP-M, INPC, IPA-DI, IPA-M, IPCA, IPCA-15 or IPC-Fipe.
15
Often there is a significant difference between the expectation for the month that comes out
and the expectation for the month that will be included in the calculation, implying a leap in the
twelve-month inflation expectation. Chart 1 shows that some leaps occur when IPCA figures
are released, exactly because of this difference.
Chart 1 – Median of Expectations for IPCA Inflation Accumulated over the Next 12 Months
(July 2015 to June 2016)
7.3
7.1
6.9
%
6.7
6.5
6.3
6.1
5.9
5.7
Jun 16
May 16
May 16
Apr 16
Mar 16
Feb 16
Feb 16
Jan 16
Dec 15
Dec 15
Nov 15
Oct 15
Sep 15
Sep 15
Aug 15
Jul 15
Jul 15
5.5
median of expectations for the inflation accumulated over the next 12 months
dates when IPCA (IBGE's CPI) was released
Source: BCB’s Market Expectation System and IBGE.
In order to smooth out these jumps, the difference is distributed pro-rata between the day of
publication of a monthly indicator and the day of publication of the same indicator for the
following month. The result is the expectation for the inflation accumulated over the next 12
months.
Continuing with the example of Question 14, suppose the maintenance of that institution's
expectations from July 9th to August 10th (as shown in Table 3). The expectation for the inflation
accumulated inflation over the next 12 months, from July 2016 to June 2017 (12th month ahead)
is 5.2397%, as already explained. When July 2016 IPCA figure is released, on August 10th, the
twelve-month period changes (out July 2016 and enters August 2017). This change involves
replacing a percentage of 0.77 by a percentage of 0.50 (and the accumulated on this day, August
10th, would change from 5.2397% for 4.9577%, causing a jump in historical series).
16
Table 3– Expectation for Inflation Accumulated over the Next 12 Months Smoothed –
Example for Institution “X”
Month to
Institution ”X”s expectations
which the
for the monthly IPCA
expectation inflation (stable from July 9
refers to
th
Expectation for inflation accumulated over the next
12 months (multiplicand of the previous column):
(1+
expectations/100)
to August 10 )
th
from July/16 to June/17
from August/16 to
July/17
jul/16
0.77
1.0077 (1.0077)*(1.0089)
ago/16
0.89
1.0089
set/16
0.31
1.0031 *(1.0031) *(1.0030)
out/16
0.30
1.0030
nov/16
0.40
1.0040 *(1.0040) *(1.0040)
dez/16
0.40
1.0040
jan/17
0.40
1.0040 *(1.0040) *(1.0035)
fev/17
0.35
1.0035
*(1.0035)*(1.0030)
mar/17
0.30
1.0030 *(1.0030) *(1.0030)
*(1.0030) *(1.0035)
abr/17
0.30
1.0030
mai/17
0.35
1.0035 *(1.0035) *(1.0035) - 1
jun/17
0.35
1.0035
jul/17
0.50
1.0050
(1.0089)*(1.0031)
*(1.0030) *(1.0040)
*(1.0040)*(1.0040)
*(1.0035)*(1.0050) - 1
= 5.2397%
=4.9577%
Source: Gerin.
The smoothed inflation distributes this leap between the consecutive publication dates, pro-
rata, until all changes are incorporated into the day August 10th. Thus, the leap is eliminated
without loss of information.
The calculation steps are described in Figure 2. If there is a change of the monthly
expectations between the dates of IPCA release, the differences are distributed pro rata in the
same way.
Figure 2 - Expectation for the Inflation Accumulated over the Next 12 Months Smoothed –
Calculation Steps for a Given Price Index
Step 1: take the “z” institutions listed in Step 2 of Figure 1. Separate those which have 13 monthly consecutive
expectations valid on day “d”, for the given price index, the first of which being the next month (the first notyet-released value for inflation)

Result for day “d”: a list with “w” institutions and their respective 13 expectations for monthly inflation

w≤z≤n
Step 2: : calculate, for each of the w institutions, the inflation accumulated over the next 12 months smoothed
For each institution with 13 monthly expectations “ej” valid (j= 1, ..., 13) on day “d”, the System calculates:
{(1 +
𝐸
100
) ∗ [(1 +
𝑒13
100
) ÷ (1 +
𝑒1
100
(𝑛𝑑𝑡⁄𝑛𝑑𝑝)
)]
− 1} ∗ 100 = S = institution’s expectation (on day “d”) for the
inflation accumulated over the next 12 months smoothed, measured by the given price index
17
“E” is the expectation for the inflation accumulated over the next 12 months, for this institution, price index,

on day “d”, as explained in Question 14;

𝑒13 is the intitution’s expectation for the monthly inflation 13 months ahead on day “d”;

𝑒1 is the intitution’s expectation for the monthly inflation 1 month ahead on day “d”;

ndt is the number of days between the release of the last inflation figure and the day “d”;

ndp is the number of days between the release of the last inflation figure and the next release of this given
price index;
Result for day “d”: “w” expectations for inflation accumulated over the next 12 months smoothed (one for

each institution).
Step 3: calculate the descriptive statistics
The System calculates mean, median, maximum, minimum, standard deviation and coefficient of variation of
the "w" expectations calculated in Step 2.
Total after the calculation: 6 descriptive statistics of expectations valid on day “d”

Source: Gerin. These steps are the same for the calculation of inflation measured by any of the price indices collected. These steps are followed
daily by the system.
Chart 2 compares IPCA Inflation Accumulated over the Next 12 Months Smoothed to Non-
Smoothed, showing the effect of smoothing over the leaps of original series.
Chart 2 –Medians of Projections for the IPCA Inflation Accumulated over the Next 12 Months
median of expectations for the inflation accumulated over the next 12 months
median of expectations for inflation accumulated over the next 12 months, smoothed
Fonte: Gerin.
To know more about price indices, see FAQ 2- Price Indices in Brazil.
18
Jun 16
May 16
Apr 16
Mar 16
Feb 16
Jan 16
Dec 15
Nov 15
Oct 15
Sep 15
Jul 15
7.3
7.1
6.9
6.7
6.5
6.3
6.1
5.9
5.7
5.5
Jul 15
%
(July 2015 to June 2016) – Smoothed vs. Non-Smoothed
16. How can I obtain daily time series of market expectations collected by
the Market Expectations System?
The BCB's Market Expectations System collects market expectations and produces
descriptive statistics (mean, median, maximum, minimum, standard deviation and coefficient of
variation) of these expectations. These descriptive statistics form daily time series, which are
available online to the public.
Figure 3 shows the initial screen consultation of historical series.
Figure 3 - Market Expectations System - Consolidated Statistics Query Screen
Source: BCB-Gerin.
17. Is it possible to query individual information?
No. The confidentiality of information is guaranteed. Only the institution itself, besides Gerin,
as the system administrator, has access to the individual data.
19
Top Five
18. What is the incentive for the institutions to maintain the expectations
updated?
With the aim of encouraging the improvement of the predictive ability of the survey
participants and rewarding their analytical effort, the BCB prepares the Top 5 ranking, a
classification system of the institutions based on the accuracy of their projections for the short,
medium and long term. The medians and means of the projections informed by the five
institutions with the best performance (the Top 5) are disclosed in the "Focus-Market Report".
19. What are reference dates?
Regarding the variables subject to the Top 5 rankings (IPCA, IGP-DI, IGP-M, exchange rate
and Selic target rate), the error or deviation from the actual values of these variables are
calculated based on expectations valid on specific dates, the “reference dates”. On these dates,
the participant must have valid expectations registered in the system, i.e. reported in the last 30
days, otherwise some penalties will apply. Furthermore, the absence of valid projections (three
monthly and one annual) on the last reference date for each period (or pair of dates in the cases
of exchange and Selic rates) implies the exclusion of the participant from the respective monthly
ranking.
Consequently, there is a greater update of information by the participants on these reference
dates. The reference dates are the following:
 IPCA: last business day preceding the date of release of the IPCA-15;
 IGP-DI: last business day preceding the date of release of the IGP-M 2nd 10-day period;
 IGP-M: last business day preceding the date of release of the IGP-M 1st 10-day period;
 Exchange Rate: last day of the previous month and last business day before or on the 15 th
of the current month;
 Selic rate: last business day before or on the Wednesday of the week preceding the Copom
meeting of the reference period and the last business day before or on the 4th Wednesday
preceding the Copom meeting of the reference period.
To be considered on a certain date, reference or not, the expectations must be included in the
Expectations System before 5:00 pm, at the latest. At 5:00 pm, the statistics are generated and
data registered thereafter will impact the statistics only on the next business day.
20.
How are the Top 5 institutions classified, for which variables and in
which horizons?
20
The Top 5 rankings of short and medium term are published every month. In the short-term
ranking, one evaluates the accuracy of the projections with a one month lag in comparison to the
actual value released for the indicator, over the last 6 months (
Figure 4, first diagram). The medium term ranking considers the average accuracy of the
projections over three consecutive 4-month periods in relation to the effective results over three
months - the reference month and the two preceding months (
Figure 4, second diagram). The long-term ranking considers the accuracy of the projections
reported along 12 months for the annual index published in January of the following year (
Figure 4, third diagram). For the rankings of short, medium and long term, the statistics
related to the five institutions with better rating (or more institutions, if any ties) make up the
historical series published on the BCB website under the reference "Top 5 Institutions".
Figure 4 – Top 5
Short Term
month:
projections (weight):
n-5
n-4
n-3
n-2
n-1
n
1
1
1
1
1
1
n-5
n-4
n-3
n-2
n-1
n
4
3
2
1
4
3
2
1
3
2
1
actual:
Medium Term
month:
projections (weight):
4
actual:
Long Term
month: Jan
projections (weight):
12
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
11
10
9
8
7
6
5
4
3
2
actual:
21
Dec YEAR
1
Source: BCB.
Since January 2009, a new annual category has been designed for the short and medium
term rankings, considering, for each institution, a linear transformation of the deviations used for
the monthly calculation in the short and medium term rankings, in such a way that the for each
month institution that obtains the lowest monthly absolute deviation in a certain ranking for a
given variable and in a given period is awarded 10 points, the institution that obtains the largest
absolute monthly deviation in the same ranking for the same variable and the same term is
assigned zero point, and the other institutions are awarded points, interpolated, between zero
and 10. After the monthly points have been calculated, the average of the monthly values for
each participant in the calendar year that has just ended is calculated and the annual rankings
are determined. In order to be considered in these rankings, the institutions must have been
classified into at least six monthly rankings in the calendar year (or four, in the case of the Selic
rate) in each horizon (having started their projections, therefore, until the last day of the sixth
month of the 12 months) and still: a) in the case of short-term, the deviations of the parcels
referring to each monthly ranking calculation are equal to the average absolute deviation of the
participating institutions for each of the dates prior to the start of their projections, according to
the deviation that would have been assigned to these institutions if they had been included in
the calculation of the ranking for each of these months - the linear transformation to the new
ranking follows the pattern already mentioned; and b) in the case of the medium-term, instead
of the average absolute deviation, the maximum absolute deviation is used. In this way, the
consistence with the calculation procedures used for the monthly Top 5 of short and medium
term is maintained. Thus, for each of the 12 months (or 8 meetings for the Selic) of the calendar
year, variable (IPCA, IGP-DI, IGP-M, Exchange Rate and Selic) and maturity (short and medium)
the institutions have scores ranging from zero to 10 and the average of these figures is the base
variable for calculating the annual ranking. In the case of the Selic rate, instead of twelve months
(and at least six participations), eight meetings (and at least four participations) should be
considered. The intermediate parcels for the calculations of the deviations and the average
notes are always rounded to the fourth decimal place.
21. Is there any precondition for the institutions to participate in the Top
5?
Some criteria applicable to all types of classification of the participating institutions have
been defined for the purpose of imposing penalties for institutions that do not comply with the
minimum requirements of transparency and timeliness in their projections: when calculating a
given monthly ranking, the institutions that have not confirmed or updated within 30 days prior
to the final reference date (or to each of the dates that make up the last couple of reference
dates, in the case of the exchange rate and the Selic - details below), and at least three monthly
projections and one annual, are excluded from the ranking.
22
For example, in the calculation of the short term ranking for the exchange rate in January
2007, which is released in February 2007, the institutions that do not have valid expectations on
the two dates that make up the last couple of reference dates for January, that is, on December
29, 2006 (last working day of the previous month), and on January 15, 2007, are not classified. If
the system identifies, for any institution, that there is no valid expectation on those dates, this
institution does not participate in this ranking, for this variable. Valid expectations on a certain
day refers to those included in the Expectations System and which have been confirmed or
updated within the 30 calendar days prior to that date.
22. Which is the formula used for the calculation of the Short Run Top 5
monthly rankings?
The equation for calculating the monthly deviations used in the preparation of short-term Top
5 rankings is presented below.
Each institution "R" receives a penalty  R CP, which is a simple average of the penalties
received in each of the six months considered for the Top 5 Short Term.
In the Short Term monthly ranking, the institutions are classified based on  R CP, defined in
the Equation 1.
Equation 1:
𝑁
𝑅
𝜓 𝐶𝑃 = { ∑ {(𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑒𝑛𝑎𝑙𝑡𝑦)𝑑𝑡 ∙ (1 − 𝑗𝑑𝑡 ) + 𝑗𝑑𝑡
𝑡=𝑁−5
∙ [(𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑒𝑛𝑎𝑙𝑡𝑦)𝑑𝑡 ∙ (1 − 𝑘𝑑𝑡 ) + (𝐸𝑑𝑡 𝜏𝑡𝑅 − 𝜏𝑡 ) ∙ 𝑘𝑑𝑡 ]}} ÷ 6
where:
 R CP = penalty assigned to the Institution R;
t = month for which the deviation is calculated;
N= month related to the last reference date of the calculation period;
d t = reference date of  in the month t;
E d t  tR = projection of the institution R which is valid in d t for  t (in the cases of exchange and
Selic rates, there are two reference dates);
 t = actual result of the surveyed variable  in month t;
(average penalty)dt = absolute average deviation of the valid projections on d t , for  t , in
relation to the actual result in month t;
(maximum penalty)dt = maximum deviation of the valid projections on d t , for  t , in relation to
the actual result in month t;
k d t = 0, when the institution does not have valid projection on d t ;
23
=1, when the institution does not have valid projection on d ;
t
jd t = 0, if d t precedes the day on which the institution first recorded its projections for
(even if the institution recorded blank cells as its projections);
= 1, if d is equal or after the day on which the institution was enabled to inform its
t
projections for  .
23. Which is the formula used for the calculation of the Medium-Run Top
5 rankings?
The equation for calculating the monthly deviations used in the preparation of medium-term
Top 5 rankings is presented below.
In the Medium Term monthly ranking, the institutions are classified based on:
 R MP, as defined in the Equation 2.
Equation 2:
𝑁
𝑅
𝜓 𝑀𝑃 = { ∑ (𝑁 − 𝑡 + 1)
𝑡=𝑁−3
3
𝑅
∙ ∑ [(𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑒𝑛𝑎𝑙𝑡𝑦)𝑑𝑡−𝑤+1 ∙ (1 − 𝑘𝑑𝑡−𝑤+1 ) + (𝐸𝑑𝑡−𝑤+1 𝜏𝑁−𝑤+1
− 𝜏𝑁−𝑤+1 )
𝑤=1
⋅ 𝑘𝑑𝑡−𝑤+1 ]} ÷ 30
where
 R MP= penalty assigned to the institution R;
t = month for which the deviation is calculated;
N= month related to the last reference date of the calculation period;
w= set of projections for the same monthly indicator;
d t -w 1 = reference date of  in the month t-w+1;
E d t -w 1 NR w1 = projection of the institution R which is valid on d t -w 1 for  N w1 (in the cases of
Exchange and Selic rates, there are two reference dates);
 N w1 = actual result of the surveyed variable  in the month N-w+1;
(maximum penalty)dt-w 1 = maximum absolute deviation of the projections valid on d t -w 1 , for
 N w1 , in relation to the actual result;
k d t -w 1 = 0, when the institution does not have valid projection on d t -w 1 ;
= 1, when the institution has valid projection on d t -w 1 .
24
24. Which is the formula used for the calculation of the Long-Run Top 5
rankings, annually released?
The equation for calculating the monthly deviations used in the preparation of long-term Top
5 rankings is presented below.
In the Long Term monthly ranking, the institutions are classified based on:
 R LP, as defined in Equation 3.
Equation 3:
𝑁
𝜓𝑅 𝐿𝑃 = { ∑ (𝑁 − 𝑡 + 1) ∙ [(𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑒𝑛𝑎𝑙𝑡𝑦)𝑑𝑡 ∙ (1 − 𝑘𝑑𝑡 ) + (𝐸𝑑𝑡 𝜏 𝑅 − 𝜏) ⋅ 𝑘𝑑𝑡 ]} ÷ 78
where:
𝑡=𝑁−11
 R LP= penalty assigned to the institution R;
t = month for which the deviation is calculated;
N= month related to the last reference date of the calculation period;
d t = reference date of  in month t;
E d t  R = projection of the institution R which is valid on d t for  (in the case of Exchange and
Selic rates, there are two reference dates);
 = actual annual result f the surveyed variable  ;
(maximum penalty ) dt = maximum absolute deviation of the projections valid on d t , for  , in
relation to the actual result;
k d t = 0, when the institution does not have valid projection on d t ;
=1, when the institution has valid projection on d t .
25. What are the formulas used for the calculation of the Annual Top 5
Rankings (Short Run and Medium rankings)?
Equations for the Calculation of the Annual Rankings
Short Term
In the Short Term annual ranking, the institutions are classified based on NBR CP , as defined
in the Equation 4, for each variable surveyed  .
Equation 4:
12
𝑅
𝑁𝐵 𝐶𝑃 = { ∑ (𝑁𝑜𝑡𝑒 𝑅 𝐶𝑃𝑚)} ÷ 12
𝑚=1
25
Equation 5:
𝑁𝑜𝑡𝑎𝑅 𝐶𝑃𝑚 = 10 ∙ [𝜓 𝑅 𝐶𝑃𝑚 − 𝜓𝐶𝑃𝑚𝑚𝑎𝑥] ÷ [𝜓𝐶𝑃𝑚𝑚𝑖𝑛 − 𝜓𝐶𝑃𝑚𝑚𝑎𝑥]
where:
 R CPm= penalty assigned to the institution R, for the month m, as per Equation 1;
 CPmmax= maximum penalty of the institutions, for the month m, as per Equation 1;
 CPmmin= minimum penalty of the institutions, for the month m, as per Equation 1.
If there is no  R CPm for any month ”m” in the 12 months period (or 8 meetings, in the case
of the Selic rate), it should be used for this month “m”,  R* CPm, defined as follows:
Equation 6:
𝑁
𝑅∗
𝜓 𝐶𝑃𝑚 = { ∑ (𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑒𝑛𝑎𝑙𝑡𝑦)𝑑𝑡 } ÷ 6
𝑡=𝑁−5
where:
t = month for which the deviation is calculated;
N= month concerning the last reference date of the calculation period;
d t = reference date of the surveyed variable  in month t;
(average penalty)dt = average absolute deviation of the valid projections on d t , for  t , in
relation to the result occurred in month t.
Medium Term
In the Medium Term annual ranking, the institutions are classified based on NB R MP , as
defined in the Equation 7, for each variable surveyed  .
Equation 7:
12
𝑅
𝑁𝐵 𝑀𝑃 = { ∑ (𝑁𝑜𝑡𝑒 𝑅 𝑀𝑃𝑚)} ÷ 12
𝑚=1
Equation 8:
𝑁𝑜𝑡𝑒 𝑅 𝑀𝑃𝑚 = 10 ∙ [𝜓𝑅 𝑀𝑃𝑚 − 𝜓𝑀𝑃𝑚𝑚𝑎𝑥] ÷ [𝜓𝑀𝑃𝑚𝑚𝑖𝑛 − 𝜓𝑀𝑃𝑚𝑚𝑎𝑥]
where:
 R MPm= penalty assigned to the institution R, for the month m, as per Equation 2;
 MPmmax= maximum penalty of the institutions, for the month m, as per Equation 2;
 MPmmin= minimum penalty of the institutions, for the month m, as per Equation 2.
If there is no  R MPm for any month ”m” in the 12 months period (or 8 meetings, in the case
of the Selic rate), it should be used for this month “m”,  R* MPm, defined as follows:
Equation 9:
26
𝑁
3
𝑅∗
𝜓 𝑀𝑃𝑚 = { ∑ (𝑁 − 𝑡 + 1) ∙ ∑ [(𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑒𝑛𝑎𝑙𝑡𝑦)𝑑𝑡−𝑤+1 ]} ÷ 30
where:
𝑡=𝑁−3
𝑤=1
t = month for which the deviation is calculated;
N= month concerning the last reference date of the calculation period;
w= a set of projections for the same monthly indicator;
d t -w 1 = reference date of the surveyed variable  in month t-w+1;
(maximum penalty)dt -w 1 = maximum absolute deviation of forecasts valid on d t -w 1 , for  N w1 ,
in relation to the result occurred.
27