HSR Vol. 37
Heinrich Best, Ronald Gebaue
& Axel Salheiser (Eds.)
Political and Functional Elites i
Central and East Euro
e since 1989/90
Heinrich Best, Ronald Gebauer & Axel Salheiser
Political and Functional Elites in Post-Socialist Transformation: Central
and East Europe since 1989/90. An Introduction. 7
Elite Continuity in Ukraine: When Networks Matter (?). 14
Cătălin Augustin Stoica
“Our Martyrs of 1989 Did Not Die for This!”: Political Capitalism in
Post-Communist Romania. 26
Frane Adam & Matevž Tomšič
The Dynamics of Elites and the Type of Capitalism: Slovenian Excep-
Continuities in the Formation of Russian Political Elites. 71
Transformation of Diplomatic Elites in Post-Communist Societies. 91
What Happened Afterwards? Change and Continuity in the Hungarian
Elite between 1988 and 2009. 108
Socialist and Post-Socialist Functional Elites in East Germany. 123
Cadrelites? Career Continuity, Discontinuity, or Disruption of former
Socialist Elites in the Early 1990s. An Event History Analysis on the
Basis of Statistically Matched Data. 139
Ronald Gebauer & Stefan Jahr
Second Life in the Bundestag? Former GDR Delegates in German
Benjamin Beckers, Ralf K. Himmelreicher & Carsten Schröder
The Evolution of Tangibles, Financial and Social Security Wealth over
the Lifecycle: Estimates for Germany. 165
Julia Simonson, Laura Romeu Gordo & Nadiya Kelle
Statistical Matching of the German Aging Survey and the Sample of
Active Pension Accounts as a Source for Analyzing Life Courses and
Old Age Incomes. 185
Rechtsanwälte und politische Prozesse in der späten DDR. Eine quanti-
tative Auswertung von MfS-ermittelten Prozessen 1984. 211
Manuel Schramm & Uwe Fraunholz
Between the Ivory Tower and the Industrial Laboratory: Universities in the
West German Innovation System, 1945-1990. 254
Claude Diebolt, Antoine Parent & Jamel Trabelsi
Revisiting the 1929 Crisis: Was the Fed Pre-Keynesian? New Lessons
from the Past 280
Karol J. Borowiecki & John W. O’Hagan
Historical Patterns Based on Automatically Extracted Data: The Case of
Classical Composers. 298
Johannes Lüder, Achim Brauer & Ronald Jurisch
Breakpoint Detection within the Time Series. Modeling Approach Upon
Paleoclimatic Proxy Data. 315
José Rodrigues da Costa, Maria Eugénia Mata & David Justino
Estimating the Portuguese Average Cost of Capital. 326
The Colonial Origins of Comparative Development: A Skeptical Note. 362
Historical Social Research, Vol. 37 — 2012 — No. 2, 326-361
Estimating the Portuguese Average Cost of Capital
José Rodrigues da Costa, Maria Eugénia Mata
& David Justino
Abstract: »Schätzung der durchschnittlichen portugiesischen Kapitalkosten«.
In spite of the importance of having a figure for the domestic average Cost of
Capital to base the estimates of the discount rates used in a number of long-
term investments, the fact is that Portugal does not yet know with confidence
its own value. Part of the answer might be attached to the number of profound
impacts that affected and disturbed its Capital Markets during the Twentieth
Century, in particular the break introduced by the Carnation Revolution in
1974. This paper translates both a test to the methodology necessary to make
such an estimate under the Portuguese constraints, and also a first estimate of
such a figure. From the daily data available for the quotations of shares listed
in the Lisbon Stock Exchange, a time series of a comprehensive index is
constructed covering on a weekly basis (Wednesdays) a time sample of 31.5
years, from January 1978 to June 2009. It also constitutes the first part of a 3-
year project intended to study the entire Twentieth Century and to produce an
estimate for the Cost of Capital comparable to the values included in the 2002
book “The Triumph of the Optimists” authored by Dimson, March and
Staunton. Although the output parallels traditional UK and USA figures, the
Portuguese estimate for the Equity Return Premium is around 8%.
Keywords: cost of capital, equity risk premium, share index, risk-free rate,
1. Economic Relevance of a
Good Estimate for the Cost of Capital
There are today several important areas in which a country needs to know its
domestic average Cost of Capital, the search for which has triggered a number
of other studies in many countries, especially in the UK and the USA, due to
their cultural environment and their availability of recorded historical data. But
the success of the American economy in the Twentieth Century may suggest
higher than normal annual rates and that may be misleading when extrapolated
to other national economies. Therefore, some years ago three professors of the
Address all communications to: José Rodrigues da Costa, Universidade Nova de Lisboa,
Faculdade de Economia, Campus de Campolide 1099-032, Lisbon, Portugal;
Maria Eugénia Mata, Universidade Nova de Lisboa, Faculdade de Economia, Campus de
Campolide 1099-032, Lisbon, Portugal; e-mail: email@example.com.
David Justino, Universidade Nova de Lisboa, Faculdade de Ciências Socais e Humanas,
Avenida de Berna, Lisbon, Portugal; e-mail: firstname.lastname@example.org.
London Business School – Dimson, Marsh and Staunton (DMS) – published a
large study, involving 16 countries (including Spain), that covers the whole
This study provided, for the first time, a long-run perspective for the cost of
capital in the world, but it also showed the diverse financial behavior of the
sampled countries, as some of them had significantly smaller capital costs in
comparison with the historical values for the USA or for the UK.
Unfortunately, Portugal was not included in that study, a limitation that might
lead some our long-term decisions to be taken based on the extrapolation of the
cost of capital from countries considered to be similar.
The only study that includes Portugal was conducted by Jorion &
Goetzmann2 but only reports the period from 1931 to 1996 and it suffers from
three limitations. The authors had to make use of indirect sources of
information for Portugal – especially the “International Financial Statistics”
published by the IMF; dividends are not included in the equity returns
estimates, and this may undervalue the estimate; finally, the risk premium is
measured as the capital returns in excess of inflation, not the risk-free rate.
The purpose of this paper is precisely to close that gap via an historical
analysis identical to the one conducted by DMS. Therefore, this is an
investigation into the past of the Portuguese Exchange share market to uncover
any potential average return that, if stationary, may be extrapolated into the
future. It is not a forecasting exercise as performed by a number of scholars
including, for example, recent works from Goyal and Welch (2008) or Ferreira
and Santa-Clara (2009), where some past economic/financial variables are used
to estimate the near future value of a stock return.
Two reasons dictated our option. The first one is an intention to make
simply an historical survey and the second one comes from the fact that we are
convinced that one of the main characteristics of any efficient market is that
any method accurate enough to deserve the attention of investors is
immediately destroyed by the subsequent decisions of those very investors. As
Ferreira and Santa-Clara wrote “…to the extent that what we are capturing is
excessive predictability rather than risk premiums, the very success of our
analysis will eventually destroy its usefulness.” That is, unless a new and
accurate methodology of forecasting is used only by its author – and for a
limited period of time – any volatile future is impossible to forecast with
certainty. So, only stable values unveiled from the past can be taken into the
future without much risk.
1 “The Triumph of the Optimists: 101 Years of Global Investment Returns”, 2002. This same
study became such an important source of information, both for scholars and for
practitioners, that it has been updated annually ever since – and expanded later to a 17th
country – thanks to a co-operative agreement established between those three authors and
the Dutch ABN-Amro Bank.
2 “A Century of Global Stock Markets”, NBER, February 2000.
The fact that this discount rate is not known with certainty in any market
does not mean that one cannot make an estimate by observing the history of his
own capital markets. That is the purpose of this paper in relation to the
particular case of the Portuguese domestic economy.
2. Literature Review
2.1. Why CAPM Model
There is now a consensus that variability of share returns requires them, on
average, to pay more to an investor than debt instruments with similar maturity
as a compensation for uncertainty. That positive spread depends on the
particular issuer under consideration, but for the whole share market of a
country there is an average difference that is called the domestic Equity Risk
There are different models that connect the individual spread of a particular
share to a) the general mood of the whole market underlying that particular
issuer and b) to other macroeconomic variables of the country, such as the
annual GDP growth rate, some factors of the industrial sector involved, etc.
However, any multivariable model requires the computation of a large number
of parameters proportional to the number of explanatory variables used by the
model. In this respect, the particular case of the Capital Asset Pricing Model
(CAPM) is very attractive because it uses only one explanatory variable – the
market average return – although this still requires the estimation of the three
i. the cost of risk-free debt ;
the particular level of risk of the issuer βRi=Rfree+
i. (Rmarket-Rfree );
ii. the average risk premium Rmarket.
Therefore, the selection of the Capital Asset Pricing Model is a simplification
measure justified on the grounds of the level of accuracy that it is still
available, and also by the widespread adoption of similar approaches by other
2.2. Historical Versus Future Returns
All the long-term decisions are forward-looking computations and require the
use of a discount rate that shall be valid for the future, not a Cost of Capital that
was in place in the past. However, this single value is not observable in the
market and there is as yet no known model that quantifies such a value for any
time-frame ahead. There are many studies that have developed methodologies
for predicting the equity premium3 but their results do not hold for the 1990s.4
Mehra and Prescott (1985) used an 1889-1978 data base for GDP and
Consumption in the USA and concluded that Arrow-Debreu asset-pricing
models could not explain the high (American) equity risk premium at the same
time as the small average risk-free return that was historically observed. Rietz
(1988) re-specified that model for a frictionless pure-exchange economy and
solved the puzzle in capturing the effects of (possible) market crashes by
abandoning the hypothesis that consumption growth rates are symmetric about
their mean (and fall above their mean as often as they fall below). Reasonable
degrees of time-preference and risk aversion were found, provided that
plausible severe crashes are not too improbable in the long-term analysis.
Barro and Ursúa (2008) went into full annual data on Consumption for 22
countries (including Portugal) to detect crises, as this is the variable “that enters
into usual asset-price equations”. To enlarge the sample they also used GDP for
35 countries (maintaining Portugal). For samples that start as early as 1870 (as
is the case for Portuguese GDP estimations) a peak-to-trough method was used
for each country to isolate economic crises (defined as cumulative declines in
Consumption or GDP by at least 10%) and 87 crises for consumption and 148
for GDP were discovered. This led to the conclusion that 3.5 years was the
average duration for disasters, having a mean of 21-22% declines, under a
coincident timing both in Consumption and GDP. The conclusion is that their
model accords with “the observed average equity premium of around 7%
levered equity”, after assuming that 3.5 is the coefficient of relative risk
Therefore, it is little wonder that people began to look again into the past in
order to estimate that historical cost, hoping that the future would not be much
different from that observed past5. But this raises a number of problems, in
particular, nothing guaranties a smooth replication of the past in the long-term
future. And most countries did not accumulate enough information about their
past – especially the distant past – to produce reliable estimates of such realized
These limitations led the whole financial industry to base their estimates for
the Cost of Capital on the single historical analysis that has been conducted by
Ibbotson Associates for the US market, since this country recorded a time
series that runs uninterrupted from the beginning of 1926. Alternatively, the
industry turned to the UK market, where Barclays Capital and Credit Suisse
First Boston both produced historical estimates for the British Cost of Capital
from a series that starts in 1919. The similarity of all three final results led most
3 Fama and Schwert (1977; 1981); Rozeff (1984); Keim and Stambaugh (1986); Campbell
and Schiller (1988 a, b); Fama and French (1988; 1989).
4 Lettau and Ludvigson (2001) and Schwert (2002).
5 Campbell and Thompson (2005), Hillebrand, Lee and Medeiros (2009).
capital budgeting, fund management practice, and regulators’ decisions to be
made traditionally from that much known American Equity Return Premium of
(around) 8.5% p.a.6
Unfortunately, and more recently, this single “anglo-saxon” value became
suspicious after the arguments coming from different grounds. On the one
hand, both DMS (2002) and Goetzmann (1999) conducted historical estimates
for some countries (including the US market) using data covering the entire
Twentieth Century and obtained not a single common historical rate, but a wide
range of different domestic average share returns, some of them significantly
far from the US value, even after considering the impact of the various
currencies involved. On top of that, Schwert (1998) noted that, extending the
US data base backward to the beginning of the Nineteenth Century (a time
series ca. 200-years long), the American average Cost of Capital becomes
much less than the traditional Ibbotson result, a fact that may indicate that the
risk premium may be non-stationary, and, if so, the future may be different
from the observed past. Finally, an Equity Return Premium of 8.5% is too large
to be compatible with both the rate of long-term economic annual growth of
any economy (estimated to be around 2%) and the level of risk aversion
normally accepted for an average investor (exponent between 1 and 2).
In relation to the first criticism, such a time variability of the Cost of Capital
within one single country or among different countries makes sense, since
markets inevitably comprise human beings and it is known that their mood
does change in response to the economic and social conditions surrounding that
market. That is, human reasons may determine, now and then, an adjustment of
the equity spread demanded by investors to take the risk of price volatility in
tandem with those same environment changes.
But why are the Ibbotson and DMS estimates for the US market (8.5%) so
much larger than the Schwert estimate (4% p.a.) for the same country? The
answer comes from what is now called7 “survival bias”: investors demand an
Equity Return Premium not only to cope with the variability of stock returns,
but also to compensate them for the potential total loss due to rare but
catastrophic crises that are always possible, as recorded in the history of any
country. That is, although people only require an extra payment to invest in
volatile shares, because shares also suffer from a kind of “credit risk”, the total
premium must be large enough to pay for both sources of risk.8.
Indeed, during the entire Twentieth Century the USA was lucky enough to
avoid the great turmoil that affected, for example, Russia – two revolutions – or
6 This is the value indicated on the most recommended book, “Corporate Finance” by
Richard Brealey and Stuart Myers in its successive editions.
7 Brown, Goetzmann, and Ross (1995).
8 As Jorion & Goetzmann (2000) stated: “To the extent that the event causing the break was
anticipated, the market seems to have been able to gauge the gravity of the unfolding
events. Price declines before breaks is consistent with increasing demand for risk
compensation for a catastrophic event”, page 14.
Germany and Japan – collapse of their economies after the loss of world wars
and/or of invasion by foreign armies. On the contrary, the US economy
developed throughout the same years in a rather smooth manner, in spite of
some “minor” crises that were observed here and there, such as the Great
Depression of 1929 and the two oil shocks of the 1970s and 1980s. In any case,
the American financial market never closed for extended periods, there was no
major nationalization affecting large sectors of that economy, and there were
no significant social events affecting the nation. On the contrary, in the
previous century there were the 1812-15 War with the British empire and the
major Civil War (1861 to 1865), which brought vast devastation to some
important regions of that country, and these may explain that, extending the
time series to include these previous 100 years, the average equity return
becomes closer to the observed values in those other more unstable countries.
Under this interpretation, the high Equity Return Premium observed during
the Twentieth Century in the US market would be the result of a pessimistic
view of the average American investor during those recent 100 years that
required them to demand a compensation to cover the expected volatility of
returns plus the risk of a potential total loss. But, in the Nineteenth Century, the
realized Equity Return Premium already incorporates the actual losses of those
catastrophic years, and this could explain the much lower premium found ex-
As to the second criticism, there are two economic models that suggest that
the 8.5% Equity Return Premium estimated for the US market must be too
large a figure:
i. Gordon’s constant growth model9 for corporations allows us to estimate
the Equity Risk Premium from
where g is the constant growth rate of the company, and D/P is the percent
return obtained from the amount D1 of (next year) dividends received from a
share currently priced at P0, and r is the cost of debt. For annual dividends on
the order of 3% to 4% of P and a real return of long-term debt of around 2%, an
annual Equity Risk Premium of 8.5% requires a growth rate larger than 6%
p.a.,10 which can only exist while a company is still in its infant stages of
development11. But even that model is over-optimistic since it assumes a
constant rate g forever. For a more realistic model with rates of growth
9 Gordon, Myron J. (1959). “Dividends, Earnings and Stock Prices”. Review of Economics
and Statistics 41: 99-105.
10 See Annex II.
11 Otherwise – if unabated – that company would, sooner or later, become larger than its
surrounding economy. Note that the consensus is for a long-term growth rate of any
economy of about 2% p.a.
decreasing from an initial high value, as the company matures, the discount
rates of future dividends must be less, meaning a smaller Equity Risk Premium
than under the constant g model;
ii. Consumption-based asset pricing seeks to estimate the Equity Risk
Premium from economic theory, as that premium ought to be the
expression of the risk aversion of investors, since the securities’ extra
returns are the price of deviating consumption from today into the future.
The appropriate measure of the risk of investing in volatile assets is to
assess the impact of that investment on the riskiness of future
consumption. This leads us to the recognition that the key to investment
risk is the correlation between asset returns and consumption variation:
the higher that correlation the more risky are those assets because these
investments pay off more to savers precisely when consumption is
already high, and vice-versa:
Risk Premium for an Asset=
where is the average investors’ risk aversion and is the correlation between
the percentage change in consumption ΔC and the asset return R. Once again,
for normal values of these four parameters12, the Equity Risk Premium obtained
would be about 100 times lower than the empirical findings. Any
accommodation based on accepting values of much larger than the classical
range13 is not possible because that would require extremely large real interest
rates, which were never found in any market for a prolonged period of time.
It has been suggested that this consumption model might be either too
conservative or too rational. As to the conservative side, Campbell and
Cochrane (1997) proposed a change in the utility functions such that “as
consumption drops toward the accustomed standard of living X, people become
more risk averse because they are less willing to accept further declines in
consumption”. That is, is not constant and can become much larger than in
classical models, especially when consumption falls and approaches that habit
On the psychological front, the development of Prospect Theory by Tversky
and Kaheman (1992) allowed bringing some irrationality to the explanation of
market behavior. This is what Benartzi and Thaler (1995) did: investors care
more about the returns obtained than about the value of their portfolios. Since
losses are particularly painful, some investors do not evaluate returns every
day, but only at large intervals of time, avoiding the useless pains due to
temporary losses. So, those investors evaluating their portfolios everyday
require a large risk premium to hold shares instead of bonds, but those taking
12 Normal orders of magnitude: =1 or 2, C is around 1% p.a., R around 20% p.a. and
13 Even if we are slightly more generous and accept around 10 and around 40%, we find a
risk premium of about 0.8% p.a.
large time intervals between evaluations have smaller probabilities of losses
and require smaller risk premia. Therefore, there are many different risk premia
in the market and such values may change over time according to the average
time horizon of evaluation of investments.
In summary: since the known theoretical models are not yet able to supply
reliable figures for future values of the ERP, we are left with the classic
approach of estimating the future from the recorded past. However, the
Ibbotson figure sounds exaggerated, not only for the US market, but also for
other countries, suggesting that the best each country can do is to develop its
own data base of stock returns and extend it backward as far as possible to
improve the quality of the estimate.
However, this avenue raises some problems: Is the historical sample large
enough to produce estimates falling within narrow confidence intervals? What
if the Equity Risk Premium is itself variable?
This question of non-stationarity is crucial for historical estimates because
the most simple analysis has implicit the assumption of stationarity. But there
are reasons for suspecting that the true Equity Risk Premium may be changing
over time, a fact that is in agreement with some tests that reveal statistically
significant changes in market variability. So, unless we have a model of how
the Equity Risk Premium varies over time, we may be misled by historical data
and/or we obtain extremely large confidence intervals even from century-long
Fortunately, there are also arguments in favor of giving some value to the
results linearly extrapolated from those historical series:
a. as mentioned above, one of the most comprehensive analyses was
conducted by DMS (2002) for the entire Twentieth Century and covers 16
countries that represent more than 95% of the free-float market
capitalization of all world equities at the start-2002; although the historical
average of Risk Premium14 varies among those countries, that premium is
always positive and covers a range (arithmetic averages) between 3.2%
and 10.6% p.a.;
b. this large range of values is compatible with the different histories
followed by the various countries in the sample, especially catastrophic
events such as revolutions, nationalizations, etc. that plagued them;
c. the average volatility of returns shown currently by most indices – around
15% p.a. – suggests that 100 years of history is not enough to reduce the
uncertainty of the estimated average equity returns; that is, the confidence
interval anticipated for those averages is still too large15; but is also
compatible with the above range of values;
14 Relative to T-Bills, not to T-Bonds.
15 Bradford Cornell: “…72 years’ worth of data is not enough to measure the risk premium
with sufficient precision to satisfy most investors … even if it is assumed that the future is
d. even if the return demanded from shares does vary over time, it is difficult
to accept that it took some fixed value in the past but, from now on, has
definitely changed; most likely, it has changed a number of times in the
past – following the business cycle – without any up or down trend, and
will do the same in the future; therefore, the average past of each country
may not be very different from its future, and we can approach that
historical average provided our data base covers a number of different
e. although there is a minimum rationality in price formation, recent studies
have revealed the degree of irrationality present in this particular area of
human behavior; so, it is possible that the high values of risk premium
found in the past series are a simple reflection of some of those
irrationalities and, unless we assume that mankind will change in the
future and be fully rational from now on, we cannot reject those high
All in all, it seems that our low level of knowledge of these matters still
recommends the use of the past as the “least worst” predictor of the future and
that justifies that, every year, the Ibbotson Group publishes a number of studies
updating the statistical information from a number of countries: Ibbotson
Associates – Stocks, Bonds, Bills, and Inflation Yearbook. Also, since the
publication of The Triumph of the Optimists in 2002, which covered 101 years
of 16 countries, the London Business School and the ABN-Amro Bank have
partnered to update those historical results every year and to extend that type of
analysis to a 17th new country. Finally, Prof. Damodaran also maintains a page
on his website where some statistical data are also accessible, in particular the
historical cost of capital.16
3. Constraints of the Portuguese Capital Market
3.1. Liquidity Constraints in the Stock Exchange
Most share markets in small countries show low levels of liquidity, due mostly
to their reduced economic dimension that translates into a small number of
large domestic corporations that are listed, in parallel with insignificant foreign
investors’ interest in all domestic companies. However, the situation in
Portugal during the 30-plus years under analysis shows some additional
constraints stemming from the following:
like the past, the estimates are so imprecise that it is not clear what the risk premium has
truly been in the past”, page 44.
a. by tradition, the largest source of funding of our domestic businesses is
bank credit, not shareholders’ capital; the banking segment has always
overshadowed the capital market in this country;
b. during 1975 (following the Carnation Revolution in 1974), a large slice of
the economy was nationalized – implying that the number of listed
companies dropped significantly in one – and all overseas companies
listed on the Lisbon Exchange ceased their operations following the
political independencies (under leftist governments) granted to those
overseas territories in that same year.
Adding to these limitations, the operations of our two domestic Exchanges
were suspended on the 25 of April 1974, only reopening for share trading in
March 197717. All in all, these factors determined that, when trading in shares
restarted, the number of listed companies was extremely reduced, none of them
were large entities, and investors were very risk averse due to the traumas
brought recently to them by the political and economic events following the
Fortunately, in a few years it was possible to overcome most of these fears
and to re-establish a “normal” capital market that was open to foreign investors
and mature enough to accommodate the large privatization program the country
executed during the 1990s. That “miracle” was even “bright” enough to call the
attention of some other European Exchanges, a fact that led in February 2002
to the merger of our two domestic organized markets with the Euronext
3.2. Share Indices in Portugal
To the best of our knowledge, only very late in the Twentieth Century did
Portugal start to compute share indices according to the standards of any other
developed capital market. In fact, it was only in February 199119 that the
Lisbon Stock Exchange launched a capitalization-weighted share index – then
called the BVL-General Index20 – with a time series dating back to the first
trading day of 1988. This index is still being calculated once a day and released
after the close of the trading session.
This initiative of the Lisbon Exchange was a response to the drawbacks
arising from the two share indices that existed at the time (beginning of 1990s):
a. the Totta & Açores Index was calculated and published every day by the
local Totta & Açores Bank, but with a methodology for the selection of the
17 Although the order from the government was dated from the 4th of March, 1977, only on
the 7th March was trading resumed. Meanwhile, the Porto Exchange remained closed until
18 Later, in April 2007 this pure European Euronext Group merged with the NYSE Group to
form the current transatlantic NYSE Euronext Group.
19 Included in the Daily Bulletin of the Exchange, for the first time, on 25th February, 1991.
20 This index was later renamed as PSI-General.
companies to be sampled and a set of rules for translating the corporate
events in the daily index value – dividend payments, stock splits, etc – that
were never made public, thereby casting a shadow of representativeness
over the values of this index;
b. the Bank of Portugal index (one single average value per month) was
based on all the companies listed in the main market of the Lisbon
Exchange, but it weighted each share price by the corresponding traded
volume, a method that overvalued those securities having more trades, not
those with more capital placed in the market.
The panorama before the Carnation Revolution of 1974 was similar to that just
described, although both the Bank of Portugal and the Portuguese National
Statistics Office were developing some indices to measure both the overall
volume of trades and the average prices.
It is important to note that the reason for the Lisbon Stock Exchange to start
that index time series only in 1988 is connected to the liquidity problems
mentioned above: before 1988, a significant number of listed shares frequently
showed zero transactions in a trading session, and when some trades took
place, the number of securities transacted was very thin, raising questions about
the economic representativeness of those agreed prices.
Currently the Portuguese Exchange computes some other share indices, in
particular some sectorial ones alongside a short index comprising only 20
companies. The reasons that led us to emphasize the BVL-General index in our
analysis were the following:
a. it is the largest and most diversified sample, as it uses all companies with
shares listed in the main market, not only the 20 most “representative”
ones as the most spoken PSI-20 index;
b. it includes large and small corporations, therefore any potential size effect
is diluted in the sample; this criterion excluded all sectoral indices from
c. it corrects for dividend payouts of the sampled shares, a feature that the
PSI-20 index does not include;
d. most important, it is the longest time series available: against a base date
of 5/Jan/1988 for this index, all the sectoral indices start at the beginning
of 1991, and the PSI-20 index starts on the very last day of 1992.
3.3. Risk-Free Interest Rates
Although it is understood that an Equity Risk Premium (ERP) measures the
average excess return demanded by investors to take the uncertainty of the
subsequent rewards obtained from those equities, there is no consensus about
the maturity of the debt instruments that should be used as that reference basis:
a short-term or a long-term rate?
At first sight, long-term rates would be preferable as they also incorporate a
premium for the long maturity of the credit: it compares similar alternatives for
funding new projects. However, long T-Bonds also suffer from high volatility
of returns due to the variability of the interest rates in the market – which
includes the effect of inflation variation – whereas short-lived T-Bills are much
less vulnerable to the current price of money, and inflation is always factored in
when each new issue is placed in the market.
This justifies the frequent double disclosure of Equity Return Premium –
excess above T-Bills and above T-Bonds – adopted in a number of countries.
This is important because, in the history of every country, there are periods of
high unanticipated inflation rates that justify long periods with negative returns
from long-term bonds if previously issued with low coupon rates. Those
negative returns may mislead us when subtracting the inflated average equity
return from such negative debt returns, leading to an excessively large ERP.
It is also not clear which level of credit risk imbedded in that interest rate
can be accepted in a real case: the cost of money for operations with a Central
Bank (or a National Treasury) or the rates of the Interbank Money Market,
which still have some residual credit risk included.
Fortunately, the limitations of the Portuguese money market simplified our
decisions in this regard:
a. because the Portuguese T-Bills were created only in 1985 and that market
was closed temporarily from 1998 to 2003, we were forced to exclude this
source of information;
b. during the first years of the period under analysis, the interest rates defined
by our Central Bank resulted from the economic policies of the
government of the day, not from any considerations of monetary policy;
obviously they were also excluded;
c. although in the time window analyzed our Interbank Money Market
offered rates for a wide range of maturities – from overnight credits to
one-year operations – the clear majority of the liquidity in that market was
always concentrated in the short-term end of that spectrum.
Therefore, we excluded the T-Bills source, opted instead for the Interbank
Money Market21 (IMM) rather than Central Bank rates, and used only
Overnight rates22 (O/N). Note that, in a number of countries, the risk-free rate is
“borrowed” from the issuing rate of one-month T-Bills, but we assumed that
the difference between the overnight and those one-month rates were always
21 So our “risk-free rates”, although very short-term, involve some residual credit risk.
22 But some details are in order at this moment:
i) when, after July 1993, the domestic market began to offer three Overnight rates – for the
same day, for the next day and for two days ahead – we selected the same day O/N case;
ii) but during some years that shortest term segment included 24-hour to 72-hour maturities,
without any distinction between the three cases.
significantly less than the estimation error of the average rate of return of
Finally, it must be said that, due to the closing of the Portuguese IMM
market at the end of 2008, we continued our time series of risk-free rate toward
2009 using the EONIA daily rate as the representative Portuguese short-term
3.4. Long-Term Memory of Defaults
The confidence in Portuguese treasury securities as risk-free assets deserves
some additional comments. Although it might be thought that treasuries are
risk-free assets because they represent a governmental commitment for the near
future, historical events in Portugal during the Nineteenth Century explain why
our treasuries cannot be used as such, at least for a significant part of the 1800s
and the initial part of the Twentieth Century.
In fact, the confidence in our treasury debt instruments was very low during
the second half of the Nineteenth Century, when the total amount of public debt
increased dramatically every year, thanks to a large surplus of public
expenditure over the simultaneous tax collection. The result was a low market
price for their placement in all the European capital markets. That is, the
Portuguese government of that time was forced to issue high nominal amounts
of public debt but could only receive much lower cash amounts from the few
Such negative historical experience ended with the declaration of a
bankruptcy in 1892 (decree of 13 June), when our government declared that it
could not fulfil all the debt contracts signed with its foreign lenders, following
the abandonment of the gold-standard just the year before (July 1891). That
default meant that all amortizations of treasuries were suspended, and the
country would pay only 1/3 of all interests due under those contracts.
Of course, even before this partial default, a number of public sources
already raised the fear about the Portuguese debt, as our credit rating was
decreasing. Specialized newspapers disclosed information on the prices and
rewards of our bonds and bills during that pre-bankruptcy period, and the
returns demanded from those instruments increased in tandem with the
mounting fears on the risk level of Portugal. The negotiations with the creditors
after 1892 lasted for ten years, only leading to an agreement when a conversion
of the loans was achieved in 1902 (law of 14 May).
The fact that capital markets do have memory means that investors always
make their decisions based on a stock of accumulated knowledge, and the
reality is that, between 1870 and 1913, the coverage of all types of news about
Portugal, in the Times of London, reached an annual average of 102 reports.
The ratio of good to bad economic news that was reported was 1.12%, exceed
only by Russia among a sample of 16 following countries: Argentina, Brazil,
Canada, Chile, China, Colombia, Costa Rica, Greece, Egypt, Hungary, Japan,
Mexico, Queensland, Sweden, Turkey, and Uruguay.23
Such a poor performance closed the doors of all international credit markets
to Portugal, and only during the First World War could a loan be obtained from
the UK, in spite of the special relationship between the two countries.
Note that in the Twentieth Century, the events in the 1960s and 1970s were
also detrimental for investors’ confidence in our capital market. Colonial wars
began in 1961, damaging colonial exports from the zones under military
pressure in the colonies. The effort to fight the war led to a different allocation
of resources and to uncertainty and even adverse perspectives on the future for
the colonial firms. The Carnation Revolution in 1974 brought a new political
model based on socialism that was consecrated in the 1976 constitutional text.
Very soon dozens of political parties were organized, most of them leftwing-
oriented. The Communist Party performed an important role, while radical
policies were adopted. Nationalizations of banks and other firms in the main
economic sectors (insurance, large industries, and road transports) were carried
out in 1975, while land expropriation in the large-property districts of Alentejo
and Ribatejo was also executed. Transactions in the domestic Stock Exchanges
were suspended in 1974 and the decolonization of all overseas territories left
Portugal confined to her European territory plus the tiny Atlantic archipelagos
of the Azores and Madeira.
Half a million Portuguese, who were living in the colonies, left for Portugal
in 1974-75, representing an influx of over 5% to the Portuguese resident
population, and requiring the Government to support them in their beginning of
new economic activities in the country. On top of that, a severe economic
recession in the country brought problems to our balance of payments. Export
difficulties led to the currency depreciation in 1977, and an IMF stand-by
agreement was required in that year.
Confidence in the prosperity of Portugal under the new democratic regime
was based on the project of joining Europe, a hope that was fulfilled only in
1986. In fact, the 1972 free-trade agreement with the then EEC was, in 1976,
transformed into an association treaty to which a membership application
followed in 1977. However, the negotiations dragged on for years, and the
1980-83 recession demanded a second intervention of technical and financial
help from IMF for the period 1983 to 1985.
Portuguese membership of EEC was finally achieved in 1986, together with
Spain, in a decade that prepared Europe for further consolidation after the
communist political regimes collapsed in the 1990s in Eastern Europe and
Russia. The integration of the Democratic German Republic and the Maastricht
23 Magee, Gary, La Trobe University, “Investors, information and the British world, 1860-
1913”, paper presented at the EBHA, Milan, 2009. <http://www.hnet.org/~business/-
Treaty led to the European Union, while in Portugal, a social-democrat
government began a privatization program.
Only at the end of the 1990s, when it became clear that Portugal would
become a member of the first wave to enter the single European currency24, did
our level of risk start to decrease, reaching the lowest levels for more than two
4. The Econometric Model
4.1. Stochastic Behavior
Although it is known that the stochastic model adopted by Black and Scholes
does not correctly describe the random behavior of the share prices, we have
assumed it to be accurate and simple enough to deserve our attention.
Therefore, we took that model to justify the regression that we used to estimate
the historical average return provided by the Portuguese shares during the 31.5
years of our sample25. That differential equation can be transformed into
and that suggests that the log values of the share prices – or of the index –
follow some straight line with a slope given by
2. It was this suggestion
that led us to fit a line to the historical periodic log values of the Portuguese
share index recorded during the years January 1978 to June 2009.
24 Mind that the Euro was first introduced in January 1999 simply as a virtual currency, while
all legacy coin and notes were introduced only in 2002.
25 Some scholars have studied other Stock Exchanges and found that, for some of them, a
Mean Reverting model of periodic returns could well describe their stochastic behavior. In
our case and for the period analyzed, an adjusted autoregressive model AR(1) produced an
R2 of only 0.07. However, this is not a universal view and some countries have even shown
a change from such a mean reverting model to a random walk behavior. Due to that low R2,
and because there is yet no consensus in academia about this question, and since mean
reverting is against the logic of market efficiency, we adopted the B&S model.
4.2. Historically Realized Return or a Trend Curve
From a series of historical index values, the first impulse is to estimate the
historical annual return from the arithmetic average of the n periodic returns
observed during the entire sample26
However, due to the use of logarithmic periodic returns, this average coincides
and that raises an important issue: this estimate does not take into account the
particular evolution of the index between those two extreme dates. That is, it is
irrelevant whether the initial S0 and/or the final value ST corresponds to a peak
(or to a trough) of a euphoric (or pessimistic) period, because the final result is
always determined solely by those two extreme prices.
The consequence is that the estimate obtained from a short slice of history is
crucially sensible to the starting and closing dates, particularly if either of those
two prices is significantly deviated from the “average value” of the index at
each time. This drawback can be minimized only for extended time series
a. based on the B&S stochastic model, the deterministic term of the
difference between the final and initial log prices grows linearly with the
interval between those extreme dates, while the disturbing random term
grows only with the square root of that same time span;
26 We obtained an historical average of 15.9% p.a. (365 days), an annualised = 9.5% and an
error of 4.5%.
b. therefore, even if the slope
2is small, this deterministic term will
sooner or later dominate the random component, for intervals of time long
enough to compensate for that reduced trend.
That is, according to the B&S stochastic model and for very long time series,
most of the difference between Ln(ST) and Ln(S0) is due to the deterministic
term – the slope of the line – because the random term affects that average only
marginally. In our case, we have around 30 years of data and, for a common
value = 15% p.a. and for an average annual return of
2=10% p.a., we
i. an accumulated return during the 30 years of 10% x 30 = 300%;
ii. and an accumulated volatility, in the same period, of 15% x √30 = 82%.
These figures mean that we have only 5% of probability that the average
annual return falls outside the range300%±2×82%/30, that is, it falls between
15.5% p.a. and 4.5% p.a.
Of course, the longer that time series, the smaller will be the impact of that
noise term in the size of the confidence interval. It is this fact that only justifies
the use of the realized return – the actual difference between the two extreme
values – for estimates of the historical cost of capital when one has more than
one century of continuous time series.
As a second best alternative we decided to estimate that average annual
return adopting the logic of a curve fitting.
4.3. Fitting an Exponential to the Historical Index Curve
Since there is a consensus that shares must provide investors with a certain
expected periodic return – although disturbed by a permanent “noise” – one can
anticipate that all share indices will tend to evolve through an “oscillating
flight” around a “middle of the road” exponential line. The degree of deviations
from that ideal trend curve will depend on the level of volatility around that
average expected periodic return. Of course, things can be linearized by taking
the logs of all index values.
That same purpose of fitting a straight line to the series of log values of the
index comes also from the idea of estimating the parameters of the B&S model
using the maximum likelihood method:
which leads, in essence, to the minimization of the square distances between
the measured points of the log index and the estimated best-fitted line.
There are, however, some particularities that cannot be overlooked:
a. the model assumes that the distribution of log prices around the straight
line follows a Normal function with a standard deviation that grows over
time, a fact that cannot be taken as granted because i) there are empirical
findings that suggest that is heteroscedastic, and ii) because there is
frequently autocorrelation between successive returns (potentially, a
residual characteristic of a certain mean reverting behavior27);
b. there is a strong autocorrelation between log prices because any realized
price for time tiis almost entirely defined by the value of the same index
for the previous moment ti-1.
That is, the simplest form of the Ordinary Least Squares methodology for the
line fitting has to be replaced by a more elaborated alternative that takes into
account the variability of and the intense autocorrelation along the time series
of log prices.
In summary, we estimated the average historical annual return using 31.5
years of the Lisbon Stock Exchange history and fitting a straight line to the log
values of the share index covering that entire sample, not forgetting that this
time series could show strong autocorrelation and some heteroscedasticity.
4.4. Measurement Errors
As mentioned above, in a significant number of days during the 10 years from
1978 to 1987, many listed shares included in the index did not trade at all. In
spite of that, when no agreed price existed, the daily index was computed using
the average value between the Bid and the Ask prices as a second best
alternative to such an equilibrium quotation. However, this decision introduced
a source of error because we knew only the range – between the two values –
where any equilibrium price could have been struck.
That is, extending the time series backward from the beginning of 1988 to
January 1978 produces a set of index values with some measurement errors.
One of them is due to this Bid/Ask spread and that can be easily estimated, but
some others can only be mentioned:
a. some companies only offered either a Bid or an Ask price, and that puts a
limit to the range of potential equilibrium prices on one side only;
additionally, it is not possible to make an estimate of an individual error
for those days and for those shares where only one side is disclosed;
b. even for those shares with an equilibrium price struck for the day, the very
low volumes of shares actually traded raises the question of the
representativeness of that quotation.
All of this suggests that the fitted straight line is estimated in the context of an
input data (Y, X) where there are some measurement errors only in Y, not in X.
But since those sampling errors do not affect the value for the estimated slope β
but lead only to a confidence interval for that estimate a little larger then the
27 For our weekly sampled series, the autocorrelation of returns is 0.267 for one week lag,
0.260 for two weeks and 0.074 for three weeks.
real one, this specific subject of error does not affect our estimate and can be
left for a future paper.
5. A First Sample of the Portuguese Market
5.1. Extending the Sample Backward
While still collecting data to construct a full series of index prices covering the
entire Twentieth Century, we were tempted to take a first glimpse of the
Portuguese market by analyzing the behavior of the BVL-General Index
published since the beginning of 1988.
However, that short sample suffers from two important drawbacks: the base
date – 5 Jan 1988 – happens to occur exactly in the aftermath of the October
1987 speculative crisis; additionally, the market is currently very depressed.
a. one may suspect that the initial value of the index might be above the
long-term trend of the market due to the heavily “inflated” quotations
observed during October 87; that is, the market was still returning to the
“normal” levels during January 1988;
b. the current index values might be too depressed because we are near the
trough of the current financial crisis, which might be far below “average”;
c. adding these two factors our estimate risks to be much below the average
historical cost of capital trend.
We therefore felt the necessity to tap the domestic market before January 1988
in order to minimize the impact of that base date and also to enlarge the size of
our time sample. In the end, we were able to add 10 more years to the existing
21.5-year series by computing a share index for the years 1978 to 1987, thus
fabricating an uninterrupted 31.5-year long time series. In further studies, we
plan to extend that index series toward the beginning of the Twentieth Century
so that we can work with a sample of the same size as those used by other
authors for other countries.
5.2. Sources of Information for the Period 1978-1987
Our main source of numerical data was the collection of Daily Bulletins
published by the Lisbon Stock Exchange for the period 1978 to 1987, available
from the Documentation Center of the Lisbon Exchange (now called Euronext
Lisbon). Similar data from the Porto Stock Exchange were not used because
this market remained closed until 1981 and also because, even after that date, it
accounted only for a minor volume of the domestic secondary market.
Prices and quantities were collected only for Wednesdays in order to
minimize the potential impact of the weekend effect, if any28. In the event a
Wednesday happened to be a bank holiday, the following Thursday was taken,
except if the market was also closed, in which case we took the best alternative
available to represent that very same week.
For the purpose of constructing a share index, it was crucial to have
information concerning all the corporate events that affected all the firms
included in the index. Three main sources were used for this: the notices
obligatorily published in the Lisbon Exchange’s Daily Bulletin by all listed
companies, the Annual Report of Activities for the relevant years of the Lisbon
Stock Exchange, and some other statistical products published by the same
Based on these sources, it was possible to adjust the weekly values of the
index for all the corporate events that were detected for each of the firms
included in the sample of the index. Note that this means in particular, that the
reconstructed index measures the total return of the market – dividends plus
capital gains/losses – not only price averages.
5.3. Tackling the Liquidity Constraints
i) Agreed Quotations Versus Bid/Ask
During the 10 years from 1978 to 1987, the trading mechanism in use at the
Lisbon Exchange was one single auction per security per trading session. This
Roll Call trading system called every security one at a time, and an equilibrium
price was then searched by the brokers in order to maximize the number of
shares that could be traded29.
As mentioned above, on a number of days, buy and sell orders for a number
of issues did not clear at all, and no trades were possible on that particular day
for that security. However, this did not preclude the market having information
of the best buy and best sell offers entered into the auction crowd. Of course,
these Bid and Ask prices did not represent an agreed quotation, but they were,
nevertheless, an indication of the general level of prices that the market was
attributing to those shares on those days.
Therefore, our option was to calculate the share index either with the single
daily (agreed) quotation found in the auction – when that information was
available – or alternatively with the simple average between the corresponding
Bid and Ask prices. Also, in a few cases, we used only the Ask or the Bid if
28 Note also that, until May 3rd 1989, the Lisbon Exchange traded only four days a week.
Reasons are mainly connected to the manual workload associated with Netting and
Settlement of all past trades. Also, from the reopening in 1976 until September 20th 1978,
there were only three sessions per week, on Mondays, Wednesdays, and Fridays.
29 There were additional criteria for the case of more than one price of equilibrium maximi-
zing the volume of trades.
that was the sole information disclosed in the Bulletin, and this in order to
avoid computing the index with a very small pool of companies.
ii) Weeks With no Price Information
Unfortunately, for a few days, not even those isolated Bid and Ask prices were
available, either because the security was suspended from trading (due to some
corporate event), or because there was no interest in entering orders to the
market. When such interruption extended only to one week or less, the index
was calculated for that particular missing Wednesday assuming that the market
would have priced that share exactly as in the previous week. But, for longer
interruptions, that particular company was temporarily excluded from the index
until its trades later resumed.
iii) Market Without Quotations
From February 1983 onward30, the Exchange market was divided into two
- The so called “Official Market” – the main market – where the larger
and “senior” companies could list their shares;
- and the “Market without Quotations” created to trade (but not list)
some junior companies or the provisional certificates of shares (and
bonds) issued by corporations already listed, while their final paper
certificates were being printed and distributed among the investors.
These differences between the two segments suggested to us to use only the
firms listed in the Official Market, but to take into account all the shares
already issued by a listed corporation (if fully liberated) when computing the
capitalization weight of that particular component of the index.
iv) Selection of Companies to Compute the Index
Due to the restricted number of corporations that had their shares listed in the
main market of the Lisbon Exchange, we decided to use almost all of them,
with the few exceptions of those so small or so infrequently traded that their
contribution to the final value of the (capitalization weighted) index would be
In the later years of the 10-year period, a growing number of companies
opened their capital to public investment and had their shares listed in our main
market, most of them with so significant a size that they deserved their
inclusion in the index from the very beginning of their listing. Table 1 indicates
the number of companies in the index throughout the period.
30 See Daily Bulletin for 13 January 1983.
Table 1: The Number of Companies in the Index Throughout the Period
Year 1st Semester 2nd Semester
1978 14 14
1979 16 16
1980 17 17
1981 17 17
1982 16 16
1983 17 17
1984 19 19
1985 20 20
1986 27 27
1987 46 63
198831 Max = 128/Min = 80 Max = 154/Min = 123
Figure 1 compares, per week, the number of companies in the index sample
with those that actually traded on the Wednesday representing that particular
week. The panorama clearly improved from 1978 to 1987, which explains why
we excluded the first year (1977) after the trade suspension imposed by the
Carnation Revolution in April 1974.
Figure 1: Comparison, Per Week, of the Number of Companies in the Index
Sample with Those that Actually Traded on the Wednesday
Representing That Particular Week
31 1988 is the first year of the already existing BVL-General Index time series.
INDEX SAMPLE AND TRADING
04/01/78 04/01/79 04/01/80 03/01/81 03/01/82 03/01/83 03/01/84 02/01/85 02/01/86 02/01/87 02/01/88
Nº of Companies in the Index and of those that traded
Nº of Companie s that traded on Wedne sday
NNº of Companie s in the Index
5.4. Heteroscedasticity and Autocorrelation
It is frequently said that shares tend to exhibit autocorrelation in their time
series, meaning that one day price variation is not fully independent of the
previous day’s performance and even from more distant dates. However, the
autocorrelation that interests us is the interdependence of the log prices of the
index over time, not the interdependence of the corresponding log returns.
Since our full time series of the index is made up of an extension of the
BVL-General index series (computed daily from the beginning of 1988) with
the new weekly sampled series for the 10 previous years (1978 to 1987), any
autocorrelation estimate required the construction of a new time series with
only weekly prices. This loss of information was compensated by the improved
quality of the final estimate of the historical average annual return provided by
the extended sample – about 50% more years.
In spite of the longer time interval between successive prices – one week
rather than one day – one can forecast a strong autocorrelation from the very
model adopted from the beginning:
- substituting, for simplicity sake, Yt for Ln(St) in the B&S model
this means that the next expected value Yt+Δt tends to be close to the
sum of today’s value Yt and a small deterministic term given by
- therefore, the distance to the predicted value Y indicated by the linear
regression line fitted to the historical evolution of the index –
Yt+Δt=a+b.Xt+Δt – tends to be almost equal to the previous day case –
distance to Yt=a+b.Xt;
- this fact translates the idea that the (log) prices of the index do not
distribute randomly around the fitted line, rather they tend to stick to
the previous values, that is, they show a very strong autocorrelation.
In fact, the autocorrelogram of the 31.5-year weekly time series covering the
interval January 1978 to June 2009 indicates the following values:
1 week 0.998
2 weeks 0.995
3 weeks 0.992
4 weeks 0.989
5 weeks 0.985
6 weeks 0.982
7 weeks 0.978
8 weeks 0.974
9 weeks 0.971
10 weeks 0.967
Here we have two conflicting views. On the one hand, the B&S model suggests
that uncertainty about the future grows over time as the variance of any
estimate for a future price also grows with the time distance to that future date;
and that may “facilitate” large future deviations around the exponential trend
line. On the other hand, in the real world, prices never move far away from
such a “middle-of-the-road” line, and empirical observations indicate that the
volatility of the periodic returns is variable and there is some autocorrelation
between successive period returns (against the random walk assumption of the
Therefore, the fitted straight line was estimated via an OLS with potential
heteroscedasticity and autocorrelation. We include a comparison with the
results from the simplest OLS approach, as well.
6.1. OLS Regression of Log Prices
(Homoscedasticity and no Correlation)
The goal of this paper is to find the slope β of the fitted straight line, a
coefficient that does not depend on any potential autocorrelation and
heteroscedasticity that may exist in the time series:
From the two parameters (α,β) of the line adjusted to the log values of the
index, the corresponding parameters of the fitted exponential are:
Adjusted R Square 0.814188514
Standard Error 76.03%
1 4157.419 4157.419 7191.5316
Coefficients Std Error
Lower 95% Upper 95%
X Variable (
Homocedasticity & No Autocorrelation
a. Average annual return32 β = 365 x 0.04795% = 17.50% p.a.
Here, we took a 365-day year;
b. Initial value of the index (on 4 Jan 1978)
α=e-10.16192+0.0004795x4Jan78=33.12 index points.
Here, the slope β is multiplied by the initial date of the new series.
Figure 2 superimposes the random evolution of the index to the best-fit
exponential. It seems that, since the peak of quotations observed at the
beginning of 2000 – the dot.com crash – our market could not recover enough
to cross back over the exponential curve, and also the current crisis has even
worsened the situation.
Figure 2: Superimposition of the Random Evolution of the Index
to the Best-fit Exponential
This evolution of the last nine years may be a pure stochastic realization, but it
may also be interpreted as:
i. the Portuguese economy has been showing a difficulty in offering high
rates of GDP growth in that same period, a fact that may already have
been recognized by the investors as a structural change in our underlying
ii. and/or, because the country joined the single currency area in the
beginning of 1999, investors may now assume that, from that moment
on, no major crisis is possible in our future that would impose a full loss
32 Note that this measures, in annual terms, the continuous rate of growth of the index (the
trend), but the relative annual variation of that trend is given by exp(b) – 1 = 19.13% p.a.
However, we are interested only in the first estimate, since it represents a geometric annual
average due to the use of the log values of the index to be compared to the annualized
geometric average risk-free rate.
Januar y1978toJun e2009
4-Jan-78 4-Jan-80 3-Jan-82 3-Jan-84 2-Jan-86 2-Jan-88 1-Jan-90 1-Jan-92 31-Dec-93 31-Dec-95 30-Dec-97 30-Dec-99 29-Dec-01 29-Dec-03 28-Dec-05 28-Dec-07 27-Dec-09
Index Values (base value 1000 on 5 Jan 88)
of their investments; if so, our Equity Risk Premium may now be in
much lower levels than before;
iii. note that, immediately after the reopening of the Stock Exchange in
1977 and also around the middle of the 1980s and 1990s, there was
increasing confidence in the recovery of our domestic economy, a fact
that was confirmed by the large number of companies that joined the
stock market, and also by the tremendous success of the privatization
program implemented from 1989 until 1999.
6.2. OLS Regression of Log Prices
(Heteroscedasticity with Autocorrelation)
The existence of autocorrelation and/or heteroscedasticity in the regression
does not change the estimate of the slope β of the fitted line, but it does change
the confidence interval of that coefficient. However, one must consider it very
likely that, during these 31.5 years, the market might have experienced
different economic environments, that is, heteroscedasticity is most likely to
exist. Also, the stochastic model adopted from the beginning suggests a strong
autocorrelation in our time series of log values of the index. Therefore, an OLS
estimate sensitive to these two characteristics was a must.
The 95% limits of confidence of the estimate are the following under the
three different assumptions:
- i. homoscedasticity and no autocorrelation
95% Confidence Intervals (homoscedasticity)
= 17.50% SJan78 = 33.12
+ = 17.91% (SJan78)+ = 48.50
- = 17.10% (SJan78)- = 22.61
- ii. heteroscedasticity but no autocorrelation
There is not a great change in the accuracy of the β estimate, and therefore, of
the confidence interval around the fitted curve.
95% Confidence Intervals
= 17.50% SJan78 = 33.12
+ = 17.93% (SJan78)+ = 50.24
- = 17.07% (SJan78)- = 21.83
- iii. heteroscedasticity and autocorrelation
Autocorrelation worsens the quality of the β estimate:
95% Confidence Intervals
= 17.50% SJan78 = 33.12
+ = 18.70% (SJan78)+ = 106.89
- = 16.30% (SJan78)- = 10.26
Under these more flexible estimates, the figure 3 compares the actual evolution
of the index to the fitted straight line and places that evolution within the
limiting borders of one standard deviation confidence interval.
Figure 3: Comparing the Actual Evolution of the Index to the
Fitted Straight Line within the Limiting Borders of
one Standard Deviation Confidence Interval
It is interesting to interpret the historical development of our equity market
from this relative time evolution of our general share index within the
estimated “confidence strip”:
a. when the market reopened after the Carnation Revolution, the quotations
were below the average, a fact that one would expect after the turmoil
associated with that political, social, and economic revolution;
b. the subsequent early recovery from the end of 1979 did not last long, due
to our domestic economic crises, which could only be tackled after a
second standby agreement was signed between Portugal and the IMF;
c. the temporal coincidence of the termination of the 1983 crisis with the
long-term recovery from the 1974-75 turmoil made possible the excessive
quotations that ended with the October 1987 crash;
d. the market then returned to more “normal” levels, but was again
negatively influenced by the 1993 crises; but, in the beginning of 1988, the
market was clearly above the average (more than one σ above), which
Januar y1978toJun e2009
4-Jan-78 4-Jan-80 3-Jan-82 3-Jan-84 2-Jan-86 2-Jan-88 1-Jan-90 1-Jan-92 31-Dec-93 31-Dec-95 30-Dec-97 30-Dec-99 29-Dec-01 29-Dec-03 28-Dec-05 28-Dec- 07 27-Dec-09
Index Valu es (base value 1000 on 5 Jan 88)
explains the excessive base value of our first and longest daily share index
– the BVL-General Index – observed on 5 Jan 1988;
e. however, that world crises of 1993 was not enough to bring the index
below average, probably due to the success of the ongoing privatization
program that attracted many investors to our shares, especially the first
large scale cash inflow from non-residents;
f. the dot.com peak at the beginning of 2000 may mark the end of this
evolution around the trend line: after that peak, our market seems to be
facing difficulties in crossing back over the “average” line, a fact that may
have economic interpretations beyond simple stochastic explanations (as
g. in particular, the current trough of the index behavior places the market
clearly away from “average” historical values; that is, although the graph
may suggest that there must now exist a “strong force” dragging the index
back toward the “middle-of-the-road” line, if our economy and our capital
market did change in 1999/2000 and the expected return has dropped to
lower values, the next world recovery may not bring our quotations back
to levels close to that center line.
6.3. Risk-free Rate
As mentioned at the beginning, during the 31.5-year time window analyzed, the
Portuguese money market suffered from severe problems of excess of
interference from the domestic government and from significant lack of
liquidity in all maturities segments other than overnight. This led us to select
very short-term rates (instead of long-term ones) from the interbank market as
the local risk-free cost of money. In detail:
a. we did not consider any Central Bank rate, due to the excessive control by
the government of the money market during a large number of the initial
years of the sample used;
b. we excluded any medium and long-term rates agreed in the IMM because
most of the days recorded no operations at all in this market;
c. in the earliest years, the very short-term segment included 24-hour, 48-
hour and 72-hour loans, without distinguishing between those three
d. from the beginning of 2009 onwards, because the local IMM market was
integrated into the much larger Euroland interbank market, we took
EONIA as the substitute for the previous domestic overnight rate.
Figure 4 depicts the evolution of the daily (annualized) rates as published by
the different sources of data.
Figure 4: The Evolution of the Daily (annualized)
Rates as Published by the Different Sources of Data
The average rate along this 31.5-year series is a geometric average that is
annualized assuming a 365-day year. But, since the input data were measured
using different frequencies, it means that:
a. when, during the years 1978 to 1988, we had only average monthly rates,
we accumulated them using a year of 12 equal months and assuming that
those published rates had been annualized through that same multiple;
b. from the beginning of 1988 onwards, rates became available on a daily
basis and the accumulation was computed assuming a 360-day year, as this
was the tradition in our domestic money market;
c. similarly for EONIA rates used for 2009, since these are reported on an
Act/360 day count convention;
d. however, the final geometric average for the whole 31.5-year window was
annualized for a 365-day year because that risk-free rate is to be compared
to an average annual equity return that also assumes a 365-day year.
The final average risk-free rate obtained is
Rf= 9.47% p.a.
6.4. Equity Risk Premium Above Short-term Rates
From the geometric equity return and subtracting the geometric risk-free rate,
the average Equity Return Premium relative to short-term rates is 8.03%.
PORTUGUESE RISK-FREE RATES
Overnight rates or similar for 1978 to 2008. EONIA rates for 2009
01/01/78 01/01/80 01/01/82 01/01/84 01/01/86 01/01/88 01/01/90 01/01/92 01/01/94 01/01/96 01/01/98 01/01/00 01/01/02 01/01/04 01/01/06 01/01/08 01/01/10
Annualised Rates for a 365-day annum
Equity Return = 17.50%
Riskfree = 9.47%
ERP = 8.03%
7. Summary and Conclusions
Extending 10 years backward the pre-existing BVL-General share index time
series that starts in the beginning of 1988, we adjusted a straight line to the log
values of that index assuming both autocorrelation and heteroscedasticity for
those prices. This is a rather detailed time series – 1652 points – since we
sampled every week (as a rule, all Wednesdays) along the 31.5 years from
January 1978 to June 2009.
The main result obtained from that curve fitting was the average annual
(continuous) return provided by that market during that window of time: 17.5%
p.a. (365-day year) with a 95% confidence interval of ±1.2%. Note that this is a
geometric average estimate, not an arithmetic one, as the underlying values are
the log prices of the index.
Because our Treasuries did not exist during some of the sampled years – the
case of T-Bills – or were very illiquid – the case of T-Bonds – the risk-free rate
was estimated using the domestic Interbank Money Market (in 2009 we used
the European reference EONIA): the geometric annualized average interest rate
for overnight operations or similar for the same period of 31.5 years was 9.47%
p.a. (again 365-day year).
These two figures led to an estimate of the historical Equity Risk Premium
in Portugal above short-term risk-free rate of 8.03% p.a., a value of the same
order of magnitude found in other countries, in particular, the traditional
Ibbotson figure estimated from the US sample starting in 1926.
For the future, this historical average might be excessive because it might
have resulted from an extra premium demanded by investors based on the
negative experiences they had gone through recently and the lack of liquidity
during the same first years after trading resumed in the Stock Exchange. And,
in fact, the most recent 8 to 9 years of the index suggests a below average
The causes of this evolution may be a simple impact of the accession of
Portugal to the European Union (in 1986), in particular the sharing of the
European currency since its inception in 1999: investors, both domestic and
from abroad, now demand a lower premium due to this European “seal of
quality”. An alternative cause may be in the low pace of GDP growth of our
economy during the same years, which is interpreted as a long-range effect
upon the current value of our shares. Of course, simple stochastic behavior may
also play a role.
This suggests additional studies in the double direction of extending even
further the series toward the beginning of the Twentieth Century, and to
include the measurement of the Equity Risk Premium in relation to long-term
real rates – after discounting for inflation – in order to better gauge the real
return obtained from long bonds.
An important dialogue may be established between macroeconomists and
finance historians in looking for evidence from the large laboratory of
experiences and facts that history makes available whenever long-term
analyses are pursued. Stock Exchange variables are now a decisive topic for the
global scholarly community and for theoretical paradigms of different schools
of economic thought.
Capitalization-Weighted Share Indices
Rules of Computation
1) The oldest Portuguese share index still being calculated is the BVL/PSI-
General33, one which started the daily series on 5 Jan 1988 with a base
value of 1000 points. This index includes all shares listed in the main
market of the Lisbon Stock Exchange and weights each component
according to the number of shares listed.
Everyday, a single value is computed based on the closing prices of all
the shares included in the sample. Also, all corporate events affecting the
price of any share beyond market sentiment are taken into account
through proper adjustments either in the numerator or the denominator of
However, for dates before January 1988, there is nothing compatible
with this index since the different series known, either never disclosed
the methodology adopted to calculate the index or followed solutions not
compatible to the above index.
Therefore, what the present paper does is to explain the solutions adopted
to replicate as close as possible the methodology of the BVL-General
index of the Lisbon Exchange for the period 1978-1987. This period is
very relevant for future developments in this area of indices because:
- the base date adopted for the BVL-General index – beginning of 1988
– might still be somewhat influenced by the excessive speculation of
the two previous years, which culminated in the spectacular crash of
October 1987; that is, it might be “overvalued”;
33 It started as BVL-General in 1991, but was later re-baptised PSI-General, the name in use
- the Portuguese share market was in the 1980s still recovering from the
“wounds” that followed the economic and social events of 1974, in
particular the “suspension” of the Exchange operations for about two
years34; if the methodology of the current index can be adapted to
express the average market behavior during that 10-year time
window, then it will be extended to the earlier periods in another
2) The source of information used to continue the index toward earlier years
is the daily bulletins published in paper form by the Lisbon Stock
Exchange and available at the Documentation Centre of (today called)
Euronext Lisbon35. However, only one day per week was used, in order
to reduce the computation burden. The selection led to the use of every
Wednesday – except if it was a bank holiday – in order to minimize
potential weekend effects upon the observed prices.
3) Since the index covers all shares listed in the main market of the Lisbon
Stock Exchange, the sample had to be modified and the index adjusted
whenever a company entered the market or left it:
For the case of a new company entering the market, the index did not
consider the first day of quotation, but added its capitalization only on
the second day of the time series:
t=first day of the new company
t+1=second day of the new company
where the denominator already includes the capitalization of the new
company on the first day of trading. Of course, for the first day, the
numerator excludes the capitalization of the new company in order to
reduce the index variation to simple changes in the sentiment of the
When a company left the market by any reason, the denominator
excludes that company for the computation of the index on the first day
already without the old company:
t = first day of the new company
t-1= second day of the new company
4) This index measures the total return of the market including the yield due
to cash dividends paid out by some of the companies in the sample. To
include this impact of the dividend, the numerator of the formula was
expanded to include the total amount of cash dividend outflow from that
34 The Exchange closed for trading on 25/April/1974 and reopened for share trading only on
35 After the Lisbon Stock Exchange joined the Euronext group of Exchanges, in February
2002, this is the legal name adopted by this Portuguese affiliate.
firm on the first Wednesday after the payment day. But, for all other
days, only the sum of capitalizations without those paid dividends were
used in the formula:
t = firstWednes da after divided pay - out
t-1= the previous Wednesday
5) Unfortunately, the market did not offer trades of shares for all listed
companies on every day. That is, there was a frequent lack of quotations
throughout the time window analyzed. However, the daily bulletin also
discloses the best Bid and the best Ask prices after each particular
auction36. Therefore, as a second-best solution, the following
methodology was adopted:
- when no trades had occurred, the average between Bid and Ask was
used as a proxy for the real traded price;
- when only the Bid or the Ask was available, that single value was used
as that proxy;
- when none of the 3 values were present on a particular Wednesday, the
value from the previous Wednesday was used;
- however, if two or more Wednesdays lacking data occurred in a row,
that company was temporarily excluded from the sample according to
the rules mentioned above for new entrants and old companies leaving
Macro-Economic View of the Risk Premium
The DCF formula for a constant rate of dividends leads to an annual equity
So, for an annual cost of debt (Treasuries) of r, the equity risk premium (ERP)
36 Note that the Stock Exchange used the Roll Call system of trading during this period, where
each listed share was called once at a time and a single equilibrium price was discovered
after confrontation of all the orders carried by the brokers for that particular asset. The
prices of those orders closest to that equilibrium but already excluded from trading
produced the daily Bid and Ask prices.
Note that this premium can be measured either in relation to T-Bills or T-
Bonds, without a consensus yet established. For an inflation rate of around π
and a real interest rate of debt of rreal, this implies a nominal cost of treasuries
of about r π, that is
But the difference g-π) measures the real growth rate of the company
Companies cannot grow forever more than the general economy surrounding it,
for which a (real) long-run rate is estimated at a maximum of 2.5% p.a. Since
the real return of long-term Treasuries is about that same size, it implies an
Equity Return Premium relative to Bonds similar to the yield from Dividends.
Therefore, a bond Equity Return Premium of 6% p.a. can only be compatible
with a much larger greal and that is only acceptable during limited time
intervals. Of course, working with an Equity Return Premium relative to bills,
that figure jumps to 8.5%, but the conclusion is the same.
The reality is even slightly worse because companies may begin with large
rates of growth g but, that pace always tends to fall as the firm matures. So for
the same D1 and P0, the discount rate and the Equity Return Premium must be
smaller than forecast from the standard Gordon formula. This means that the
excess of Equity Return Premium suggested by the standard Gordon’s formula
is even more excessive.
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