Analysis of the relationship between book value and market value in the bank
and insurance sector: the impact of information on intangibles presented in
financial statements
S.Pucci, M.Cenci, R.Luly
(Università Roma Tre)
1.
Introduction
2.
Literature review
3.
Model
3.1. Data
3.2. Results
3.3 Concerns on the impact of intangibles information on non-systemic risk
4.
Limitation of the analysis and possible evolutions
References
Appendix
Key words: intangibles, financial statements, book value, market value, banks, insurances
Abstract: The present paper is part of the research done during a PRIN project dedicated to the analysis of company
information on intangible assets following a multi-stakeholder approach referring to the financial sector. This paper
combines the conclusions reached towards the multi-stakeholder approach (given by a score for each entity included in
the sample attributable to unrecognized intangible assets) with a mathematical model that permits evaluation of the link
between book value and market value. The aim is to try to verify if the increase or decrease in the disclosure of intangible
assets information in financial statements influences the relationship between book and market value. The analysis was
conducted using a formula – derived from the Daniel and Titman’s model which binds the annual return of the banks and
insurances - measured as the logarithm of the ratio between book value and market value – with the information supplied
on intangibles in the end of year accounts.
1.
Introduction
The links between the accounting information of listed firms and their market prices have been analysed by many authors
and papers. This kind of research starts from Kalecki’s idea that “ the rate of the investment decisions of a single
1
entrepreneur depends on his capital accumulation and on the velocity of change of marginal net profitability ” . The
1
principle of increasing risk of Kalecki shows that, even in a perfectly competitive market, risk increases with investment
both for economic and financial reasons: the braking efficiency effect of risk is proportional to the weight that the
investment has for the equity investor. For example, if we compare the position of two companies (the first exposed only a
little to the tightening of the income statement, the second with higher fixed costs) with the same overall profits, though
differently distributed over time, we can infer that they have a different degree of exposure to risk. Although the profit is
the same, the second firm is more exposed to the risk of fluctuations in dividends. This affects the valuation ratio and
could have negative consequences on the company evaluation. The research started from the above considerations and, at
the same time, linked the performances for the period 2006-2011 to the ratio between book value (B) and market price
(M) for banking and insurance companies on the basis of data provided by Mediobanca, which shows a significant
reduction in the ratio M /Bduring the period examined. It was decided to determine whether values of the ratio M/B < 1 existing for some of these companies - could be explained by overestimation of financial statement assets of financial
institutions or by negative goodwill/intangible assets and therefore if an important role is played by the information
available on the value of recognized and unrecognized intangible assets. The numbers which represent intangible assets
are defined with a score derived by the application of a multi-stakeholder approach to the information in the financial
statements and social and environmental accounts of the banks and companies included in the sample analysis . The
model used to measure the relationship between book and market value is bases on a formula – derived from the Daniel
and Titman’s model – measured as the logarithm of the ratio B/M. A stochastic process is used to obtain information on
the variables from which the future evolution of the B/M ratio will depend. This analysis is particularly relevant in
connection with the financial crisis and the "loss of reputation" issue of the entire financial sector.
2
2.
Literature review
The literature on the role, the evaluation and the accounting of intangible assets and on the relationship between book
and market value is vast and belongs to different disciplines. For this reason this paper focuses only on the part of this
literature that is closely linked to the concepts and the model used in this paper. Among the numerous works regarding
the role and evaluation of intangibles the following have constituted a useful point of reference for this paper: B.LEV, 2001
(who defines the characteristics and the value of intangible assets); B.LEV, J.H.DAUM, 2004; A. DAMODARAN, 2009 (who
analyses the role of these assets in the evaluation of a firm); D. ZEGHAL, A. MAALOUD, 2011.
For the part of the work that refers to Management Commentary and KPIs, useful reference points are: C.A.ADAMS,
2008 (that analyses the theme of corporate social responsibility and the reputational risk management); EUROPEAN ON
FINANCIAL ANALYSTS SOCIETIES, 2009 (in which the authors analyse the problem of the integration of traditional
information and KPI); GLOBAL REPORTING INITIATIVE, 2009 (in which it is possible to fine both guidelines in the
application of KPI and the main stakeholders and joined KPI).
The papers examined referring to bank intangibles assets are: W.BEAVER, C.EGER, S.RYAN, M.WOLFSON, 1989;
A.DAMODARAN, 2009 (that analyses the relevance of intangibles in financial sector); O. DEEV, 2011; F.FIORDELISI,
P.MOLYNEUX, 2006 (in which the problems is analysed from a shareholders perspective); H.ISIDRO, D.GRILO, (that
analyse the accounting based valuation model for commercial banks); J.M.KOLBECK, 2004, (in which the author tries to
analyse how investors incorporate information about intangibles in the prices of banks); J.M.KOLBECK, T.D.WARFIELD,
2007 (in which the authors analyse the effects of banks intangibles assets on abnormal earnings); Z.MATOLCSY,
A.WYATT, 2005 (that analyses the relationship between intangible assets and dispersion of earnings forecasts).
In addition to the previous literature, used to build the mathematical model, other papers have also been considered
regarding the search for links between the information provided by financial statements of listed companies and their
market price, which has been the main subject of many important studies in finance. The extrapolation of links between
the official market price and increasing market efficiency would be extremely useful to investors. Many works have studied
the predictive capabilities of financial statement data - such as book value - on the price of the underlying equity security
(E.F. FAMA, K.R. KENNET, 1992; E.F. FAMA, K.R. KENNET, 1993; E.F. FAMA, K.R. KENNET, 1995; E.F.
M.KALECHI, The Principle of Increasing risk, Economica, New Series Vol.4, N.16, Nov 1937, pp.440-447, pag.447
The way in which the score for the level of information is attributed to the single banks of the sample is analyzed in:
S.PUCCI, Le risorse immateriali nel settore bancario, Giappichelli, Torino, 2013, chap.4.
1
2
2
FAMA, K.R. KENNET, 1998), while others have studied the reactions of share prices to information obtained from the
financial statements of companies (K.DANIEL, S.TITMAN, 2006; W.F.M. DE BONDT, R.H. THALER R.H., 1985; W.F.M.
DE BONDT, R.H. THALER R.H, 1987). The analysis in this paper follows this last approach and focuses on the temporal
evolution of the ratio between book value and market prices of Italian banks and insurances in order to determine
whether there is a common factor in the financial sector that justifies the fact that the recent market prices of these
institutions are, in some cases, lower than their book value, considering the impact of intangible assets.
3.
The model
When the book value to market price ratio is >1, the company is less exposed to takeover and to the possibility of top
managers losing control than when this ratio is less than one.
A basic analysis could highlight that, to buy shares on the market is less expensive than to buy company assets according to
accounting data that is evaluated at a higher value. Of course, this analysis disregards the fact that, as a result of increased
demand for stocks, the share price would rise. However, the maintenance of a situation in which the relationship between
book value and market value is > 1 must be analysed to understand what the causes of this mismatch are and to identify
which elements influence the expectations of the market. The analysis is performed by tying the annual yield of each
company to two components. The first is identified by tangible information derived from financial statement data that
should summarise past performance and growth prospects, while the second is derived from information on unrecognised
intangibles or on the related reactions of investors to the realisation of unpredictable events in the current year that
influence the development of share prices.
We will refer to a year in which, at time t-1, the yield at time t is not known and is a random variable that will be denoted
by
r  t  1, t  . Using the suggested decomposition, it is possible to define the following equation:
r  t  1, t   Et 1  r  t  1, t    r
T
 t  1, t   r  t  1, t 
I
(1)
where:
 represents the expected return on the period
Et 1 
 r  t  1, t  
r
r
t 1, t  ;
T
 t  1, t 
I
 t  1, t  is the random variable that represents the return due to intangible elements.
is the random variable that represents the return due to tangible elements;
Similar to what it is suggested by DANIEL AND TITMAN (2006), it is assumed that the logarithm of the book value to
market value ratio at time t is a proxy for the return on time
t 1, t  and it is assumed that this proxy follows a Markov
stochastic process. This means that, at time t, all the information about the past evolution will be contained in the
information known at time t-1, which immediately precedes it.
Indicating with:
B the book value at time t,
t
M the market price at time t,
t
the following equation is given:
 B 
 B 
 B 
 Mt 
log  t   log  t 1   log  t   log 

 Mt 
 M t 1 
 Bt 1 
 M t 1 
3
(2)
where:
 B 
log  t 1  , known at t-1 time, is a proxy of the expected return on
 M t 1 
 B 
log  t  is a proxy of the book value return on
 Bt 1 
t 1, t  period;
t 1, t  period;
 M t  is a proxy of the expected return linked to intangible information.
log 

 M t 1 
The proposed model is based on the decomposition of the logarithm inversion of the valuation ratio in the sum of three
different components each of them has a precise financial meaning.
The analysis will consider the effect of temporal regression based on the official data published in the financial statements
of the banks of the sample.
To improve the model some adjustments have been made. For example an adjustment for the dividends distributed in the
period analysed. Considering this adjustment the final equation may be written as:
𝑏𝑚𝑡 = 𝑏𝑚𝑡−1 + 𝑟𝑏 (𝑡 − 1, 𝑡)−𝑟𝑖 (𝑡 − 1, 𝑡)
(3)
where:
 Bt 
log 
  bmt
 Mt 
 B  Dt  Nt 
log  t
  rb (t  1, t )
Bt 1


 Mt 
log 
  r i (t  1, t )
 M t 1 
This formula has been applied for every banks of the sample (cfr.3.1.) and has been also used to obtain a global
evaluation.
3.1 Data
The data used to verify the effectiveness of the proposed model, for analysing the impact of intangible information on the
valuation ratio, refer only, at this first stage, to the Italian bank and insurance sector. In particular, data has been taken
from the financial statements of the listed Italian banks and insurances that apply IFRS to present their annual results.
There are 17 listed banks and 7 listed insurances in the sample and their names are given in the Appendix. To improve
the significance of the intangibles disclosure ratios, the details existing in the financial statements are integrated with some
data presented in the social and environment reports. This integration determines a relevant effect on the results of the
model because, in some cases, companies give in their official financial statements very few data on unrecognized
intangible assets: this choice – derived also by the IAS-IFRS prescriptions - determines lower values of the disclosure
ratios with a different impact on the allocation of entity income in the three components of the formula (2).
To obtain the indexes on the disclosure level of unrecognised intangibles, used in the proposed formula, all the
information on intangibles in financial statements and in social and environment accounts have been used according to a
multi-stakeholder approach. The steps are: the creation of a stakeholders list and of KPI indicators, the definition of a
score that should be assigned to every company referring to the existence or the absence of positive value to some KPIs
defined, considering the GRI model principles; the composition of the final list that joins to every companies its score (the
results are in Appendix).
4
Both Mediobanca data and historical amounts derived from the market and from financial statements have been used to
define book value and market value.
3.2 Results
There are more levels of analysis that are used to validate the model proposed: the first refers to the application of the
formula (3) to every bank and insurance and to the analysis of the correlation of the main variables of the model (tab.
3.2.1.a., tab.3.2.1.b., tab.3.2.2.), the second refers to the match of information of unrecognised intangibles and the
performance of intangible proxy (tab. 3.2.3.a. and 3.2.3.b) and the last concerns the relationship between risk and
intangibles.
Considering the first aspect there are two results that worth to remember. The application of formula (3) to every
companies for the 2006 – 2011 period has shown that, in the years following the financial crisis (2010-2011), market
evaluation has heavily penalized the bank sector and that it is very difficult to attribute this penalty to the information given
in the financial statements referring to intangibles. The situation is a bit different in the previous period in which the
increase of intangibles information could have determined a better market value. To complete this analysis it has been
verified the level of correlation between the model variables: the results may be summarised in the following tables:
Tab.3.2.1.a. – bank sector
bm
bm
r (t-1,t)
r (t-1,t)
1
0.74139
-0.14213
-0.32919
1
-0.19805
0.343466
1
0.016486
t
bm
t
bm
t-1
t-1
b
r (t-1,t)
b
r (t-1,t)
i
1
i
Tab.3.2.1.b. – insurance sector
bm
bm
r (t-1,t)
r (t-1,t)
1
0.870013
-0.11238
-0.23114
1
-0.20001
0.256465
1
0.103517
t
bm
t
bm
t-1
t-1
b
r (t-1,t)
b
r (t-1,t)
i
1
i
There are no relevant differences between the correlation index in the bank and in the insurance sector.
The results obtained are in line with what is generally known in financial literature. The negative correlation between the
variables bmt, and rb (t-1, t) shows that increases in the distribution of earnings negatively affect the relationship between
book value and market value. The negative correlation between detected bmt and ri (t-1, t) is clearly due to the fact that in
correspondence to increases in market value, the ratio between book value and market value must necessarily decrease. It
may be also noted that, since both the variable bmt-1 and rb (t-1, t) are positively correlated with intangible information
level, the increasing of transparency in in financial statements should be read positively by the market. The limited
number of observations on which the analysis is based do not allow to use, at this stage, the results for forecasting
purposes. The thing can be said with enough certainty is that, if some negative events do not intervene in the market,
referring to Italian banks for which the B/M ratio 2011 is lower than the same ratio in 2010, it could be possible that, for
the future, there will be a new rapprochement of the book value and the market value. It is also important to note that at
the level of single entities the relationship existing for the whole sample is not necessary true (as it is possible to verify from
Annex 2).
5
The results of the following analyses on the correlation between the proxy results of tangible and intangible assets are
shown in Tab.3.2.2. It should be remembered that the component of equation (3) - that identifies the proxy of the return
joined to intangibles information – is influenced both by some unpredictable events for the entire market and by the
investor reactions on the information provided in financial statements. In this section, the correlation between the
information relating to intangible assets not accounted for and the proxy performance information associated with
intangibles is determined for each bank of the sample. The analysis was performed assuming as indicators of the level of
information regarding unrecognised intangible assets, for each bank, the sum of the values assigned to the detailed
information and general information contained in the banks' balance sheets for the years 2008, 2009 and 2010 determined
applying the multi-stakeholders analysis and refers to the impact that this data has on the market in the following year. In
practice, it is assumed that the information contained in the 2008 budget has an effect on stock prices of the year 2009 and
so on.
The results of the analysis on the correlation and covariance between the proxy results of intangibles and indicators for
banks are shown in the following table:
Table 3.2.2. – bank sector
correlation
cov
B.1
-0.67772
-0.07593
B.2
-
0
B.3
-0.99959
-0.28882
B.4
-
0
B.5
-
0
B.6
-
0
B.7
-
0
B.8
-
0
B.9
-
0
B.10
-
0
B.11
-0.95424
-0.21128
B.12
-
0
B.13
-
0
B.14
-0.8207
-020318
B.15
-
0
B.16
-
0
B.17
-
0
It is easy to deduct that if the ratio referring to unrecognised intangibles is stable, to define a relationship between the
proxy of intangibles income and the level of the information existing in the financial statements for these assets is not
possible. While a relevant negative correlation exists when the disclosure, presented in the financial statements, relating to
intangibles increases. In different words, if you have more disclosure on intangibles, a lower influence on market return
exists.
The results of the comparison between the intangibles ratio and the income relating to these assets, as determined using
the proposed model, are shown in the following table referring the bank sector:
6
Tab.3.2.3.a bank sector
Intangibles ratio
Intangibles income proxy
2008
2009
2010
2009
2010
2011
B.1
20
18
20
-0.07057
-0.00675
-0.28461
B.2
57
57
57
0.062622
-0.42265
0.129938
B.3
26
28
29
0.323513
-0.06007
-0.23045
B.4
53
53
53
0.12118
-0.1302
-0.01578
B.5
22
22
22
0.374186
-0.13375
-0.49794
B.6
53
53
53
-0.0045
-0.33323
-0.28145
B.7
52
52
52
-0.07444
-0.38142
-0.4594
B.8
49
49
49
0.006844
-0.25303
-1.00403
B.9
17
17
17
0.186362
-0.15916
-0.52982
B.10
63
63
63
0.216206
-0.40211
-0.09268
B.11
27
29
29
0.190677
-0.1987
-0.37071
B.12
51
51
51
-0.2037
-0.36673
-0.46813
B.13
57
57
57
0.196506
-0.61333
1.083433
B.14
29
29
33
0.086578
-0.09717
-0.23387
B.15
28
28
28
0.096321
-0.10647
0.045173
B.16.
58
58
58
0.021878
-0.38793
-0.28914
B.17
51
51
51
0.689264
-0.21096
-3.16337
Correlation index
-0.13835
-0.79664
0.028913
It is also possible to argue that if, in the period 2009 -2011, the results referring to the intangibles income proxy are
compared to the intangibles income proxy of the previous year, the sign of correlation changes in 2011 (the sign is negative
in 2009-2010 and positive in 2011). However, it may be observed that a higher value of the 2011 ratios do not determine
a lower value of the intangibles income proxy.
The results of the comparison between the intangibles ratio and the income relating to these assets, as determined using
the proposed model, are shown in table 3.2.3.b referring to the insurance sector:
Tab.3.2.3.b insurance sector
Intangibles ratio
Intangible income proxy
2008
2009
2010
2009
2010
2011
I.1
61
61
61
0.040655
-0.22125
-0.27547
I.2
67
67
67
-0.1416
-0.57287
-0.67764
I.3
62
62
62
0.089485
-0.28097
-0.20036
I.4
57
57
57
0.366268
-0.34204
-0.03578
I.5
21
21
21
-0.07171
-0.54981
-0.01434
I.6
44
44
44
-0.12292
-0.25353
-0.61496
I.7
22
22
22
0.012019
-0.06436
-0.16834
correlation index
0.22731
7
-0.18539
-0.42302
Relating to the insurance sector, it should be noted the substantial stability of the level of disclosure referring to
intangibles assets. This stability does not permit to analyze from a statistical point of view the relationship between the
amount of income referring to intangibles and the information given.
From the analysis of the data collected, it can be deducted that:
-
the correlation is positive in 2009,
-
the correlation is negative in 2010 and 2011. In these two years the ratio values move in a different manner from
the intangibles income proxy. It can be deducted that the companies with a higher value in disclosure show a
lower intangible income proxy.
3.3 Concerns on the impact of intangibles information on non-systemic risk
The risk joined with market return is generally measured in listed shares with the return variance. In the hypothesis of
CAPM , the variance may be classified in two components: the systematic risk (that is referred to events that interest the
whole market and all the entities that belong to that market) and the non-systematic risk (that measures the risk of a
specific company and that is also dependent to the disclosure level offered by the company to market operators). Part of
the developed analysis – that it should be further implemented - tries to verify if the data referring to unrecognized
intangibles shown in financial statements have influence on banks and insurances companies un-systematic risk .
3
In this part of analysis, a dynamic model is used and this model is based on two stochastic processes: the first one refers to
the time evolution of the performance of tangible assets and assets recognized in financial statements, the second is related
to the evolution of the market return which also incorporates information relating to unrecognized intangible assets. Using
a hypothesis in the consolidated financial practice, it is assumed that both the book value and the market value will follow
a stochastic process of multiplicative Brownian type.
The results obtained, at this first stage, show a difference between insurance and bank sector. For the banks, the
correlation between past information and return index is always negative: this evidence suggests that an increase in the
information level on intangibles in financial statements determines a decrease in the unsystematic risk. It is also interesting
to notice that the correlation value decreases in the period examined and this seems to suggest an increasing attention of
the investors in information on intangibles that is not accounted for in the financial statements. The results obtained for
the insurance companies are not satisfactory at this stage because they show an increase of the correlation between the
variables and a transition from negative values to positive values: this is probably connected with constancy of the level of
information offered by the sector in relation to intangibles.
From this first step analysis, it can be also inferred that the information relating to unrecognized intangible do not produce
certain effects on the variability of the valuation ratio: for companies for which the intangible information ratios are
negatively correlated with the market yield, a greater disclosure could produce a decrease in the expected market return
but also a decrease in variance; for companies for which the information ratios relating to unrecognized intangibles are
positively correlated with the market yield on the market, a greater disclosure could cause an increase in the expected
market return expected.
3
F. Black, M. Jensen, M. Sholes, The capital asset pricing model: some empirical tests, Studies in the Theory of Capital
Markets, New York, 1972 Black F.Campbell . y., Vuolteenaho T., Bad beta good beta, American Economics Review, vol.
94, n.5, 2004 pp.1249-1275; Cordazzo M., L’impatto borsistico dell’informativa sugli intangibili, Franco Angeli ed.,
Milano, 2007; Mossin J., Equilibrium in a Capital Asset Market, in Econometrica, vol.34, n.4, 1966, pp768-783; Ross S.
A., The arbitrage theory of capital asset pricing , Journal of Economic Theory, vol 13, 1976 pp. 341-360; Sharpe W.F.,
Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of Finance, vol. 19, 1964, pp. 425442.
8
4.
Limitation of the analysis and possible evolutions
The limits of the model and of the practical application – which could be removed with a further level of analysis - may be
summarized as follows:
- the lack of analysis of the links and possible interrelations between existing information on recorded and unrecorded
intangibles and the contents of the notes of banks in terms of risks and their management;
- the absence of a specific analysis referring to the existence and to the effects of any impairment operated by companies
during the reporting period.
On the basis of what has been reported, this analysis could be further improved both from the theoretical and practical
points of view. Theoretically, the analysis of the valuation of intangible assets could be expanded to verify whether and
how the adoption of different valuation models 'flips' the existing level of disclosure. It could also implement the
evaluation choice solution, considering a larger number of indicators, especially those related to the financial sector.
From the practical point of view, improvements could include: increasing the number of banks and insurance in the
sample, to include foreign entities that adopt IAS-IFRS to check for any differences in approach within the financial sector
itself; improving the comparison between the relevance of the data provided in financial statements at the end of the year
and those reported in the environmental and social budgets; increasing the numbers of companies considered including
industrial sector; developing a more detailed mathematical model to assess the relationship between book value and
market value in view of the existence of a certain level of information on intangibles.
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9
B.LEV, Intangibles: Management, Measurement and Reporting, Brookings Institution Press, 2001
B.LEV, J.H.DAUM, The dominance of intangibles assets: consequences for enterprises management and corporate
reporting, Measuring Business Excellence, vol. 8, 2004
H.ISIDRO, D.GRILO, Value driving activities in Euro-zone banks, ……..
M.KALECHI, The Principle of Increasing risk, Economica, New Series Vol.4, N.16, Nov 1937, pp.440-447
E.F. FAMA, K.R. KENNET, The cross-section of expected stock returns, Journal of Finance, n. 47, 1992, pp.427-465
E.F. FAMA, K.R. KENNET, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics,
n. 33, 1993, pp.3-56
E.F. FAMA, K.R. KENNET, Size and book-to-market factors in earnings and returns, in Journal of Finance, n. 50, 1995,
pp.131-156
E.F. FAMA, K.R. KENNET, Market efficiency, long-term returns and behavioral finance, Journal of Financial
Economics n. 49, 1998, pp.283-306
F.FIORDELISI, P.MOLYNEUX, Shareholder value in banking, Palgrave MacMillian, London, 2006
J.M.KOLBECK, Investor Valuations and Measuring Bank Intangibles Assets, Journal of Accounting, Audit and Finance,
vol.19, 29, 2004, pp. 29- 60
J.M.KOLBECK, T.D.WARFIELD, Unrecorded Intangibles Assets: Abnormal Earnings and Valuation, Accounting Horizon,
vol.21, n.1, pagg.23-41, 2007
Z.MATOLCSY, A.WYATT, Capitalized Intangibles and Financial Analysts, Intellectual Property Research Institute of
Australia, Working Paper, n.4/2005
D. ZEGHAL, A. MAALOUD, The accounting treatments of intangibles – A critical review of the literature, Accounting
Forum, val.35, n.4, 2011
10
Appendix 1 – List of the banks and insurances in the sample
B.1 BANCO DESIO BRIANZA
B.2 BANCO POPOLARE
B.3 BANCO DI SARDEGNA
B.4 CARIGE
B.5 CREDEM
B.6 CREDITO ARTIGIANO
B.7 CREDITO VALTELLINESE
B.8 BANCA ETRURIA
B.9 FINNAT
B.10 BANCA INTESA
B.11 MEDIOBANCA
B.12 MONTE DEI PASCHI DI SIENA
B.13 BANCO POPOLARE DI MILANO
B.14 BANCO POPOLARE EMILIA ROMAGNA
B.15BANCA POPOLARE DI SONDRIO
B.16 UBI BANCA
B.17UNICREDIT
I.1 CATTOLICA ASSICURAZIONI
I.2 FONSAI
I.3 ASSICURAZIONI GENERALI
I.4 MEDIOLANUM
I.5 MILANO ASSICURAZIONI
I.6 UNIPOL ASSICURAZIONI (UGF)
I.7 VITTORIA ASSICURAZIONI
11
Appendix 2 –-Statistichal data
B.1 IM EQUITY
bmt 1
rb  t  1, t 
ri  t  1, t 
-0.243
-0.668
0.516
-0.148
533.671.958
0.230
-0.243
0.132
-0.416
731.263.000
497.306.539
0.386
0.230
0.143
-0.071
2010
754.360.000
493.960.348
0.423
0.386
0.077
-0.007
2011
745.679.000
371.609.528
0.696
0.423
0.027
-0.285
2012
776.469.066
254.675.112
1.115
0.696
0.046
-0.378
t
Bt
Mt
bmt
2006
480.888.000
937.805.945
-0.668
2007
634.162.000
808.593.481
2008
671.794.000
2009
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0.435
0.137
0.157
-0.217
Standard deviation
0.455
0.502
0.182
0.167
bmt 1
rb  t  1, t 
ri  t  1, t 
Correlation
bmt
1
0.939069
-0.83634
-0.37451
1
-0.87665
-0.05562
1
0.246026
1
12
B.2 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
2007
9.635.661.851
6.503.191.182
0.393
2008
8.681.348.000
2.220.038.871
1.364
0.393
-0.104
-1.075
2009
10.355.274.000
2.363.507.418
1.477
1.364
0.181
0.063
2010
10.476.505.000
1.548.818.423
1.912
1.477
0.034
-0.423
2011
7.755.998.008
1.763.729.753
1.481
1.912
-0.301
0.130
2012
7.016.670.373
2.218.773.346
1.151
1.481
-0.100
0.230
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2008 to 20124
1.477
1.325
-0.058
-0.215
Standard deviation
0.277
0.562
0.179
0.542
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0.198027
0.291516
-0.22617
1
-0.20531
0.863691
1
-0.03953
1
4
listed since 2007
13
B.3- IM EQUITY
t
Bt
Mt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
1.039.194.253
766.427.142
0,304
2007
1.133.065.982
720.830.884
0,452
0,304
0,135
-0,061
2008
1.164.987.349
361.375.391
1,171
0,452
0,057
-0,690
2009
1.188.224.688
499.411.351
0,867
1,171
0,041
0,324
2010
1.156.663.226
470.297.220
0,900
0,867
-0,023
-0,060
2011
1.164.180.575
373.500.241
1,137
0,900
0,019
-0,230
2012
1.127.402.667
363.797.256
1,131
1,137
-0,032
-0,026
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,943
0,805
0,033
-0,124
Standard deviation
0,273
0,355
0,061
0,332
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,444219
-0,6918
-0,43873
1
-0,76507
0,607905
1
-0,11981
1
14
B.4 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
2.758.605.204
3.571.118.496
-0,258
2007
2.921.663.105
3.577.417.134
-0,202
-0,258
0,079
0,002
2008
3.725.809.868
2.450.023.971
0,419
-0,202
0,264
-0,379
2009
3.929.599.671
2.765.656.066
0,351
0,419
0,067
0,121
2010
3.813.226.598
2.428.016.687
0,451
0,351
-0,017
-0,130
2011
3.200.374.266
2.389.994.848
0,292
0,451
-0,168
-0,016
2012
3.985.253.763
1.678.635.551
0,865
0,292
0,219
-0,353
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,363
0,176
0,074
-0,126
Standard deviation
0,343
0,320
0,157
0,203
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,502837
0,333824
-0,60954
1
-0,56133
0,319732
1
-0,67956
1
15
B.5 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
1.171.394.069
2.588.563.974
-0,793
2007
1.348.304.588
2.349.358.328
-0,555
-0,793
0,257
-0,097
2008
1.589.602.350
1.143.063.217
0,330
-0,555
0,259
-0,720
2009
1.615.035.420
1.661.794.339
-0,029
0,330
0,032
0,374
2010
1.592.122.725
1.453.750.119
0,091
-0,029
0,011
-0,134
2011
1.524.513.811
883.564.699
0,545
0,091
-0,002
-0,498
2012
1.715.329.053
1.373.444.186
0,222
0,545
0,130
0,441
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,101
-0,068
0,114
-0,106
Standard deviation
0,377
0,515
0,121
0,461
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,470961
-0,43347
-0,36367
1
-0,70993
0,6376
1
-0,25458
1
16
B.6 IM EQUITY
t
Bt
Mt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
446.082.799
295.770.067
0,411
2007
463.811.054
301.750.685
0,430
0,411
0,061
0,020
2008
779.905.476
443.761.897
0,564
0,430
0,545
0,386
2009
759.040.440
441.768.358
0,541
0,564
-0,004
-0,005
2010
759.556.299
316.574.076
0,875
0,541
0,027
-0,333
2011
891.276.715
238.915.153
1,317
0,875
0,194
-0,281
2012
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 20115
0,745
0,564
0,165
-0,043
Standard deviation
0,360
0,186
0,226
0,287
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,923625
-0,01036
-0,67599
1
-0,13734
-0,62939
1
0,705998
1
5
There is a merger with B.7 in 2012
17
B.7 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
870.459.433
761.311.443
0,134
2007
1.549.240.404
1.187.088.202
0,266
0,134
0,581
0,444
2008
1.690.594.000
1.125.545.748
0,407
0,266
0,099
-0,053
2009
1.965.009.000
1.044.805.595
0,632
0,407
0,167
-0,074
2010
2.083.414.000
713.487.642
1,072
0,632
0,061
-0,381
2011
1.900.165.946
450.683.420
1,439
1,072
-0,086
-0,459
2012
1.944.780.727
516.384.953
1,326
1,439
0,023
0,136
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,857
0,658
0,141
-0,065
Standard deviation
0,491
0,505
0,231
0,333
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,922824
-0,79436
-0,61916
1
-0,69321
-0,3173
1
0,815045
1
18
B.8 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
469.204.000
717.205.556
-0,424
2007
523.567.066
437.065.255
0,181
-0,424
0,161
-0,495
2008
677.013.974
277.098.486
0,893
0,181
0,275
-0,456
2009
685.130.538
279.001.573
0,898
0,893
0,012
0,007
2010
691.121.267
216.628.463
1,160
0,898
0,020
-0,253
2011
668.869.160
79.373.018
2,131
1,160
0,003
-1,004
2012
595.614.937
1.645.386.263
-1,016
2,131
-0,116
3,032
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,708
0,807
0,059
0,138
Standard deviation
1,054
0,872
0,138
1,456
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
-0,25892
0,250229
-0,8593
1
-0,86721
0,714021
1
-0,61273
1
19
B.9 IM EQUITY
t
Bt
Mt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
115.883.000
322.999.488
-1,025
2007
185.636.000
279.671.616
-0,410
-1,025
0,804
-0,144
2008
194.672.000
165.799.872
0,161
-0,410
0,048
-0,523
2009
174.494.000
199.765.440
-0,135
0,161
-0,027
0,186
2010
176.395.000
170.372.160
0,035
-0,135
0,012
-0,159
2011
199.425.044
100.300.032
0,687
0,035
0,125
-0,530
2012
204.593.285
97.542.144
0,741
0,687
0,048
-0,028
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,180
-0,115
0,168
-0,200
Standard deviation
0,456
0,576
0,316
0,282
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,749597
-0,52513
-0,3506
1
-0,76715
0,294212
1
-0,03093
1
20
B.10 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
15.323.151.911
28.875.522.443
-0,634
2007
48.441.995.036
52.393.970.364
-0,078
-0,634
1,170
0,596
2008
45.718.734.618
26.770.249.940
0,535
-0,078
-0,035
-0,672
2009
47.785.009.966
33.231.461.431
0,363
0,535
0,061
0,216
2010
48.849.207.808
22.228.868.254
0,787
0,363
0,048
-0,402
2011
44.270.913.231
20.261.197.913
0,782
0,787
-0,098
-0,093
2012
44.290.051.639
21.364.203.531
0,729
0,782
-6,320
0,053
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,520
0,293
-0,863
-0,050
Standard deviation
0,337
0,556
2,715
0,450
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,813985
-0,44768
-0,68911
1
-0,55574
-0,23909
1
0,0211
1
21
B.11 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
5.479.374.900
11.670.710.612
-0,756
2007
6.098.880.236
9.613.181.794
-0,455
-0,756
0,116
-0,194
2008
5.249.990.089
5.591.369.138
-0,063
-0,455
-0,133
-0,542
2009
4.641.229.696
6.765.938.967
-0,377
-0,063
-0,119
0,191
2010
4.919.643.871
5.546.708.607
-0,120
-0,377
0,079
-0,199
2011
4.938.669.517
3.828.580.477
0,255
-0,120
0,006
-0,371
2012
4.421.588.075
4.014.584.386
0,097
0,255
-0,111
0,047
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
-0,111
-0,253
-0,027
-0,178
Standard deviation
0,271
0,352
0,109
0,267
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,560505
-0,2437
-0,36821
1
-0,62052
0,516109
1
-0,17186
1
22
B.12 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
7.674.526.000
8.619.861.975
-0,116
2007
7.661.460.000
6.695.758.206
0,135
-0,116
0,047
-0,253
2008
14.239.323.417
8.313.278.511
0,538
0,135
0,670
0,216
2009
16.589.926.595
6.781.167.298
0,895
0,538
0,163
-0,204
2010
15.621.429.263
4.699.306.601
1,201
0,895
-0,049
-0,367
2011
9.408.929.459
2.942.579.852
1,162
1,201
-0,507
-0,468
2012
9.408.929.459
2.636.523.512
1,272
1,162
-0,604
-0,110
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,867
0,636
-0,047
-0,197
Standard deviation
0,449
0,546
0,467
0,238
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,96239
-0,63099
-0,36801
1
-0,78856
-0,48583
1
0,658759
1
23
B.13 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
3.058.298.502
1.473.786.554
0,730
2007
3.247.164.004
1.074.897.155
1,106
0,730
0,112
-0,316
2008
3.052.313.711
508.416.933
1,792
1,106
-0,050
-0,749
2009
3.667.245.246
618.816.038
1,779
1,792
0,194
0,197
2010
3.653.520.252
335.115.564
2,389
1,779
0,007
-0,613
2011
4.012.600.697
990.201.915
1,399
2,389
0,094
1,083
2012
3.928.874.660
1.459.788.863
0,990
1,399
-0,021
0,388
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
1,576
1,533
0,056
-0,002
Standard deviation
0,519
0,584
0,093
0,693
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,307253
-0,09176
-0,49601
1
0,246683
0,666651
1
0,402871
1
24
B.14 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
2.532.898.000
4.047.837.293
-0,469
2007
2.449.519.000
3.595.777.261
-0,384
-0,469
0,000
-0,118
2008
2.398.890.000
2.293.354.424
0,045
-0,384
-0,011
-0,450
2009
2.488.757.000
2.500.757.814
-0,005
0,045
0,079
0,087
2010
2.684.627.000
2.269.194.924
0,168
-0,005
0,124
-0,097
2011
3.254.457.000
1.795.990.669
0,594
0,168
0,227
-0,234
2012
3.254.457.000
1.740.134.256
0,626
0,594
0,000
-0,032
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,174
-0,008
0,070
-0,141
Standard deviation
0,385
0,387
0,094
0,184
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,861562
0,45452
-0,00931
1
0,269145
0,468488
1
0,064195
1
25
B.15 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
1.338.125.000
2.151.049.014
-0,475
2007
1.592.236.000
2.769.510.830
-0,554
-0,475
0,212
0,253
2008
1.492.021.195
1.814.837.558
-0,196
-0,554
-0,062
-0,423
2009
1.683.715.881
1.998.339.683
-0,171
-0,196
0,172
0,096
2010
1.722.830.035
1.796.502.753
-0,042
-0,171
0,062
-0,106
2011
1.676.472.699
1.879.517.820
-0,114
-0,042
-0,010
0,045
2012
1.711.323.846
1.349.688.174
0,237
-0,114
0,030
-0,331
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
-0,140
-0,259
0,067
-0,078
Standard deviation
0,256
0,206
0,106
0,260
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,652578
-0,53605
-0,65469
1
-0,08458
0,10729
1
0,804769
1
26
B.16 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
4.166.564.401
5.343.133.118
-0,249
2007
10.962.140.301
9.285.959.066
0,166
-0,249
0,986
0,553
2008
10.358.681.650
5.371.637.819
0,657
0,166
-0,056
-0,547
2009
10.662.230.000
5.490.455.042
0,664
0,657
0,046
0,022
2010
10.328.266.000
3.725.070.146
1,020
0,664
-0,011
-0,388
2011
7.609.828.759
2.789.733.948
1,003
1,020
-0,305
-0,289
2012
8.607.720.373
3.161.525.000
1,002
1,003
-3,740
0,125
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,752
0,543
-0,513
-0,087
Standard deviation
0,334
0,497
1,642
0,402
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,91197
-0,58017
-0,62385
1
-0,64253
-0,35546
1
-0,02059
1
27
B.17 IM EQUITY
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
31.433.443.503
325.026.697.298
-2,336
2007
50.619.820.930
367.685.250.628
-1,983
-2,336
0,481
0,123
2008
50.989.663.132
119.620.671.562
-0,853
-1,983
0,070
-1,123
2009
54.091.949.125
238.314.243.545
-1,483
-0,853
0,060
0,689
2010
57.771.134.386
192.989.327.537
-1,206
-1,483
0,070
-0,211
2011
49.649.325.295
8.160.173.803
1,806
-1,206
-0,152
-3,163
2012
57.989.269.191
21.456.020.527
0,994
1,806
0,155
0,967
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
-0,454
-1,009
0,114
-0,453
Standard deviation
1,505
1,478
0,207
1,517
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,561464
-0,63941
-0,52912
1
-0,17179
0,399846
1
0,604135
1
28
I.1 Equity
Mt
bmt
rb  t  1, t 
Bt
2006
1.114.890.578
1.930.898.715
-0,549
2007
1.286.854.938
1.621.289.957
-0,231
-0,549
0,154
-0,175
2008
1.140.864.505
1.173.684.963
-0,028
-0,231
-0,120
-0,323
2009
1.265.436.081
1.222.384.619
0,035
-0,028
0,164
0,041
2010
1.286.934.645
979.762.907
0,273
0,035
0,031
-0,221
2011
1.243.890.697
743.848.269
0,514
0,273
-0,033
-0,275
2012
1.302.713.822
663.342.777
0,675
0,514
0,066
-0,115
Statistical data for
bmt 1
ri  t  1, t 
t
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,206
0,002
0,044
-0,178
Standard deviation
0,345
0,373
0,110
0,130
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,974036
-0,23392
-0,036
1
-0,17515
0,12425
1
0,841649
1
29
I.2 Equity
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
2.819.446.743
9.534.908.384
-1,218
2007
2.791.071.414
7.069.222.604
-0,929
-1,218
0,038
-0,299
2008
2.600.544.385
3.180.361.937
-0,201
-0,929
-0,060
-0,799
2009
2.526.281.767
2.760.447.454
-0,089
-0,201
-0,027
-0,142
2010
1.822.481.345
1.556.630.239
0,158
-0,089
-0,327
-0,573
2011
1.251.352.709
790.481.409
0,459
0,158
-0,376
-0,678
2012
1.627.332.680
1.180.181.553
0,321
0,459
0,263
0,401
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
-0,047
-0,303
-0,081
-0,348
Standard deviation
0,498
0,645
0,238
0,440
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,908601
-0,31034
0,073736
1
-0,0564
0,443569
1
0,797283
1
30
I.3 Equity
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
10.435.443.839
38.612.601.358
-1,308
2007
10.914.701.412
43.690.867.575
-1,387
-1,308
0,057
0,124
2008
10.627.238.218
26.792.161.193
-0,925
-1,387
0,048
-0,489
2009
13.803.124.676
29.300.189.570
-0,753
-0,925
0,269
0,089
2010
14.958.588.614
22.123.169.351
-0,391
-0,753
0,083
-0,281
2011
14.585.033.002
18.106.436.281
-0,216
-0,391
-0,021
-0,200
2012
14.405.470.595
21.391.438.908
-0,395
-0,216
-0,011
0,167
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
-0,678
-0,830
0,071
-0,098
Standard deviation
0,435
0,474
0,105
0,265
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,856214
-0,26872
-0,17283
1
-0,35791
0,314472
1
0,203267
1
31
I.4 Equity
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
548.196.502
4.515.355.741
-2,109
2007
509.011.975
4.001.904.946
-2,062
-2,109
0,078
-0,121
2008
592.027.069
2.212.191.210
-1,318
-2,062
0,352
-0,593
2009
599.722.419
3.190.735.026
-1,672
-1,318
0,117
0,366
2010
584.909.791
2.266.431.276
-1,355
-1,672
0,156
-0,342
2011
642.897.146
2.186.781.711
-1,224
-1,355
0,279
-0,036
2012
675.064.906
2.815.451.581
-1,428
-1,224
0,132
0,253
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
-1,510
-1,623
0,186
-0,079
Standard deviation
0,310
0,389
0,106
0,359
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,392751
0,729117
-0,2674
1
-0,17718
0,771234
1
-0,6154
1
32
I.5 Equity
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
1.605.664.622
1.838.243.746
-0,135
2007
1.761.805.034
1.645.764.253
0,068
-0,135
0,127
-0,111
2008
2.044.557.029
825.328.080
0,907
0,068
0,152
-0,690
2009
1.977.064.874
768.216.224
0,945
0,907
-0,033
-0,072
2010
1.411.262.296
443.307.992
1,158
0,945
-0,337
-0,550
2011
977.710.929
436.996.749
0,805
1,158
-0,367
-0,014
2012
894.788.866
610.667.464
0,382
0,805
-0,089
0,335
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,711
0,625
-0,091
-0,184
Standard deviation
0,406
0,527
0,222
0,376
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,542462
-0,47852
-0,57488
1
-0,87213
0,328007
1
-0,1342
1
33
I.6 IM Equity
t
Mt
Bt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
5.280.319.434
113.927.238.858
-3,072
2007
5.333.578.426
99.739.208.353
-2,929
-3,072
0,028
-0,133
2008
4.330.892.720
45.946.230.517
-2,362
-2,929
-0,208
-0,775
2009
4.459.712.023
40.631.764.295
-2,209
-2,362
0,036
-0,123
2010
4.696.085.378
31.532.661.262
-1,904
-2,209
0,052
-0,254
2011
4.337.909.170
17.048.536.676
-1,369
-1,904
-0,079
-0,615
2012
5.632.554.401
1.090.559.696
1,642
-1,369
0,276
-2,749
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
-1,522
-2,307
0,017
-0,775
Standard deviation
1,633
0,637
0,160
1,003
Correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,890376
0,725791
-0,94874
1
0,6612
-0,70891
1
-0,60712
1
34
I.7 Equity
t
Bt
Mt
bmt
rb  t  1, t 
bmt 1
ri  t  1, t 
2006
173.110.130
183.466.344
-0,058
2007
215.362.367
204.163.050
0,053
-0,058
0,353
0,107
2008
259.677.382
252.049.000
0,030
0,053
0,285
0,211
2009
272.893.102
255.096.646
0,067
0,030
0,097
0,012
2010
294.780.600
239.195.180
0,209
0,067
0,136
-0,064
2011
318.655.451
202.136.772
0,455
0,209
0,212
-0,168
2012
364.683.049
328.674.391
0,104
0,455
0,136
0,486
Statistical data for
bmt , bmt 1 , rb  t  1, t  , ri  t  1, t 
Expectation from 2007 to 2012
0,153
0,126
0,203
0,097
Standard deviation
0,161
0,183
0,100
0,232
correlation
bmt
rb  t  1, t 
bmt 1
1
ri  t  1, t 
0,15901
0,07274
-0,63414
1
-0,339
0,66093
1
-0,34674
1
35