1
Optimal Portfolios or…Investment Strategies?
Author: Darasteanu Catalin Cristian
Abstract
The Bucharest Stock Exchange performed poorly for the interval of time
1999-2001 from de point de view of return. However, there were some stocks
which had very attractive returns given the level of risk. These stocks were able
to compete other capital markets from Romania.
This article takes into analysis the best stocks of Romanian market for the
period 1999-2001. In the same time it groups these stocks in portfolios and it
shows that the return of the overall portfolios is higher than the return of some
several financial markets. In the same time the article makes a discussion on the
debate active versus passive management and it shows why and how the active
management could work for this particular market. It should be emphasized
however that the purpose of the article is not to make a prediction of stocks’
returns for the next period of time. The portfolios that are going to be constructed
are static and based on historical returns.
Key words: risk-return, strategic portfolios, beta, active versus passive
management, cut-off point method
I. Introduction
For investors, Bucharest Stock Exchange was not a very attractive
market1. Even though the emerging markets are characterized by high volatility
and high returns offered (see Campbell R. Harvey’s studies), BSE offered rather
a large amount of uncertainty without satisfying its investors. Indeed if we take a
look at the evolution of BET and BET-C indexes, we notice the lack of
attractiveness of the market. The vertical axis represents the value in points of
the two indexes of the market. The horizontal axis represents the number of
observations taken into analysis (i.e. 721).
*Master student in finance at International Centre for Advanced Mediterranean Agronomic StudiesMediterranean Agronomic Institute of Chania, Greece (E-mail: catalin@maich.gr)
1
See details in reports of Bucharest Stock Exchange or National Bank of Romania; also see Pogonaru
(2000, pg. 24-30).
2
800
700
600
500
400
300
100
200
300
400
BETC
500
600
700
BET
Source: Bucharest Stock Exchange
Figure 1: Evolution of BET and BET-C
In order to see why the stock market performed poorly, let us further take a look
at the following two graphs. First of them shows the evolution of daily returns of
the market indexes. The second one describes the evolution of returns of T-bills.
Both of them are constructed after the data was processed taking into account
the classic formula of capitalization. We should add also here that for
convenience purposes, the evolution of T-bills was considered continuously. The
distribution of T-bills’ returns is considered to be a log-Normal distribution.
1.4
2.2
2.0
1.3
1.8
1.2
1.6
1.4
1.1
1.2
1.0
1.0
0.9
0.8
100
200
300
BETC
400
500
600
700
50
BET
Source of data: Bucharest Stock Exchange
100
150
200
SER01
Source of data: “Pagina pietei de capital din
Romania” (www.kmarket.ro)
Figure 2: Stocks versus T-bills
The graphs show very clear that T-bills, despite of the theory of capital markets,
outperformed stocks. This example is very illustrative for the evolution of Romanian
3
capital markets during transition period since we all know that in general stocks offer
higher returns than do the T-bills. T-bills are considered the risk-free asset and they are
supposed to offer the smallest return among all assets that are traded in the capital
markets. Though, in Romania the situation was different: without undertaking any risk,
investors could be better off by investing in T-bills and not in stocks.
The question that might arise here is why would investors choose the stock
market since they can be better off by choosing riskless assets? The theory of active
management could answer to this question: there are ways in which investors can beat
the market. This is a very important academic and practical debate.
II. Active versus Passive Management
Nowadays, the academic environment of capital markets offers a large
debate about active versus passive management. Let us first specify what these
concepts include:
1. Active management: The practice of picking individual stocks based on
fundamental research and analysis in the expectation that a portfolio of selected
stocks can consistently outperform market averages.
2. Passive management: The practice of buying a portfolio that is a proxy for the
market as a whole on the theory that it is so difficult to outperform the market that
it is cheaper and less risky to just buy the market.
One of the most passionate protectors of passive management is Eugene
Fama, the one who constructed the so famous theory of efficient markets. The
point of professor Fama is that there cannot be investors that can beat
consistently the market. And this is because the stocks prices are extremely
difficult to predict. Fama made himself famous also through another theory, i.e.
the random walk theory, in which Gene Fama shows that the variations in stock
prices are unpredictable. In fact, prices are walking randomly on the screen of
the stock market. Fama explain the success of some active managers by saying
that in a normal, bell-shaped distribution of returns on investment portfolios, the
majority of the returns, or data, can be found in the “bell,” or bulge, which centers
around the weighted average return for the entire market. At the ends, both right
and left, we find what are known at “outliers,” those returns which are either very
bad (left side) or very good (right side). Of course, few managers are either very
good or very bad. Those returns on the right and left tails are known as outliers
since they live on the outlying fringes of the curve. Similarly, “fat tails” refers to
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larger than normal tails of the curve, meaning that there are more data on the
extremes than you might expect.
Another convinced passive manager is Rex Sinquefield, chairman of
Dimensional Fund Advisors. He explains that the problem here is understanding
how the market mechanism works. The central point is that no one person has
very much information. In fact, regardless of how smart they are, or how informed
they are, they have a tiny fraction of the information that is available to the entire
market at any point in time. The markets are completely interrelated. It is not
credible that there is one person who systematically has more information than a
dispersed market of six billion people. That’s not remotely credible. But that’s the
condition that somebody has to prove. “That there is such a person who has all
this information — and the information changes second by second — who is so
good that he or she is going to come to better conclusions than the worldwide
market that is setting hundreds of millions of prices every moment? That’s not
plausible”, says Sinquefield.
Finally, Merton Miller, a late Nobel laureate (in 1990), explains also why
passive management outperforms the active management: “I favor passive
investing for most investors, because markets are amazingly successful devices
for incorporating information into stock prices. I believe, along with Friedrich
Hayek [also a Nobel laureate, and a contemporary of John Maynard Keynes] and
others, that information is not some big thing that’s locked in a safe somewhere.
It exists in bits and pieces scattered all over the world. Everybody has a little
piece of the total information.” (interview for “Investment Gurus”).
Let us take now an example of active manager. Richard Driehaus is considered
nowadays to be one of the most successful managers who consistently
succeeded in beating the market. His philosophy is: “Striving to build portfolios of
stocks undergoing significant positive change.” The pylons of his philosophy is:
 Aggressive growth companies, by definition, are the fastest growing
companies in the economy, in terms of revenues and earnings.
 Earnings growth is the principal factor in determining common stock prices
over time.
 Thus, investing in the fastest growing companies should lead to realization
of potentially superior investment returns over the long term.
 The fastest growing companies also tend to be the most adaptable and
dynamic companies within the economy, and they can adjust rapidly to
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change. These qualities should also lead to potentially superior returns for
investors over the long term.
III. The idea of optimal portfolio
First time, in the history of modern portfolio theory, Markowitz described the
relation between risk and return and he constructed the so famous theory MeanVariance. Based on this theory, investors could construct optimal portfolios. It
was a very important step for capital markets theory. William Sharpe said about
Markowitz that he came up with an idea and there was a light and an order in
how investors were going to choose their stocks.
Since that point, a lot of literature has tried to identify ways in constructing
optimal portfolios. However, in practice many models, even though perfectly logic
as construction, tended rather to fail when applied in practice. And one of the
reasons is that they all have a set of assumptions that cannot depict the whole
reality of stocks markets. Another difficulty is related to the fact that many of
models are static (actually this is one of the critics of Markowitz model).
Nevertheless, we should mention here that there is a lot of uncertainty in how
prices of stocks are moving over time. Also, there is a lot of noise in data. Gene
Fama, the one who described the theory of random walk, said that with so many
changes in prices it is extremely difficult to predict the future returns. Moreover,
W. Sharpe (one of the authors of Capital Asset Pricing Model), agreed that we
see in practice only realized returns.
For emerging markets, prediction seems to be just a nice term. The high
volatility is a constant obstacle in front of this process.
Since the prediction is difficult to be made in stock markets, it would be
reasonable to say that constructing optimal portfolios is quite difficult in practice.
This is why it seems that it is better to adopt some investment strategies by
taking into account the appetite toward risk of different groups of investors. This
study will continue by describing ways of choosing portfolios of stocks traded at
Bucharest Stock Exchange that, in an aggressive environment, could succeed in
beating 3 capital markets:
1. the T-bills market;
2. the mutual funds market;
3. the foreign exchange market (expressed here by the evolution of
dollar).
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IV. Methodology of research
In the present study the cut-off point method is used to construct strategic
portfolios. This method is derived from the single-index model. The method is
based on idea of including or excluding stocks in a portfolio depending on
relation between risk and return. The single-index model was applied for
Bucharest Stock Exchange (Darasteanu, 2002) and one of its conclusions is that
there is a positive relation between risk and return. In the same time, for most of
the stocks, the betas calculated were statistically significant. Even though the
adjusted R-squared proved that Beta is for sure not the only one measure of risk
for this particular market, the values of t-statistic showed that single-index model
is in general a valid model.
The cut-off point method
This method says that the desirability of any stock is directly related to its
excess return to Beta ratio. In general, Excess return is the difference between
the expected return on he stock and the riskless rate of interest. We will
introduce in the model the historic returns that were realized for the period 19992001.
The time series data is depicted from 04.01-1999 until 05.11.2001 and it
includes closing prices of stocks traded at Bucharest Stock Exchange. Based on
these prices, daily returns were computed (see Darasteanu, 2002). The sample
consisted of all stocks that were traded until the end of interval. However, we
have excluded the investment funds, Romanian Bank of Development, SNP
Petrom and Abrom Barlad (for all of them the number of observations was
inconsistent with the purpose of this study).
One important assumption that is used is that short sales are not allowed.
The excess return to Beta ratio measure the additional return on a security
per unit of nondiversifiable risk. The form of this ratio should lead to its easy
interpretation and acceptance by security analysts and portfolio managers,
because they are used to thinking in terms of the relationship between potential
rewards and risk. The numerator of this ranking device is the extra return over a
chosen asset that we earn from holding a security other than that specific asset.
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The denominator is the nondiversifiable risk (the risk we cannot get rid of) that we
are subject to by holding a risky security rather than the chosen asset.
More formally, the index we use to rank stocks is “excess return to Beta”
or
Ri  Ra
i
(1)
where:
Ri – the historical return on stock i
Ra – the return an asset a, where a can be dollar, T-bills or a mutual fund.
βi – the Beta of stock i.
If stocks are ranked by excess return to Beta (from highest to lowest), the
ranking represents the desirability of any stock’s inclusion in a portfolio. In other
words, if a stock with a particular ratio of (Ri-RF)/ βi is included in a portfolio, all
stocks with a higher ratio will also be included. On the other hand, if a stock wit a
particular (Ri-RF)/ βi is excluded from a portfolio; all stocks with lower ratios will be
excluded. When How many stocks are selected depends on a unique cut-off rate
such that all stocks with higher ratios of (Ri-RF)/ βi will be included and all stocks
with lower ratios excluded. We call this ratio cut-off ratio C*.
The rules for determining which stocks are included in a strategic portfolio
are as follows:
1. Find the “excess return to Beta” ratio for each stock under consideration,
and rank from the highest to lowest.
2. The desired portfolio consists of investing in all stocks for which (Ri-RF)/ βi
is greater than a particular cut-off point C*. Shortly, we will define C* and
interpret its economic significance.
Setting the Cut-off Rate (C*)
The value of C* is computed from characteristics of all the securities that
belong in the portfolio. To determine C* it is necessary to calculate its value as if
there were different numbers of securities in the optimum portfolio. Designate Ci
as a candidate for C*. The value of Ci is calculated when i securities are
assumed to belong to the strategic portfolio.
Since securities are ranked from the highest to lowest in terms of excess
return to Beta, we know that if a particular security belongs to in the strategic
portfolio, all higher ranked securities also belong in this portfolio. We proceed to
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calculate values of a variable Ci as if the first ranked security was in the strategic
portfolio ( i =1), then the first and second ranked securities were in the strategic
portfolio ( i =2), then the first, second, and the third ranked securities were in this
portfolio ( i =3), and so forth. These Ci are candidates for C*.
According to the theory, we know that we have found optimum C*, when
all securities used in the calculation of Ci have excess returns to Beta below Ci.
Calculating the Cut-off Rate C*
Recall that stocks are ranked by excess return to risk from the highest to
lowest. For a portfolio of i stocks Ci is given by
i
 m2 
Ci 
R
j
 RF  /  j
 ej2
j 1
  j2
2
1  m  2

j 1   ej
i




(2)
where:
 m2 - the variance in the market index;
 ej2 - the variance of a stock’s movement that is not associated with the
movement of the market index.
This looks horrible. But we can show that is not so bad like it looks. While
equation 2 is the from that should actually be used to compute Ci, this expression
can be stated in a mathematically equivalent way that clarifies the meaning of Ci.
Ci 

 iP RP  Ra
i

(3)
where:
 iP - the expected change in the rate of return on stock i associated with a 1%
change in the return on the portfolio P.
R P - The expected return of the portfolio P.
All other terms were defined above.
Terms  iP and R P are, of course, not known until the portfolio P is
determined. Hence, equation (3) could not be used to actually determine the socalled optimal portfolio. Rather, equation (2) should be used. However, this
9
expression for Ci is useful in interpreting the economic significance of our
procedure. Recall that securities are added to the portfolio as long as:
Ri  Ra
i
Ci
(4)
Rearranging and substituting in equation (3) yields
Ri  Ra   iP RP  Ra 
(5)
The right-hand side is nothing more than the excess return on a particular
stock based solely on the expected performance of the optimum portfolio. The
term on the left-hand side is the security analyst’s estimate of the excess return
on the individual stock. Thus, if the analysis of a particular stock leads the
portfolio manager to believe that it will perform better than it would be expected,
based on its relationship to the optimal portfolio, it should be added to the
portfolio.
Constructing the strategic portfolio
Once the securities that are contained in the strategic portfolio are
determined, it remains to show how to calculate the percent invested in each
security. The percentage invested in each security is
Xi 
Zi
Z j
(6)
included
where:
Zi 
i
 ei2
 Ri  Ra


 C *
 i

(7)
The second expression determines the relative investment in each
security while the first expression simply scales the weights on each security so
they sum to one and, thus, ensure full investment. Note that the residual variance
on each security  ei2 plays an important role in determining how much to invest in
each security.
Let us stress that the results obtained by applying the cut-off point method
are identical to the results that would be achieved if the problem were solved by
using the established quadratic programming codes. However, the solution can
be reached in a fraction of the time with a set of relatively simple calculations.
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Other methodological specifications related to the present study
Recall that the present study intends to construct 3 portfolios of stocks
traded at Bucharest Stock Exchange (BSE) for the period 4.01.1999-5.11.2001.
These portfolio, in conditions of unstable market and with not satisfactory returns
offered by the market as a whole, would “beat” the increase of dollar (chosen for
foreign exchange market), the market of mutual funds and the T-bills. Every each
portfolio is constructed as a function of the risk-aversion of investors (for
instance, the most risk averse investors would prefer a portfolio which offers
enough returns to beat the T-bills portfolio). The study, apart from methodology
presented above, uses historical returns and not expected returns. Also, daily
returns are being used. These daily returns, and also the risk premiums derived
from the model, are transformed, on an average base, to yearly returns.
In other words, the study starts from a possible question of an investor: “If
I want to invest in BSE’s stocks and I want to construct a portfolio good enough
to outperform the asset <<a>> which stocks should I select? And what is the
excess return that I can get?”
V. Results and discussions
Let us first present, shortly, the performance of the three assets taken into
account for the period 1999-2001.
The foreign exchange market
As we have mentioned, we use the dollar in our calculations. The reason
is that most of individual investors in Romania have a very high level of trust in
this currency. In periods with high instability in financial markets, economies of
population were oriented to dollar. The question that is being asked here is if the
investment in dollar was a very profitable one.
Let us take a look at the annual increase of dollar:
Table 1: Annual increase of dollar
Year
Exchange rate
(ROL FOR 1$)*
Increase in exchange rate
(%)
1998
1999
11076
18255
64.82
2000
2001
25926
31597
42.02
21.87
Source: National Bank of Romania
* Value of exchange rate taken in the last day of transaction for each year
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The market of mutual funds
First, all mutual funds that are operating in Romania were analyzed. The
source of data was “Pagina Pietei de Capital din Romania” (“Page of the Capital
Market from Romania”). A first selection was done among all of mutual funds,
more specifically there were selected only those mutual funds with activity for the
whole interval of time taken into analysis. Among 21 mutual funds, only 15 were
analyzed. In order to make a tougher restriction for the portfolio supposed to beat
these funds, there was selected the most performing mutual fund, i.e. Capital
Plus, as we can see from the following table:
Table 2: Performance of Romanian mutual funds in 1999-2001
FUNDS
VARIATION IN
VARIATION IN
VARIATION IN
1999
2000
2001
(%)
(%)
(%)
Active Dinamic
82.81
45.12
35.41
Active Clasic
78.90
37.07
24.94
Active Junior
81.01
35.89
24.48
Ardaf
87.18
23.63
25.48
Armonia
30.11
43.98
33.84
DEGREE OF
RISK*
Low
Low
Low
Low
Low
Capital Plus
105.84
63.93
48.54
Low
Fortuna Classic
Fortuna Junior
Fortuna Gold
Fund for External
Commerce
Fund for National
Opportunity
Monetar Stabilo
Monetar Tezaur
Protector
Transilvania
92.05
0.00
0.00
103.62
45.12
0.00
48.41
53.77
29.97
36.59
42.64
39.90
Low
Low
Low
Low
0.00
38.85
42.02
Low
92.82
26.66
0.00
68.89
49.39
49.62
0.00
57.06
37.24
36.47
20.89
46.52
Low
Low
Low
Low
Source: “Pagina Pietei de Capital din Romania”
* The scale for measuring the risk is from 0 to 5; the low level of risk corresponds to an interval between 0 and 2
T-bills market
T-bills are generally known as the riskless asset in the economy and also
as offering the lowest returns among the financial markets. However, in
Romania, due to economic problems (the state needed substantial financial
resources), T-bills have been very attractive for investors.
We will use for our study the T-bills with discount. The evolution of these
assets is shown in the next table:
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Table 3: Evolution T-bills in Romania in 1999-2001
Year
1999
2000
Month
January
February
March
April
May
June
July
August
September
October
November
December
-billion ROL2001
Nominal
Value
Interest
Rate
Weighted
Nominal
Value
Interest
Rate
Weighted
Nominal
Value
Interest
Rate
Weighted
5,25
7,08
6,3
2,85
9,91
7,29
1,38
6,95
3,94
3,84
5,06
5,12
0,7
0,9
0,79
1,12
1,07
1
0,74
0,69
0,56
0,52
0,59
0,76
3,675
6,372
4,977
3,192
10,6037
7,29
1,0212
4,7955
2,2064
1,9968
2,9854
3,8912
6,69
9,1
5,51
7,62
10,25
7,69
7,55
4,6
5,29
1,82
0,61
3,87
0,74
0,72
0,58
0,49
0,46
0,46
0,42
0,44
0,47
0,5
0,51
0,5
4,9506
6,552
3,1958
3,7338
4,715
3,5374
3,171
2,024
2,4863
0,91
0,3111
1,935
7,63
7,25
10,11
7,19
6,97
3,93
4,7
3,29
6,19
6,5
4,7
5,62
0,5
0,51
0,5
0,49
0,47
0,42
0,36
0,36
0,38
0,36
0,35
0,36
3,815
3,6975
5,055
3,5231
3,2759
1,6506
1,692
1,1844
2,3522
2,34
1,645
2,0232
Average
Yield
0,815857
0,587107
0,435393
Source: National Bank of Romania
We can see the evolution of T-bills also from the following graph (including
the first semester of year 2002):
Source: “Pagina Pietei de Capital din Romania”
Figure 3: Evolution of T-bills
Generating strategic portfolios
Based on our discussion from above, by using the method of cut-off point
the following portfolios were found to beat the three financial markets mentioned.
We will make our discussions after presenting the results.
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Table 4: BSE portfolio (a) versus dollar portfolio
Symbol
(Tier)
INX
(I)
Excess
return
on beta
0.033
Cut-off Point
(Ci)
0,16
Risk
Premium
(daily basis)
0,0053
Beta*
3,84334E-05
Percent
of
Investment
12,22
Return
of Portfolio*
(daily)
0,0009
AMP (II)
0,029
0,1
0,0032
4,8965E-05
4,877
0,0002
ENP (II)
0.027
0,22
0,0099
0,00010
7,319
0,0008
MEF (II)
0.02
0,18
0,0035
0,00012
8,282
0,0004
MPR (II)
0.017
0,26
0,0017
0,00016
20,28
0,0007
ARS (II)
0.012
0,18
0,0014
0,00018
5,618
0,0002
AMO (II)
0.010
0,18
0,0019
0,00019
4,074
0,0001
EPT (II)
0.007
0,07
0,0016
0,00020
2,916
1E-04
BRM (II)
0.007
0,32
0,0022
0,00025
7,998
0,0003
CPL (II)
0.006
0,7
0,002
0,00029
5,313
0,0002
RBR (I)
0,005
0,15
0,0008
0,00029
2,627
7E-05
NVR (II)
0.005
0,21
0,001
0,00032
6,13
0,0002
ARM (II)
0.004
0,03
0,0001
0,00032
0,295
5E-06
AZO (I)
0,003
0,3
0,0009
0,00034
5,016
0,0001
ASP (I)
0,003
0,18
0,0005
0,00035
1,29
6E-06
COS (II)
0.002
0,52
0,0002
0,00035
0,962
2E-05
PTS (II)
ZIM (II)
0.002
0.001
0,88
0,19
0,0004
0,0002
0,00035
0,00035
3,955
0,404
8E-05
8E-06
ART (II)
0.001
0,3
0,0002
0,00035
0,319
6E-06
SLC (II)
0,0004
0,33
0,0001
0,00035
0,036
6E-07
TRS (II)
0,0004
0,21
0,0002
0,00036
0,064
1E-06
100.00
0,0045
PORT.
VALUES
0.27
* Source: Catalin Cristian Darasteanu “Testing CAPM on stocks traded at Bucharest Stock Exchange”, Pagina Pietei
de Capital din Romania, 2002
We will make here the following notations:
1. Portfolio (a) represents the 100% BSE stocks portfolio that was
constructed in order to outperform the increase of dollar;
2. Portfolio (b) is the portfolio of stocks traded at BSE that outperform Capital
Plus Investment Fund;
3. Portfolio (c) is the portfolio of stocks that outperformed a 100% portfolio of
T-bills.
The following findings take into account higher restrictions. It supposes
that investors are willing to undertake a higher level of risk. As a result, the
number of securities declines consistently compared with the number of shares
from table 4. We will present these findings in the following 2 tables:
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Table 5: BSE portfolio (b) versus Capital Plus Mutual Investment Fund
Symbol
(Tier)
INX
(I)
Excess
return
on beta
0,025
AMP (II)
0,024
Cut-off Point
(Ci)
0,16
Risk
Premium
(daily basis)
0,0041
0,22
0,0087
Beta*
2,97315E-05
Percent
of
Investment
24,34
Return
of Portfolio*
(daily)
0,0017
7,59077E-05
17,13
0,002
ENP (II)
0,018
0,1
0,002
8,24652E-05
7,947
0,0004
MEF (II)
0,013
0,18
0,0023
0,000101052
14,16
0,0007
MPR (II)
0,005
0,26
0,0005
0,000112116
15,42
0,0005
AMO (II)
0.003
0,18
0,0007
0,000117604
3,134
0,0001
BRM (II)
0.003
0,32
0,001
0,000139541
8,915
0,0003
CPL (II)
0.002
0,7
0,0008
0,000151895
4,516
0,0002
EPT (II)
0.002
0,07
0,0004
0,000155089
2,107
7E-05
ARS (II)
0.002
0,18
0,0002
0,000156642
2,322
7E-05
100.00
0,0061
PORT.
VALUES
0.22
* Source: Catalin Cristian Darasteanu “Testing CAPM on stocks traded at Bucharest Stock Exchange”, Pagina Pietei
de Capital din Romania, 2002
Table 6: BSE portfolio (c) versus T-bills
Symbol
(Tier)
(I)
Excess
return
on beta
0,02822
AMP (II)
0,02529
INX
Cut-off Point
(Ci)
0,16
Risk
Premium
(daily basis)
0,0046
0,22
0,0091
Beta*
3,3E-05
Percent
of
Investment
18,46
Return
of Portfolio*
(daily)
0,0013
8,2E-05
12,12
0,0014
ENP (II)
0,02262
0,1
0,0025
9E-05
6,712
0,0003
MEF (II)
0,01565
0,18
0,0027
0,00011
11,45
0,0006
MPR (II)
0,01004
0,26
0,001
0,00013
21,05
0,0007
AMO (II)
0,00592
0,18
0,0007
0,00014
4,837
0,0001
AMO (II)
0,00586
0,18
0,0011
0,00015
4,188
0,0002
BRM (II)
0,00457
0,32
0,0014
0,00018
9,191
0,0004
CPL (II)
0,00386
0,7
0,0012
0,0002
6,011
0,0002
EPT (II)
0,00375
0,07
0,0009
0,00021
2,72
9E-05
NVR (II)
0,00118
0,21
0,0002
0,00021
2,225
6E-05
AZO (I)
0,00049
0,3
0,0001
0,00021
0,918
2E-05
RBR (I)
3,40E-04
0,15
5,17E-05
0,0002
0,127
3E-06
100.00
0,0054
PORT.
VALUES
0.24
* Source: Catalin Cristian Darasteanu “Testing CAPM on stocks traded at Bucharest Stock Exchange”, Pagina Pietei
de Capital din Romania, 2002
If we look at these tables carefully, some interesting conclusions can be
derived. First of all, investors could beat the market. And not only the market, i.e.
not only the market indexes (i.e. BET and BET-C indexes), but also they could
beat several capital markets. So we have proved that even though BSE
15
performed poorly. It could offer in the same time some very nice investment
possibilities.
However, it is surprising that companies traded at Tier II outperformed
most of the companies traded at Tier I, which are considered the most powerful
and stable companies in the market. This reminds somehow about one of the
findings of Eugene Fama. He discovered that small stocks performed better than
large stocks. We find the same result for Bucharest Stock Exchange. When we
construct portfolios of stocks, we can notice that small stocks are more powerful
than large stocks. Even though, when we take all stocks from the second tier,
they have poor returns (it is very reasonable to say this since BET’s performance
is much higher than BET-C’s performance and we know that in BET index are
included the most 10 performing stocks from Tier I), our findings reveal that
among these small stocks there are several securities which have excellent
performances in terms of risk and return.
If we take a look at the portfolio that could beat the Capital Plus Fund we
can notice the presence of only one stock from Tier I, namely Otelinox Targiviste
(symbol INX). Even though this is the best stock in the portfolio as relation riskreturn (and also in all three portfolios), investors would allocate their wealth in a
proportion higher than 75% to stocks traded at Tier II. Also, we can see than we
could not diversify our capital among stocks from Tier I. Even in the other two
portfolios, where we have other few stocks from Tier II (Azomures Targu-Mures,
AZO, Rulmentul Brasov, RBR, or Astra Romana, ASP), when we look at
investment percentage, small stocks are much better. For instance, if an investor
were to choose portfolio BSE (c), i.e. the portfolio that could beat a portfolio
consisting of 100% T-bills, that investor would not allocate even 1% of his capital
to securities Azomures Targu-Mures and Rulmentul Brasov.
The results presented above are bettered visualized when we transfer
them in a diagram. We will construct a diagram that include the evolution of 5
portfolios, three of them presented in table 4,5 and 6 respectively and the other
two representing the BET and BET-C portfolios. We should mention here that
based on an average basis, the results were transformed into annual data.
16
EVOLUTION OF PORTFOLIOS
250
BET%
RETURNS
200
BET-C%
150
T%
$%
100
MF%
50
04/11/2001
04/09/2001
04/07/2001
04/05/2001
04/03/2001
04/01/2001
04/11/2000
04/09/2000
04/07/2000
04/05/2000
04/03/2000
04/01/2000
04/11/1999
04/09/1999
04/07/1999
04/05/1999
04/03/1999
04/01/1999
0
TIME
Figure 4: Performance of different portfolios
The graph indicates that the portfolio that beat the Capital Plus Fund (in
the graph denoted by MF%) is the most performing among all these five
portfolios. It means that at a higher level of risk (at least theoretically) that
investors were willing to undertake, they would be rewarded with a higher level of
return. We see also that if investors had chosen the strategy of passive
management, i.e. the strategy of investing in an index, and if they had chosen as
index the market index BET-C, they would have rather lost. They would have
rather preferred the BET index for their strategy.
Let us think now a little bit about diversification. We know that investors
diversify in order to lower their risk, even though this means to accept a lower
level of return. According to our results, choosing portfolio BET would not be very
good decision since there are two portfolios that are more diversified and more
efficient, i.e. the portfolio that outperformed the increase of dollar (it includes 21
securities) and the portfolio that outperformed the portfolio consisting 100% of Tbills (it includes 13 securities). We notice that even the portfolio that beat Capital
Plus has the number of stocks as the portfolio BET.
17
Risk-Return relation of the portfolios
We will accept as measure of risk the beta of portfolio, i.e. the beta
generated fro each portfolio by taking into account the percentage of investment
in each stock and the Beta of each individual security. Also, the return of the
portfolio has been computed by using the same method. However, we will not
use daily returns but rather yearly returns, which were generated by using an
average technique. We will use here only the three portfolio generated by using
the cut-off method and we will analyze, at the portfolio level, if for a higher level
of risk investors would get a higher level of return.
We present the results in the following table:
Table 7: Relation Risk-Return
BSE PORTFOLIOS VERSUS:
RETURN
Portfolio (b)1
Portfolio (c)
Portfolio (a)
152.68
134.82
112.5
BETA
0.22
0.24
0.27
We notice here an “abnormality”, i.e. the higher the risk the lower the
return. It seems that it would not pay to care about diversification since with 10
stocks one could decrease the risk and still increase the return in comparison
with a portfolio that includes 21 securities (i.e. the portfolio that outperformed the
dollar). This can be more accurately visualized in the following diagram:
RETURN v s. BETA
160
RETURN
150
140
130
120
110
0.20
0.22
0.24
0.26
0.28
BETA
Figure 5: Return-Risk of portfolios
1
See page 13 for notations; the order of portfolio in table was chosen by using the return criterion, i.e. from
the highest to the lowest return
18
The slope of the line is negative, indicating the negative relation
between risk and return of portfolios. The question that arises here is: “Why is
that?” One possible answer comes from the tables that include the stocks of
these portfolios. For instance, recall table 4 in which we have constructed a
portfolio to outperform the increase in dollar. If we divide these stocks into 2
groups depending on percentage of investment (more specifically we put in one
group the most desired stocks and in the other the rest of securities), we see
that, in general, the Beta of the second half of the table is higher than the Beta of
stocks from the first part. So, instead of decreasing the risk through
diversification, it seems that we actually have increased it. We can notice that
basically, the cut-off method has helped us to find more efficient portfolios with
lower level of risk. However, we cannot generalize this result.
Also, we can see that the differences in Betas are so small that the
increase in risk from one portfolio to another is almost insignificant. And this is
quite normal since the portfolios include the same securities (some of them being
eliminated in some portfolio BSE (b) and BSE (c) respectively). The securities
that are eliminated in the portfolios that beat the Capital Plus and T-bills portfolio
do not have a high percentage in the BSE portfolio that outperformed the dollar.
And this is the reason that basically our results are not opposite to the concept of
diversification. Even though we have in portfolio BSE (a) more stocks than in the
other two, in fact, by looking at investment percentage, we diversified only
through number of securities and not through allocation of our capital consistently
in these stocks.
VI. Conclusions
In the present study we have done a comparison between Bucharest
Stock Exchange and some several capital markets from the point of view of the
risk-return relation. We have seen how we can construct portfolios of stocks (in a
volatile environment) that can outperform the other capital markets.
We have used the method of cut-off point (which is derived from the
single-index model) in order to construct portfolios of securities. We have seen
that for the period 1999-2001 we could make such a selection of securities that
could bring investors considerable returns.
The empirical evidence presented here shows that the most performing (in
terms of the relation risk-return) stocks are found in the second tier (however, we
19
should mention that the most performing stock is in the first tier, i.e. Otelinox
Targoviste-INX). This is a proof that several small (value) stocks were performing
better than cap (growth) stocks. Though, we cannot make this fact a general
statement for the case of BSE from the methodological point of view. We specify
that the time series data covered nearly three years, which is not enough for
testing the hypothesis that small (value) stocks are better than cap (growth)
stocks. In the same time, on average, stocks traded at the first tier (i.e.
cap/growth stocks) beat the stocks traded at the second tier (i.e. small/value
stocks).
Also, the evidence shows that, when using diversification, portfolios of
stocks are the most performing assets among financial markets in Romania.
References:
1. Catalin Cristian Darasteanu, “Testing CAPM on stocks traded at
Bucharest Stock Exchange”, Pagina Pietei de Capital din Romania
(www.kmarket.ro), May 2002;
2. Edwin J. Elton, Martin J. Grubber and Manfred W. Padberg, “Optimal
portfolios from simple rank devices”, Journal of Portfolio Management,
Vol. 4, No. 3, Spring 1978, pp. 15-19;
3. Eugene Fama, “Risk, return and equilibrium: some clarifying comments”,
Journal of Finance, XXXVIII, No. 1, March 1968, pp. 29-40;
4. Florin Pogonaru, “Romanian capital markets: a decade of transition”,
Romanian Center for Economic Policies, (www.cerope.ro), Oct. 2000, pp.
24-30;
5. Gordon j. Alexander and Bruce G. Resnick, “More on estimation risk and
simple rules for optimal portfolio selection”, Journal of Finance, Vol. 40,
No. 1, March 1985, pp. 125-134.