American Journal of Oper ations Research, 2011, 1, 236-242
doi:10.4236/ajor.2011.14027 Published Online December 2011 (
Copyright © 2011 SciRes. AJOR
Performance of Risk Measures in Portfolio Construction
on Central and South-East Eur opean Emerging Markets
Jelena Vidovic
Department of Fi na nce , University Centre for Professional Studies, Split, Croatia
Received May 24, 2011; revised June 30, 2011; accepted July 8, 2011
Aim of this paper is to characterize different risk measures in portfolio construction on seven Central and
South-East European stock markets; Slovenia, Croatia, Hungary, Poland, Chez Republic, Romania and Tur-
key. Selected countries are members of EU, except Croatia and Turkey which have candidate status. Em-
pirical part of this paper consists of three stages; at first descriptive statistics on stock returns was performed,
afterwards different risk measures were employed in portfolio construction and in the last part, portfolios
were tested in the out-of-sample period. Results indicate presence of extreme kurtosis and skewness in stock
return series. Resulting portfolios incorporate stocks with extremely high kurtosis and stocks with negative
skewness. Portfolio construction based only on risk and return results in major exposure to extreme returns
and unsatisfactory portfolio out-of-sample results.
Keywords: Alternative Risk Measures, Central and South-East European Emerging Markets, Portfolio,
Skewness, Kurtosis
1. Introduction
Transition economies in Central and South-Eastern
Europe (CSEE) represent very attractive investment area
for foreign investors. In the past few years these stock
markets witnessed tremendous growth both in number of
listed securities as well as in market capitalization. In
2007 stock market indices grew tremendously. In 2007
value of stock market index on Zagreb Stock Exchange
rose 63.20%, Slovene stock market index rose 71.0%,
while German stock market index rose 22.3%. Risk and
illiquidity of stocks are the main problem on these mar-
kets especially in the recent period when the global
economy was struck by financial crisis. Aim of this pa-
per is to define characteristics of stock returns on CSEE
equity markets. Portfolios of stocks will be formed on
these markets using five risk measures: variance, semiva-
riance, lower partial moment when target return is equal
to 0, Mean Absolute Deviation and Conditional Value at
Risk. Out-of-sample analysis of formed portfolios char-
acterizes selected risk measures and their performance in
presence of kurtosis and skewness.
Paper is organized as follows: Section 2 presents a
brief review of previous researches. Risk measures
employed in forming portfolios are presented in Sec-
tion 3. Section 4 discusses data and methodology. Sec-
tion 5 presents results of empirical analysis. Results
include portfolio composition and their out-of-sample
performance. In Section 6 main conclusions were dr-
2. Previous Researches
The analysis of emerging capital markets has increased
substantially in the recent years, however many studies
had failed to take into account the characteristics of
emerging markets in their analysis. The underlying as-
sumption of the standard mean-variance model is that
stock returns must be normally distributed, however this
is in direct contradiction with the empirical evidence
concerning the distribution of emerging markets returns.
[1-5] concluded that Central and South-Eastern European
equity markets have fat tails indicating presence of many
extreme observations. According to [3] who examined
the use of downside risk measures in construction of an
optimal portfolio, the use of downside risk measures re-
sults in significant improvement in the out-of-sample
performance of those portfolios. [6] examined benefits of
diversification into three leading Central European eq-
uity markets using lower partial moment in the presence
of nonnormality of returns on those markets. Their study
shows that investors could benefit diversifying into Cen-
tral European equity markets. These results are supported
by the relatively low short term correlations as well as
the lack of cointegration between these markets and de-
veloped equity markets, their prospects for future eco-
nomic growth and positive impact associated with their
recent accession to the EU. Similar conclusion was
brought in [7] where EU accession was highlighted as
the key contributor to the reduction of risk on these mar-
kets. [8] indicates that South-Eastern Europe emerging
markets are loosely related in periods of normal eco-
nomic activity while in conditions of economic recession
they exhibit strong interrelationship. [9] concluded that
return distribution appears to be leptokurtic for all Euro
stock markets. Investors are more exposed to the risk
since the distribution of returns has a greater exposure to
outlier events and bias to the downside.
3. Risk Measures
Many researches had their idea of the “best” risk meas-
ure to be applied in the portfolio selection; mean lower
partial moment [10-12], Mean-absolute deviation (MAD)
[13] and Conditional Value-at-Risk (CVaR) [14]. This
study involves empirical analysis of most important risk
measures proposed and compared in literature in con-
struction of optimal portfolios on selected markets.
Variance which is by its definition measure of disper-
sion considers the positive and negative deviations from
the mean as potential risk.
Variance of security is defined as:
ExE x
 (1)
where 2
-variance of security , i
is random return
on security , and is expectation operator.
In the case of variance, over-performance relative to
the mean is penalized just as much as under-perfor-
mance. In order to overcome this anomaly [10] pro-
posed semivariance as risk measure. The natural exten-
sion of the semivariance [11,12] is the lower partial
moment risk.
Semivariance is a statistical measure equal to sum of
square deviations from the mean, taking into account
only observations below the mean:
 
Exx Ex
, (2)
Semivariance = (3)
Two alternative downside risk measures are examined
in this paper. The first uses the mean as target rate, the
mean semivariance, and the second uses a target rate of
zero. These two risk measures are denoted as LPMM and
LPM0. Both measures compute risk using only returns
below the mean return or alternatively below a target
return. In the presence of negative skewness in a return
series downside returns will occur in larger magnitudes
than upside returns, the opposite is true in the presence of
positive skewness.
The absolute deviation of random variable is expected
absolute value of difference between the random variable
and its mean. [13] proved that minimizing Mean Abso-
lute Deviation (MAD) is similar to minimizing variance
if stock returns are multivariate normally distributed.
Mean absolute deviation can be calculated using follow-
ing expression:
MAD ii
Ex Ex
The Conditional Value-at-Risk (CVaR) can be ex-
plained trough Value-at-Risk (VaR) [15]. Following
equation defines conditional expectation in the lower tail
of the distribution of returns and is equal to average of
returns beyond VaR at level
CVaRxEx xVaRx
 
Unlike Value-at-Risk, the CVaR is coherent risk
measure [16,17].
4. Data and Methodology
Analysis includes seven stock markets form CSEE re-
gion, five countries are members of EU: Poland, Czech
Republic, Hungary and Romania, while two; Croatia and
Turkey have candidate status. On every market ten
stocks [18,19] from correspondent stock index were se-
lected. Data series consists of 500 daily closing prices for
each security in time period from November 2007 until
the end of October 2009. Stocks were selected according
to following criteria: stock was listed before 2007 and all
stock prices were available in period from November
2007 until October 2009, selected stocks are members of
national stock index which includes best stocks in the
country irrelevant which sector they belong. Stocks
which have the biggest share in construction of national
index have advantage.
Series of daily logarithmic returns for each stock were
calculated. In order to determine whether the stock re-
turns follow the normal distribution in this paper are
presented results of descriptive statistics (mean, standard
deviation, skewness and kurtosis) and normality tests.
Normality tests conducted in this paper are Shapiro
Wilk (W test) and Kolmogorov-Smirnov (K-S) D test
Copyright © 2011 SciRes. AJOR
Copyright © 2011 SciRes. AJOR
Using five risk measures for each stock market portfo-
lios were estimated. Estimated portfolios were analyzed
in the out-of-sample period from November 2008 until
October 2009. For each estimated portfolio Cumulative
Abnormal Returns (CAR-s) against German stock index
DAX [6] were calculated. Standard event study method-
ology was used, abnormal daily returns of each portfolio
against DAX index were calculated:
Romania, Chez Republic and Croatia. As expected the
standard deviation indicates high level of risk in the
CSEE markets. According to results of normality tests
almost all 80 observed CSEE stocks do not pass nor-
mality test. Descriptive statistics indicates that all st-
ocks have negative returns what is expected due pres-
ence of crisis, kurtosis is always greater than zero and
statistically significant indicating fat tails and presence
of many extreme observations. According to data from
Table 2 and Table 5, stocks from Turkey and Poland
have lowest kurtosis coefficients which do not exceed 2,
while values of kurtosis coefficients from Table 1, Ta-
ble 3, Table 4, Table 6 and Table 7 show that all
stocks from Croatia, Romania, Slovenia, Chez Republic
and Hungary have very high kurtosis coefficients.
Similar conclusion can be drawn by observing results of
normality tests; only two stocks from Poland pass W
test and only one stock from Turkey passes KS normal-
ity test. Nonnormality, extreme returns and high kurto-
sis are rather rule than exception when observing stock
returns in emerging CSEE markets. Correlation coeffi-
cients of all stocks are very high and positive indicating
existence of crisis on capital markets giving little space
for diversification. This situation is characteristic for all
capital markets in the region.
itit mt
Rrr (6)
where it is daily return () for portfolio and is
the appropriate benchmark return.
The CAR from the beginning of the first day until the
last day of trading is the summation of abnormal returns.
CARs were estimated assuming benchmark was the
portfolios normal return.
5. Empirical Results
Selected markets could be divided in two groups depen-
dently on risk level measured by standard deviation;
countries with lower level of risk are: Poland, Turkey,
Hungary and Slovenia while higher risks can be found in
Table 1. Results of descriptive statistics for stocks from Croatia and their portfolio weights.
SKEWNESS 0.317* –0.218 0.425* 1.043* 1.131*–0.107 –0.701* –0.074 0.803*0.216
KURTOSIS 5.064* 5.982* 6.462* 10.44* 8.604*2.047*13.053* 3.451* 9.753*2.69*
Resulting portfolios
MV, LPMM, LPM0, CVaR, MAD0.00% 0.00% 69.16%0.00% 0.00%0.00%0.00% 30.84% 0.00%0.00%
*Denotes statistical significance at 5% level.
Table 2. Results of descriptive statistics for stocks fr om Poland and their portfolio weights.
SKEWNESS 0.244 –0.107 0.658* 0.1520.007–0.553* –0.116 –0.077 0.0780.017
KURTOSIS 1.335* 1.358* 10.034*1.752*0.775*7.307* 1.319* 0.188 1.681*0.831*
Resulting portfolios
MV 57.22% 0.00% 38.59%0.00%4.19%0.00% 0.00% 0.00% 0.00%0.00%
LPMM 55.72% 0.00% 41.22%0.00%3.06%0.00% 0.00% 0.00% 0.00%0.00%
LPM0 55.30% 0.00% 41.94%0.00%2.75%0.00% 0.00% 0.00% 0.00%0.00%
CVaR 56.65% 0.00% 39.60%0.00%3.76%0.00% 0.00% 0.00% 0.00%0.00%
MAD 51.63% 0.00% 48.37%0.00%0.00%0.00% 0.00% 0.00% 0.00%0.00%
*Denotes statistical significance at 5% level.
Table 3. Results of descriptive statistics for stocks fr om Romania and their portfolio weights.
SKEWNESS –0.571*–0.228 –0.475*0.242 0.255 –11.15* –0.467*–0.563* 0.195 –0.414*
KURTOSIS 5.129* 3.797* 5.625* 1.341* 3.565* 153.136* 3.742* 4.94* 4.244* 5.979*
Resulting portfolios
MV 0.00% 0.00% 0.00% 39.18%0.00% 0.00% 22.26%0.00% 0.00% 38.55%
LPMM 0.00% 0.00% 0.00% 39.65%0.00% 0.00% 24.28%0.00% 0.00% 36.07%
LPM0 0.00% 0.00% 0.00% 39.62%0.00% 0.00% 24.15%0.00% 0.00% 36.24%
CVaR 0.00% 0.00% 0.00% 40.06%0.00% 0.00% 26.07%0.00% 0.00% 33.87%
MAD 0.00% 0.00% 0.00% 34.03%0.00% 0.00% 0.00% 0.00% 0.00% 65.97%
*Denotes statistical significance at 5% level.
Table 4. Results of descriptive statistics for stocks fr om Slovenia and their portfolio weights.
SKEWNESS 0.006 0.189 0.168 –0.16 –0.026 0.413* 0.154 –0.41* –0.321* 0.528*
KURTOSIS 2.79* 3.311* 8.792* 6.189* 3.363* 4.785* 2.827* 1.637* 2.514* 3.528*
Resulting portfolios
MV 0.77% 0.00% 15.33% 49.22% 15.71% 0.00% 0.00% 0.00% 18.97% 0.00%
LPMM 1.59% 0.00% 12.36% 50.19% 16.72% 0.00% 0.00% 0.00% 19.14% 0.00%
LPM0 2.55% 0.00% 12.06% 51.20% 16.40% 0.00% 0.00% 0.00% 17.79% 0.00%
CVaR 0.00% 0.00% 28.69% 47.30% 2.16% 0.00% 0.00% 0.00% 21.85% 0.00%
MAD 25.39% 0.00% 0.00% 74.61% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
*Denotes statistical significance at 5% level.
Table 5. Results of descriptive statistics for stocks fr om Turkey and their portfolio weights.
SKEWNESS 0.012 0.484* 0.32* –0.259 –0.1260.316*–0.079 0.376* 0.379* 0.479*
KURTOSIS 2.165* 1.337* 2.514*1.285* 1.324*2.308*2.104* 2.010* 1.620* 2.921*
Resulting portfolios
MV 16.40% 0.00% 0.00%37.89% 36.81%0.00%0.00% 6.33% 2.57% 0.00%
LPMM 15.61% 0.00% 0.00%35.94% 37.82%0.00%0.00% 7.63% 3.00% 0.00%
LPM0 15.30% 0.00% 0.00%35.47% 38.28%0.00%0.00% 7.32% 3.63% 0.00%
CVaR 25.55% 0.00% 0.00%6.35% 44.52%2.32% 1.31% 18.02% 1.93% 0.00%
MAD 0.00% 0.00% 0.00%69.30% 30.70%0.00%0.00% 0.00% 0.00% 0.00%
*Denotes statistical significance at 5% level.
Observed stock returns have asymmetric distribution.
Skewness coefficients are quite different between coun-
tries generally, and between stocks within every stock
market. Generally, skewness coefficients are statistically
significant for major part of stocks but the sign of skew-
ness coefficients is quite different. According to Tab le 3
and Table 6 most stocks from Romania and Chez Re-
public have statistically significant negative skewness.
Table 1 and Table 5 show that most stocks from Croa-
tia and Turkey have positive skewness coefficient. Ac-
cording to Table 2, Table 4 and Table 7 most stocks
from Slovenia, Poland and Hungary do not have statisti-
cally significant skewness coefficient.
Using five different risk measures portfolios on every
market were formed and their CARs were calculated.
esults indicate that application of standard MV model
Copyright © 2011 SciRes. AJOR
Table 6. Results of descriptive statistics for stoc ks fr om Che z Republic and their portfolio weights.
SKEWNESS –0.116 –0.614*–0.103 –0.713*0.224 –1.314*–3.066* 0.252 0.357*–0.303
KURTOSIS 7.073* 4.996* 7.483*6.184*5.753*10.762*36.486* 12.543* 8.274*2.35*
Resulting portfolios
MV, LPMM, LPM0, CVaR, 0.00% 0.00% 0.00%0.00%26.67%0.00%0.00% 73.33% 0.00% 0.00%
MAD 0.00% 0.00% 0.00%0.00%0.00%0.00%0.00% 99.89% 0.00%0.11%
*Denotes statistical significance at 5% level.
Table 7. Results of descriptive statistics for stocks fr om Hungary and their portfolio weights.
SKEWNESS –0.788* 0.868* 1.05* –0.363* –0.26 0.218 0.015 –0.493* 0.061 –0.027
KURTOSIS 6.432* 6.178* 10.694* 4.062* 7.818* 6.445* 3.433* 7.443* 6.406* 7.033*
Resulting portfolios
MV 53.41% 0.00% 0.00% 19.65% 0.00% 0.00% 0.00% 0.00% 26.94% 0.00%
LPMM 50.65% 0.00% 0.00% 16.66% 0.00% 0.00% 0.00% 0.00% 32.69% 0.00%
LPM0 50.83% 0.00% 0.00% 16.84% 0.00% 0.00% 0.00% 0.00% 32.33% 0.00%
CVaR 51.02% 0.00% 0.00% 17.05% 0.00% 0.00% 0.00% 0.00% 31.93% 0.00%
MAD 35.35% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 64.65% 0.00%
*Denotes statistical significance at 5% level.
is questionable when CSEE emerging markets are ob-
served. In order to overcome the nonnormality problem
downside risk measures, LPMM and LPM0 were intro-
duced. According to results from Tables 1 to 7, MV,
LPMM and LMP0 portfolios have similar composition
and similar stock weights and consequentially they have
similar results in the out-of-sample period. These con-
clusions are compatible with [6]. MAD portfolios from
all 7 markets share common characteristic; MAD portfo-
lios are composed from smaller number of assets than
other portfolios. CVaR portfolios are very hard to char-
acterize because their composition is quite different than
composition of other portfolios and their out-of-sample
performance is different than performance of other port-
folios. If MAD portfolios and CVaR portfolios are com-
pared, CVaR portfolios are more stable while MAD
portfolios have faster drops. These results are in accor-
dance with results of previous researches [21,22]. This
can be proved by examining volatility of CVaR and
MAD portfolios in the out-of-sample period measured by
standard deviation of portfolio returns in Table 8. Gen-
erally, comparison of CARs in the out-of-sample period
does not give answer on the best risk measure. Accord-
ing to results from Table 8, application of standard MV
model on these markets is quite questionable. Better re-
sults are possible what can be seen in case of Turkey,
Slovenia, Romania and Poland were MAD or CVaR
portfolios over-perform MV, LPMM and LPM0 portfo-
lios. These results do not have continuity. CVaR portfo-
lio over-performs in case of Romania and gives good
results in case of Slovenia. MAD portfolios have better
results in case of Poland, Slovenia and Turkey but these
portfolio returns are always accompanied by higher vola-
tility in the out-of-sample period. In case of Hungary
best result is achieved by application of standard MV
6. Conclusions
In this paper behavior of risk measures in situation of
nonnormality and their impact on portfolio composition
were investigated. Employed statistical methods affirmed
presence of nonormality and extreme kurtosis accompa-
nied with skewness which is statistically significant for
major part of stocks. The use of downside risk measures
does not give significant improvement in the portfolio
performance in the out-of-sample period. Employed risk
measures are not able to recognize excess kurtosis and
skewness in stock returns allowing highly risky securities
to enter portfolio. CARs were calculated in order to fol-
low the performance of resulting portfolios in the out-of-
sample period. According to results, CVaR portfolios
have slightly more stable returns in the out-of-sample
period while MAD portfolios have highest volatility.
LPMM, LPM0 and variance portfolios have similar
omposition, volatility and out-of-sample results. Natural c
Copyright © 2011 SciRes. AJOR
Table 8. Performance of resulting portfolios in the out-of-sample period.
Risk measure Portfolios expected
return (%) Expected monthly
return (%) Standard deviation of
portfolio return CAR at the end of
period (%)
MV, LPMM, LPM0, CVaR, MAD –0.0021 0.0005 2.2235 –0.5130
MV –0.1698 –0.1242 2.2089 –26.9950
LPMM –0.1686 –0.1218 2.2119 –26.7923
LPM0 –0.1683 –0.1211 2.2131 –26.7692
CVaR –0.1693 –0.1233 2.2098 –27.9404
MAD –0.1655 –0.1152 2.2297 –26.3223
MV –0.1230 –0.1480 3.0093 –24.4724
LPMM –0.1182 –0.1458 3.0307 –23.5257
LPM0 –0.1185 –0.1459 3.0292 –23.5895
CVaR –0.1140 –0.1438 3.0531 –22.6873
MAD –0.1755 –0.1731 3.0527 –34.9204
MV 0.0041 0.1809 2.9196 0.3880
LPMM 0.0026 0.1781 2.9464 0.2446
LPM0 0.0033 0.1801 2.9698 0.3111
CVaR 0.0335 0.2319 2.8635 3.1472
MAD 0.0448 0.2642 3.5960 4.2149
MV 0.1276 0.1307 2.8488 31.5103
LPMM 0.1262 0.1291 2.8428 31.1751
LPM0 0.1262 0.1289 2.8409 31.1710
CVaR 0.1079 0.1098 2.7865 26.6409
MAD 0.1463 0.1504 3.1612 36.1460
Chez Republic
MV, LPMM, LPM, CVaR –0.0451 –0.7725 2.2258 –9.8411
MAD –0.0777 –0.0200 2.5121 –16.9433
MV 0.1322 0.1511 2.2899 28.2907
LPMM 0.1292 0.1469 2.2857 27.6593
LPM0 0.1294 0.1472 2.2858 27.6985
CVaR 0.1296 0.1475 2.2859 27.7422
MAD 0.1128 0.1238 2.4001 24.1482
extension of this paper would be presentation of risk
measure which should take into account information on
skewness and kurtosis of stock returns.
7. References
[1] G. Bekaert and R. H. Campbell, “Research in Emerging
Copyright © 2011 SciRes. AJOR
Markets Finance: Looking to the Future,” Emerging Mar-
kets Review, Vol. 3, No. 4, 2002, pp. 429-448.
[2] G. Bekaert and C. Harvey, “Emerging Markets Finance,”
Journal of Empirical Finance, Vol. 10, No. 1-2, 2003, pp.
3-56. doi:10.1016/S0927-5398(02)00054-3
[3] S. Stevenson, “Emerging Markets, Downside Risk and
the Asset Allocation Decision,” Emerging Markets Re-
view, Vol. 2, No. 1, 2001, pp. 50-66.
[4] R. Susmel, “Extreme Observations and Diversification in
Latin America Emerging Equity Markets,” Journal of In-
ternational Money and Finance, Vol. 20, No. 7, 2001, pp.
971-986. doi:10.1016/S0261-5606(01)00014-6
[5] J. Vidović and Z. Aljinović, “Research on Stock Returns
in Central and South-East European Transitional Econo-
mies,” Proceedings KOI 10th International Symposium
on Operational Research in Slovenia, Nova Gorica, 23 -
25 September 2009, pp. 237-246.
[6] C. G. Gilmore, G. M. McManus and A. Tezel, “Portfolio
Allocations and the Emerging Equity Markets of Central
Europe,” Journal of Multinational Financial Manage-
ment, Vol. 15, No. 3, 2005, pp. 287-300.
[7] C. A. J. Middleton, S. G. M. Fifield and D. M. Power,
“Investment in Central and Eastern European Equities,”
Studies in Economics and Finance, Vol. 24, No. 1, 2007,
pp. 13-31. doi:10.1108/10867370710737364
[8] T. Gklezakou and J. Mylonakis, “Interdependence of the
Developing Stock Markets, before and during the Eco-
nomic Crisis: The Case of South Europe,” Journal of
Money, Investment and Banking, Vol. 11, 2009, pp. 70-
[9] J. Bley, “European Stock Market Integration: Fact or
Fiction?” Journal of International Financial Markets, In-
stitutions and Money, Vol. 19, No. 5, 2009, pp. 759-776.
[10] H. M. Markowitz, “Portfolio Selection: Efficient Diversi-
fication of Investments,” John Wiley & Sons, New York,
[11] P. C. Fishburn, “Mean-Risk Analysis with Risk Associ-
ated with Below-Target Returns,” American Economic
Review, Vol. 67, No. 2, 1977, pp. 116-126.
[12] V. S. Bawa and E. B. Lindenberg, “Capital Market Equi-
librium in a Mean-Lower Partial Moments Framework,”
Journal of Financial Economics, Vol. 5, No. 2, 1977, pp.
198-200. doi:10.1016/0304-405X(77)90017-4
[13] H. Konno and H. Yamazaki, “Mean-Absolute Deviation
Portfolio Optimization Model and Its Application to To-
kyo Stock Market,” Management Science, Vol. 37, No. 5,
1991, pp. 519-531. doi:10.1287/mnsc.37.5.519
[14] S. Uryasev, “Conditional Value-at-Risk (CVaR): Algo-
rithms and Applications,” Working Paper, University of
Florida, 2002.
[15] A. Alexandre, M. Houkari and J.-P. Laurent, “Spectral
Risk Measures and Portfolio Selection,” Journal of Bank-
ing and Finance, Vol. 32, No. 9, 2008, pp. 1870-1882.
[16] C. Acerbi and D. Tasche, “On the Coherence of Expected
Shortfall,” Journal of Banking and Finance, Vol. 26, No.
7, 2002, pp. 1487-1503.
[17] R. T. Rockafellar and S. Uraysev, “Optimization of Con-
ditional Value-at-Risk,” Journal of Risk, Vol. 2, No. 3,
2000, pp. 21-41.
[18] G. Y. N. Tang, “How Efficient Is Naive Portfolio Diver-
sification? An Educational Note,” Omega—The Interna-
tional Journal of Management Science, Vol. 32, No. 2,
2004, pp. 155-160.
[19] L. R. Irala and P. Patil, “Portfolio Size and Diversifica-
tion,” SMCS Journal of Indian Management, Vol. 4, No.
1, 2007, pp. 1-6.
[20] S. S. Shapiro, M. B. Wilk and H. J. Chen, “A Compara-
tive Study of Various Tests of Normality,” Journal of the
American Statistical Association, Vol. 63, No. 324, 1968,
pp. 1343-1372. doi:10.2307/2285889
[21] Y. Simaan, “Estimation Risk in Portfolio Selection: The
Mean Variance Model versus the Mean Absolute Devia-
tion Model,” Management Science, Vol. 43, No. 10, 1997,
pp. 1437-1446. doi:10.1287/mnsc.43.10.1437
[22] E. Angelelli, R. Mansini and G. M. Speranza, “A Com-
parison of MAD and CVaR Model with Real Features,”
Journal of Banking & Finance, Vol. 32, No. 7, 2008, pp.
1188-1197. doi:10.1016/j.jbankfin.2006.07.015
Copyright © 2011 SciRes. AJOR