IJMF-07-2011-0056

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International Journal of Managerial FinanceEvaluation of Malaysian mutual funds in the maximum drawdown risk measureframeworkMohammad Reza Tavakoli Baghdadabad Paskalis Glabadanidis

Article information:To cite this document:Mohammad Reza Tavakoli Baghdadabad Paskalis Glabadanidis, (2013),"Evaluation of Malaysian mutualfunds in the maximum drawdown risk measure framework", International Journal of Managerial Finance,Vol. 9 Iss 3 pp. 247 - 270Permanent link to this document:http://dx.doi.org/10.1108/IJMF-07-2011-0056

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Users who downloaded this article also downloaded:Nurasyikin Jamaludin, Malcolm Smith, Paul Gerrans, (2012),"Mutual fund selection criteria:evidence from Malaysia", Asian Review of Accounting, Vol. 20 Iss 2 pp. 140-151 http://dx.doi.org/10.1108/13217341211242187Fikriyah Abdullah, Taufiq Hassan, Shamsher Mohamad, (2007),"Investigation of performance of MalaysianIslamic unit trust funds: Comparison with conventional unit trust funds", Managerial Finance, Vol. 33 Iss 2pp. 142-153 http://dx.doi.org/10.1108/03074350710715854Athanasios G. Noulas, John A. Papanastasiou, John Lazaridis, (2005),"Performance of mutual funds",Managerial Finance, Vol. 31 Iss 2 pp. 101-112 http://dx.doi.org/10.1108/03074350510769523

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Evaluation of Malaysian mutualfunds in the maximum drawdown

risk measure frameworkMohammad Reza Tavakoli Baghdadabad

Graduate School of Business, National University of Malaysia, Bangi,Malaysia, and

Paskalis GlabadanidisBusiness School, University of Adelaide, Adelaide, Australia

Abstract

Purpose – This paper aims to evaluate the risk-adjusted performance of the management styles ofMalaysian mutual funds using nine modified performance evaluation measures generated by themaximum drawdown risk measure (M-DRM) based on the modern portfolio theory. The purpose is toreport the findings in a manner which is realizable by the average investors and portfolio managers.Design/methodology/approach – This paper evaluates the performance of more than 400Malaysian mutual funds using risk-adjusted returns over the two sub-periods of 2000-2005 and2006-2011. The M-DRM, as a different measure from downside risk, is applied to improve ninerisk-adjusted performance measures of Sortino, Treynor, M-squared, Jensen’s alpha, information ratio(IR), MSR, upside partial ration (UPR), FPI, and leverage factor. It proposes a new single-factor modelto test the maximum drawdown beta and alpha in the M-DRM framework.Findings – The evidence clearly indicates that the replacement framework in terms of MDB, themaximum drawdown beta, and the maximum drawdown CAPM can be replaced by the conventionalframeworks in terms of MVB, beta, and the CAPM and also MSB, downside beta, and D-CAPMfor modifying nine performance evaluation measures from the management styles of Malaysianmutual funds.Practical implications – The research evidence reported in this paper can be applied as input in theprocess of decision making by small and average investors and portfolio managers who are seekingthe possibility of participating in the global stock market through mutual funds.Originality/value – This paper is the first study to estimate a new regression model in the M-DRMframework to evaluate the performance of Malaysian mutual funds. In addition, it proposes ninemodified performance evaluation measures in the M-DRM framework for the first time.

Keywords Maximum drawdown risk measure (M-DRM), Maximum drawdown beta, Downside risk,Semi-variance, Mutual fund, Malaysia, Unit trusts, Financial risk

Paper type Research paper

1. IntroductionDue to the primary studies of Treynor (1965), Jensen (1968), and the subsequent studiesof Sortino and Price (1994), Modigliani and Modigliani (1997), Sortino et al. (1999),Pedersen and Rudholm (2003), and Ferruz and Sarto (2004), the performancemeasurement of a managed portfolio has attracted remarkable interest in the economicand financial literature. From a general view, two vital approaches may be recognizedand followed for performance measurement. The first approach considers the returnsof managed portfolios, and its purpose is to define and interpret the conventionalreward-to-risk measures under symmetric conditions. The second approach investigatesthe returns of the managed portfolios and concentrates on utilizing and introducing themeasures which make it possible to infer the choices made by investment managersunder asymmetric conditions.

The current issue and full text archive of this journal is available atwww.emeraldinsight.com/1743-9132.htm

Received 26 July 2011Revised 9 January 2012

17 July 201219 November 201230 November 2012

Accepted 1 December 2012

International Journal of ManagerialFinance

Vol. 9 No. 3, 2013pp. 247-270

r Emerald Group Publishing Limited1743-9132

DOI 10.1108/IJMF-07-2011-0056

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The first approach has empirically concentrated on the performance evaluationof managed portfolios in the domestic fund markets (i.e. Carhart, 1997; Baer et al., 2006;Afza and Rauf, 2009), and international fund markets (i.e. Eun et al., 1991; Droms andWalker, 1994; Bauer et al., 2005) in the mean-variance (MV) framework. However, thefirst approach is an inappropriate method of performance evaluation for two reasons:first, it is only a desirable approach when the returns have a symmetric distribution,and, second, it can only be employed as a risk measure when the distribution of returnsis normal. Furthermore, both the symmetry and the normality of portfolio returnsare seriously questioned by the empirical evidence on the issue (i.e. Arditti, 1971;Simkowitz and Beedles, 1978; Chunhachinda et al., 1997).

Again, the second approach extends alternative frameworks in responding to therequirements of the market asymmetric condition. In this context, this study extendsa recently proposed approach in the mean-maximum drawdown framework asmaximum drawdown risk (M-DRM) measure. This risk measure has been extendedto evaluate the investment portfolios. It is less used to evaluate the performance ofdifferent types of funds. Unlike the downside risk, M-DRM evaluates the loss from alocal maximum to the next local minimum and is intuitively appealing for institutionalinvestors (Hamelink and Hoesli, 2003).

The drawdown of returns is a more acceptable measure of risk for several reasons:first, investors logically prefer a risk measure as down-side volatility (i.e. Nantell andPrice, 1979; Stevenson, 2001; Galagedera, 2007). Second, unlike the downside risk,M-DRM evaluates the loss from a local maximum to the next local minimum and isintuitively appealing for institutional investors (Hamelink and Hoesli, 2003). Third, themaximum drawdown risk is more beneficial than the variance (standard deviation)when the dispersion of returns is asymmetric and just as beneficial when thedispersion is symmetric; accordingly the maximum drawdown risk is a better riskmeasure in comparison with the variance. Finally, the maximum drawdown riskcombines into one measure the information generated by three statistics, variance,semi-variance, and skewness, thus, making it possible to utilize a single-factor modelto estimate the expected returns.

This study proposes a replacement risk measure for fund managers and diversifiedinvestors, the maximum drawdown b (MD-b), and also an alternative pricing model inthe M-DRM framework to estimate maximum drawdown a (MD-a). It also extends themaximum drawdown risk concepts upon seven risk-adjusted measures of Sortino,M2, information ratio (IR), MSR, FPI, UPR, and leverage factor, and then runs a single-factor regression model based on the M-DRM to estimate the MD-b and the MD-a andmodify two other measures of Treynor and Jensen’s a over the management styles ofMalaysian mutual funds. After extending the risk-adjusted measures in the M-DRMframework and testing the maximum drawdown single-factor regression model,we evaluate the performance of mutual funds using data from the management stylesof Malaysian mutual fund market for two separated sub-periods from 2000 to 2005 and2006 to 2011.

The evidence described supports the M-DRM upon the conventional risk measures,and, in particular, the MD-b. The empirical evidence also indicates that mean returnsare much more sensitive to differences in MD-b than to equal differences inconventional b. Moreover, this study modifies nine measures of Sortino, Treynor, M2,Jensen’s a, IR, MSR, UPR, FPI, and leverage factor. Finally, this paper questions theconventional framework in terms of MVB, b, CAPM, and also mean-semi variancebehavior (MSB), downside b, and D-CAPM, and suggests replacing them with the

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replacement framework in terms of mean-maximum drawdown behavior (MDB), theMD-b, and the maximum drawdown CAPM.

The paper is structured as follows. In Section 2, the MVB, MSB, and MDBframework are reviewed. In Section 3, empirical evidence is described. Finally, asummary and conclusion is considered in Section 4.

2. MVB vs MDB frameworkWe first explain the conventional MVB and MSB framework, their relevant pricingmodel (CAPM), and also the risk-adjusted measures associated with the MVB. Then weelaborate the proposed approach of this paper as the MDB framework along with itsrelevant proposed pricing model and also its modified risk-adjusted measures.Then we briefly explain how to estimate the MD-b (MD-b) to replace the conventionaland downside b, and, finally, we propose new risk-adjusted measure in terms of theM-DRM to evaluate the performance of Malaysian mutual funds.

2.1 MVB, asset pricing, and traditional measuresThe conventional MVB framework explains that an investor’s utility (U) istheoretically determined by the mean (mP) and variance (sP) of returns associatedwith the investor’s portfolio, where U is defined as U¼U(mP, sP). In such a framework,the risk of a certain fund i is measured by the fund’s standard deviation (SD) of returns(si), which is mathematically defined by Equation (1):

si ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiE½ðRi � miÞ2�

qð1Þ

where R and m are returns and mean returns, respectively. However, when security i isjust one out of many in a completely-diversified portfolio, its risk is computed by itscovariance with respect to the market portfolio (sim), which is mathematically definedby Equation (2):

sim ¼ E½ðRi � miÞðRm � mmÞ� ð2Þwhere m is defined as the market portfolio. Interpretation of the covariance is notstraightforward, as the statistic is both unbounded and scale-dependent. A morebeneficial measure of risk can be computed by dividing this statistic by the output offund i’s SD of returns and the market portfolio’s standard deviation, thus, getting fundi’s correlation with respect to the market index (rim) as follows:

rim ¼sim

si:sm¼ E½ðRi � miÞðRm � mmÞ�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

E½ðRi � miÞ2� � E½ðRm � mmÞ2�q ð3Þ

Alternatively, the covariance between fund i and the market index can be divided bythe variance of market index, thus, getting fund i’s b (bi) as follows:

bi ¼sim

s2m

¼ E½ðRi � miÞðRm � mmÞ�E½ðRm � mmÞ

2ð4Þ

This risk measure is directly applied in the model most widely utilized to estimate theexpected returns on fund, the CAPM, as given by Equation (5):

EðRiÞ ¼ Rf þ biðRm � Rf Þ ð5Þ

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where E(Ri), Rf and Rm denote the expected return on fund i, the risk-free rate, and therequired return on the market, respectively.

The CAPM can be run by an ex-post regression model to estimate a as aperformance important measure as given by Equation (6):

a ¼ fEðRiÞ � ½Rf þ biðRm � Rf Þ�g ð6Þ

Variance and its relevant SD are only an appropriate risk measure if the returnsdispersion is symmetric. The MVB approach is only valid under symmetry conditions.

The MVB approach was gradually considered as a basis for introducing therisk-adjusted measures. These measures have been empirically pioneered by Treynor(1965), Jensen (1968), Sortino and Price (1994), Modigliani and Modigliani (1997),Sortino et al. (1999), Pedersen and Rudholm (2003), and Ferruz and Sarto (2004). Thestatistical techniques extended by them are the most commonly applied portfolioperformance measures using variance even now. First, Treynor (1965), using theCAPM as a benchmark, adjusted the excess return by the funds b. Then, Jensen (1968)proposed the measure, namely, a coefficient, which explains the difference between theactual excess return and the expected excess return, as described by Equation (6).Consequently, Sortino and Price (1994) proposed a new performance measure tocalculate each of the funds through dividing the mean excess return by the total risk ofthe fund. This measure is particularly attractive in an international setting because itdoes not depend directly on the market portfolio. To improve the prior measures,Modigliani and Modigliani (1997) suggested the performance measure of M2, whichmultiplies the Sharpe measure by the benchmark SD and then adds the risk free rate ofreturn to that. They also proposed the leverage factor through dividing the market SDby the fund’s SD. Subsequently, Sortino et al. (1999) proposed the upside potentialratio (UPR) as the probability-weighted average of returns above the free risk rate.In addition, Pedersen and Rudholm (2003) suggested the IR as a measure similar to theSharpe measure, except the numerator is the total instead of the excess of returns.They also suggested another performance index, namely, firm’s performance index tocompare the Sharpe measure and median Sharpe measure. Finally, Ferruz and Sarto(2004) suggested a revised ratio of Sharpe measure for bear markets through replacingthe relative return premium instead of the difference ri�rf.

However, there have been several reasons to select the aforementioned performanceevaluation measures. The major motivation for using Sortino and FPI measure is thatthey allow a direct comparison of the risk-adjusted returns of any mutual funds,regardless of their correlations with a benchmark. Moreover, Sortino’s measureconsiders the total market risk, which can provide a better understanding of the overallinvestment performance of a fund (i.e. Roy, 1952; Du, 2008). The reason for utilizingthe M2 and leverage factor is that they are intuitively quite appealing for investors.The idea that underlies the methodology of these measures is to adjust the returns of amutual fund to the level of risk in an unmanaged stock market index and then evaluatethe returns on the risk-matched fund. These two measures have two distinctadvantages over earlier techniques. First, they report the risk-adjusted performance ofa mutual fund as a percentage, which is easily understood by a lay investor. Second,they permit investors to calculate the degree of leverage that is needed to attain thehighest return possible for a given level of risk (Modigliani and Modigliani, 1997;Arugaslan et al., 2008). IR is also similar to the Sortino ratio. However, since the Sortinomeasure is the excess return of an asset over the return of a risk free asset divided by

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the variability or SD of returns, the IR is the active return to the most relevantbenchmark index divided by the SD of the “active” return or tracking error that:estimates ex-post value added and relates this to ex-ante opportunity available in thefuture, and describes the opportunities accessible to the active manager (Sortino andPrice, 1994; Pedersen and Rudholm, 2003). For MSR, This new measure providesconsistent rankings for any set of portfolios (Ferruz and Sarto, 2004). Finally, theUPR ratio is an appropriate measure to rank portfolio performance based on acombination of the upside potential and the measures under asymmetric conditionslike downside risk.

2.2 MSB and asset pricingIn the MSB framework, the utility of a certain investor is given by U¼U(mD,

PD2 ),

whereP

D2 describes the downside variance of funds (semi-variance of funds).

Accordingly, the risk of a fund i is computed by the fund’s downside SD of returns (P

i),which is given by: X

i

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEfmin½ðRi � miÞ; 0�2g

qð7Þ

Equation (7) is, in other words, a particular case of the semi-SD that can be expressedwith respect to market index B(

PBi) as:

XBi

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEfmin½ðRi � BÞ; 0�2g

qð8Þ

This paper will denote the semi-SD of fund i simply asP

i. In a framework of downsiderisk, the counterpart of fund i’s covariance to the market portfolio is resulted by itsdownside covariance (

PiM), which is defined by Equation (9):

XiM

¼ Efmin½ðRi � miÞ; 0Þ� �min½ðRM � mM Þ; 0Þ�g ð9Þ

Moreover, the co semi-variance is unbounded, but it can also be standardized bydividing it by the output of fund i’s SD of returns and the market’s SD of returns,accordingly, obtaining the fund i’s downside correlation (YiM) as follows:

YiM ¼P

iMPi :P

M

¼ Efmin½ðRi � miÞ; 0� �min½ðRM � mM Þ; 0�gffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEfmin½ðRi � miÞ; 0�

2g � Efmin½ðRM � mM Þ; 0�2g

qð10Þ

Alternatively, the co semi-SD can be divided by the market’s semi-variance of returns,accordingly obtaining fund i’s downside b (bi) as follows:

bDi ¼

PiMP2M

¼ Efmin½ðRit � mitÞ; 0� �min½ðRMt � mMtÞ; 0�gEfmin½ðRMt � mMtÞ; 0�2g

ð11Þ

The downside b, which is alternatively defined as bi¼ (P

i/P

M)YiM, can be describedinto a CAPM-like model in the downside risk framework (D-CAPM). Such a model, asthe one suggested in this paper, is defined by Equation (12):

EðRiÞ ¼ Rf þ bDi :ðRm � Rf Þ ð12Þ

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2.3 MDB, asset pricing, and the proposed measuresIn the replacement MDB framework, the investor’s utility is defined by U¼U(mP ,

PP2),

whereP

P2 denotes the maximum drawdown risk of returns on the investor’s portfolio.

In this context, the risk of a certain fund i is individually measured by the fund’sdownside SD of a combination of loss from a local maximum to the next local minimumand risk premium as given by Equation (13):

Xi

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEfmin½ðDt�1 þ ðRit � mitÞ; 0Þ�2g

qð13Þ

where D0 is equal to 0, Dt denotes the maximum loss that an investor suffers from 0 to t.Equation (13) is, in fact, a special case of the semi-deviation, which can be moregenerally expressed with respect to any benchmark return B(

PBi) as follows:

XBi

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEfmin½ðDt�1 þ ðRit � BÞ; 0�2g

qð14Þ

This paper will denote the M-DRM of fund i simply asP

i. In M-DRM framework, thecounterpart of fund i’s covariance to the market portfolio is resulted by its M-DRMcovariance, or co M-DRM (

PiM) for short, which is given by Equation (15):

XiM

¼ Efmin½ðDt�1 þ ðRit � mitÞ; 0Þ�

�min½ðDt�1 þ ðRMt � mMtÞ; 0Þ�gð15Þ

The co M-DRM is unbounded, but it can also be standardized by dividing it by theoutput of fund i’s M-DRM of returns and the market’s M-DRM of returns, hence,obtaining fund i’s M-DRM correlation (YiM) as follows:

YiM ¼P

iMPi �P

M

¼ Efmin½ðDt�1 þ ðRit � mitÞ; 0Þ� �min½ðDt�1 þ ðRMt � mMtÞ; 0Þ�gffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEfmin½ðDt�1 þ ðRit � mitÞ; 0Þ�2g � Efmin½ðDt�1 þ ðRMt � mMtÞ; 0Þ�2g

qð16Þ

Alternatively, the co M-DRM can be divided by the market’s M-DRM of returns,accordingly obtaining fund i’s M-DRM b (bi

M�DRM) as follows:

bM�DRMi ¼

PiMP2M

¼Efmin½ðDt�1 þ ðRit � mitÞ; 0Þ� �min½ðDt�1 þ ðRMt � mMtÞ; 0Þ�gEfmin½ðDt�1 þ ðRMt � mMtÞ; 0Þ�2g

ð17Þ

This M-DRM b, which is alternatively defined as biM�DRM¼ (

Pi/P

M)YiM, can bedescribed into a CAPM-like model in the M-DRM framework. Such a model, as the onesuggested in this paper, is given by Equation (18):

EðRiÞ ¼ Rf þ bM�DRMi � ðRm � Rf Þ ð18Þ

As observed by a direct comparison of the two Equations (5) and (12), the proposedmodel replaces the b of the CAPM and bD of the D-CAPM by the M-DRM b, the

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appropriate measure of systematic risk in the M-DRM framework. This replacement isthe most important contribution of this study.

To estimate MD-b and a, as main contribution of this study, the ex-posed maximumdrawdown CAPM model is given by Equation (19):

yt ¼ l0 þ l1 � xt þ et; ð19Þ

where the appropriate method to compute and estimate biM�DRM and a is to test

a linear regression between the independent variable xt¼min[(Dt�1þ (RMt�mMt), 0)]and the dependent variable yt¼min[(Dt�1þ (Rit�mit), 0)], which obtain thebi

M�DRM and a as the slope of the regression model and a constant by Equation (19),where bi

D¼ l1 and a¼ l0.2.3.1 A brief discussion on the M-DRM b. The M-DRM b of any fund i given by

Equation (17) can be computed and estimated in at least three ways: first, throughdividing the co M-DRM between fund i and the market index given by Equation (15)through the M-DRM of the market index given by Equation (13) for i¼M;that is bi

M�DRM¼ (P

iM/P

M2 ) Moreover, this coefficient can be computed and

estimated by multiplying the ratio of M-DRM of fund i and the market index, theformer given by Equation (13) and the next given by Equation (13) for i¼M, by theM-DRM correlation between fund i and the market index, given by Equation (16); thatis, bi

M�DRM¼ (P

i/P

M)YiM. Both described methods are mathematically similarbecause of the fact which YiM¼

PiM/(P

i �P

M); hence, biM�DRM¼

PiM/P

M2 )¼P

i �P

M �YiM/P

M2¼ (P

i/P

M)YiM.Finally, the M-DRM b of any fund i can be computed by regression analysis.

Let yt¼min[(Dt�1þ (Rit�mit), 0)] and xt¼min[(Dt�1þ (RMt�mMt), 0)], and let my and mx

be the mean of yt and the mean of xt, respectively. If a regression model is run by yt asthe dependent variable and xt as the independent variable (i.e., yt¼ l0þ l1 � xtþ et,where e is an error term and l0 and l1 are coefficients to be estimated), the estimate ofl1 would be given by Equation (20):

l1 ¼E½ðxt � mxÞðyt � myÞ�

E½ðxt � mxÞ2�ð20Þ

Alternatively, as defined in Equation (17), biM�DRM can be computed by Equation (21):

bM�DRMi ¼ E½xt � yt�

E½x2t �

ð21Þ

In fact, the appropriate method to compute and estimate biM�DRM using the regression

model is to test a linear regression without considering a constant between theindependent variable xt¼min[(Dt�1þ (RMt�mMt), 0)] and the dependent variableyt¼min[(Dt�1þ (Rit�mit), 0)], which obtain the MD-b as the slope of the regressionmodel as yt¼ l1 � xtþ et, where bi

M�DRM¼ l1. This is as one of the most importantcontributions of this paper.

2.3.2 The proposed measures in the M-DRM framework. As another contribution,this study modifies nine conventional risk-adjusted measures of Sortino, M2, IR, MSR,UPR, FPI, and leverage factor in which the M-DRM of any fund and market index arefirst computed to directly insert in the measures. Then, the single-factor regressionmodel in the M-DRM framework, as described in the aforementioned section, is

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proposed to estimate the MD-b and the MD-a for modifying two other measures ofTreynor, and Jensen’s a. The considered measures are modified as follows:

(1) The modified Sortino measureThis study inserts the M-DRM computed by Equation (13) into the conventionalSortino measure to propose a new measure, namely, the modified Sortinomeasure (Si

D):

SDi ¼

�RiPi

ð22Þ

where �Ri andP

i are the mean excess return (Ri�Rf) and the M-DRM of fundreturn i, respectively.

(2) The modified M2 measureThis study inserts the M-DRM computed by Equation (13) into the traditionalM2 measure to propose a new measure, namely, the modified M2 measure (Mi

D):

MDi ¼

Ri � RfPi

XmþRf ð23Þ

To compute the M-DRM of market index (P

m), this study proposes Equation (24):

Xm¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEfmin½ðDt�1 þ ðRmt � mmtÞ; 0Þ�2g

qð24Þ

where D0 is equal to 0. Given the sample observations for Xm, t t¼ 0, 1,y, T, themaximum drawdown Dt(Xm, t) or simply Dt represents the maximum loss ofmarket index from 0 to t.

(3) The modified leverage factorThis study inserts the M-DRM computed by Equations (13) and (24) into thetraditional leverage factor to propose a new measure, namely, the modifiedleverage factor (Li

D):

LDi ¼

PmPi

ð25Þ

As the modified leverage factor is greater than one it implies that the M-DRMof the fund is less than the M-DRM of the market index. Therefore, investorsshould consider levering the fund by borrowing money and investing in thatparticular fund.

As the leverage factor is lower than one it implies that the M-DRM of thefund is greater than the M-DRM of the market index. Therefore, investorsshould consider un-levering the fund by selling out part of their holding in thefund and investing the proceeds in a risk-free security, such as a Treasury bills.

(4) The modified Treynor measureThe modified Treynor is computed by Equation (26):

TDi ¼

Ri � Rf

bDi

ð26Þ

where the MD-b is estimated by Equation (19).

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(5) The modified Jensen’s a measureAs described in Section (2.3), this paper estimates MD-a to propose themodified Jensen’s a measure by Equation (27):

yt ¼ l0 þ xtl1 þ e ð27Þ

where yt is defined as the dependent variable, yt¼min[(Dt�1þ (Rit�mit), 0)], xt

is as the independent variable, xt¼min[(Dt�1þ (RMt�mMt), 0)], which obtainsthe MD-b as the slope of the regression model as yt¼ l1 � xtþ et, wherebi

M�DRM¼ l1 and a¼ l0.(6) The modified IR

This study improves the ratio proposed by Pedersen and Rudholm (2003) usingEquation (13) by embedding the M-DRM instead of the conventional SD, andproposes a new measure, namely, the modified IR (IRD):

IRD ¼ rPPi

ð28Þ

(7) The modified MSRThis study extends the index proposed by Ferruz and Sarto (2004) byembedding the M-DRM into Equation (13) to propose a new measure, namely,the modified MSR index (MSRi

D):

MSRDi ¼

�ri=�rfPi

ð29Þ

(8) The modified fund’s performance indexThis study extends the index proposed by Pedersen and Rudholm (2003) onmutual funds and utilizes Equation (13) to propose a new measure, namely, themodified fund’s performance index (FPID):

FPID ¼ SRD

MSRD�100 ð30Þ

where SRD and MSRD are the modified Sharpe ratio and median modifiedSharpe ratio, respectively.

(9) The modified UPRThis study extends the index proposed by Sortino et al. (1999) on mutual fundsand uses Equation (13) to propose a new ratio, namely, the modified upsidepotential ratio (UPRD):

UPRDi ¼

PTt¼1¼ 1

Tðri � rf ÞPi

ð31Þ

2.4 The evidence of M-DRMThe majority of the previous performance measures are based on a risk measure,which evaluates the overall risk of an asset. However, the risk measurement mayfollow alternative approaches (i.e. Biglova et al., 2004; Ortobelli et al., 2005;Rachev et al., 2008) like the M-DRM.

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The M-DRM concept, which is theoretically different with downside risk, was firstintroduced by Grossman and Zhou (1993), and Dacorogna et al. (2001). Theyinvestigated two risk-adjusted performance measures for investors with risk-aversepreferences in the Sharpe measure and the maximum drawdown framework.Their measures were more robust vs clustering of losses and had the considerableability to fully characterize the dynamic behavior of investment strategies. Chekhlovet al. (2000, 2005) proposed a risk measure, namely, drawdown-at-risk, which includedthe maximum drawdown and average drawdown as its limiting cases to evaluatethe managed portfolios. They first showed that the portfolio allocation problem isefficiently solved by the DRM-based risk measures and then reported that the real-lifeasset-allocation problem is improved using these measures. Krokhmal et al. (2001) andthen Steiner (2011) compared risk management methodologies to optimize a portfolioof hedge funds based on the risk measures of conditional value-at-risk and conditionaldrawdown-at-risk. They found that a considerable advantage of the DRM-based riskmeasures is to implement robust and efficient portfolio allocation algorithms whichcan successfully manage optimization problems with thousands of instruments andscenarios. In an interesting study, Hamelink and Hoesli (2003) investigated the role ofreal estate in a mixed-asset portfolio when the maximum drawdown is utilized insteadof the SD. They showed that the maximum drawdown concept is one of the mostnatural measures of risk, and that such a framework can help reconcile the optimalallocations to real securities and the effective allocations by institutional investors.They found that most portfolios optimized by return-DRM in comparison with MVportfolios get a much lower maximum drawdown and a slightly higher SD.Their optimal allocations in the form of DRM measures had much more efficient incomparison with the MV-based allocations. Alexander and Alexandre (2006) using amaximum drawdown constraint, provided a characteristic of optimal portfolios in theMV framework. Gilli and Schumann (2009) investigated alternative specifications likepartial and conditional moment, quantile, and maximum drawdown as risk replacementmeasures to analyze the empirical performance of portfolios. Their findings showedthat these DRM-based alternative risk and performance measures in many cases arebetter than the MV approaches. Caporin and Lisi (2009) extended the M-DRM conceptsby enlarging the set of analyzed measures in the framework of this risk measure.They showed that when the number of assets is larger than the sample dimension, theMV approaches cannot be useful and should use the alternative DRM-based approach.Kim (2010) studied the circumstances, in which the M-DRM is related to a rationalinvestor’s choice of an investment portfolio. He showed that an investor facing extremeuncertainty makes a choice based on M-DRM. Finally, Schuhmacher and Eling (2011)asserted that M-DRM theoretically is as good as the Sharpe measure and can bereplaced with the MV approach.

However, it can be concluded that previous studies apply the M-DRM in optimizingthe MV and its relevant portfolios. To date, none of the studies extend the concepts ofthese risk measures on the risk-adjusted performance evaluation measures, such asthose used in this paper.

3. Empirical evidence and data3.1 DataThis study utilizes the monthly data of different categorizes of Malaysian mutualfunds. The data are extracted from the database of Bloomberg and considers all of thefunds that have an investment objective concentrated on mutual funds. The research

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sample excludes mutual funds: which are invested in specific sectors, which have aperformance guarantee, which have a limited duration, and which have continuousoperation without stopping during the research period. The research populationincludes the monthly returns adjusted by dividend from more than 700 Malaysianmutual funds for the 11-year period from first month of 2000 to the third month of 2011.We decompose the research time period based on two sub-periods – 2000 to 2005 as theOut-sample and 2006 to 2011 as the In-sample – to consider more samples for analysis.These detached sub-periods help to consider dead funds in each of the sub-classes andreduce the limitations related to survivorship bias. Another reason of the selection ofthe sub-periods is that, we consider one of the largest equity busts in the Malaysiafund market during the financial crisis 2007-2008; it means that we compare theperformance of mutual funds during a period almost without crisis (2000-2005)and a period under crisis (2006-2011). In such a framework, this paper considers 91out-sample funds and 359 in-sample funds based on sub-classes of management styles.The monthly return data for the 90-day Treasury bills as free risk rate, andthe Malaysian MSCI index and the Malaysian Standard and Poor’s (S&P) index asbenchmark indexes, and also the Kuala Lumpur Composite Index (KLCI), as marketindex, are extracted from the Bloomberg database.

3.2 Survivorship biasA feature in investigating many mutual funds is related to the comparison between theperformance evaluation of surviving and non-surviving mutual funds with evidencethat the surviving mutual funds outperform the non-surveying funds. The evidence ofElton et al. (1996) indicated that survivorship bias is larger in the small mutual fundsthan in the large mutual funds, as the small mutual funds having a high probability offolding. They determine the size of the survivorship bias for the US mutual fundsindustry as about 0.9 percent per annum, where the survivorship bias is defined andevaluated as average a for the surviving funds minus average a for the non-survivingfunds (The a is defined as the risk-adjusted return over the S&P 500).

In this study, 91 of the mutual funds out of sample (or 20 percent from the researchpopulation) and 359 of the in-sample funds (or 50 percent from the research population)are investigated as the research sample. Again, the long-run time period of 2000-2011 isconsidered to minimize the impact of survivorship bias and generalize the sampleresult to statistical population of this study. Table I reports the results of computingthe average a of the sub-sets of the surviving and non-surviving mutual funds.

Number of funds Average a

Out-sample between 2000 and 2005Survivors 91 0.276585Non-survivors 639 0.102416Difference – 0.174169In-sample between 2006 and 2011Survivors 359 0.216452Non-survivors 371 0.121031Difference – 0.095421

Note: This shows a comparison of average a between surviving and non-surviving mutual funds atthe statistical significance level of 5 percent

Table I.The descriptive result

of survivorship bias

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Surprisingly, this study finds that the sub-group of the surviving funds outperformsthe group of the non-surveying funds during the research period, as reported bya positive and significant average a of 0.276585 for the out-sample funds and a of0.216452 for in-sample funds (see Elton et al., 1996). For the non-surviving funds, theaverage as are 0.102416 and 0.121031 for out-sample and in-sample funds, respectively,which display low statistical significance. The differences between the average as forsurvivors and non-survivors are 0.174169 and 0.095421 for out-sample and in-samplefunds, respectively.

Table I shows a comparison of average a between surviving and non-survivingmutual funds at the statistical significance level of 5 percent.

3.3 Normality testSince the maximum drawdown risk measure is usually used under the asymmetriccondition, this paper investigates whether the majority of the research sample followsan asymmetric distribution. In this context, Table II shows that all of the managementstyles of the out-sample funds have positive skewness, while all of the in-sample fund’sstyles have a negative skewness except the market neutral style. The results of thekurtosis also indicate that six styles have leptokurtic distributions, while five styleshave a platikurtic distribution for out-sample funds. The kurtosis for in-samplestyles reports that two styles have leptokurtic distributions and other nine styles havea platikurtic distribution.

The results of the Jarque-Bera ( JB) test detects that the hypothesis of the normalityof returns dispersion is not accepted for nine out-sample styles while the other two out-sample styles show normal return dispersions at the significant level of 5 percent. Theresults of JB for in-sample styles show that all of the styles are rejected at the 5 percentlevel. Moreover, the results reveal that the Malaysian benchmark indexes areasymmetrical on the left and they have a leptokurtic distribution. The JB statisticrepresents that the hypothesis of the normality of returns distribution for the Malaysiabenchmark indexes, S&P, KLCI, and MSCI, are not normally distributed over theout-sample styles, except MSCI index at the 1 percent level. In addition, the JB test ofbenchmark indexes are not normally distributed over the in-sample styles, except theKLCI index at the 1 percent level. Thus, the asymmetrical nature of the researchsample confirms the fact that portfolio returns are not, in general, normally distributed(i.e. Arditti, 1971; Simkowitz and Beedles, 1978; Chunhachinda et al., 1997).Accordingly, the asymmetric returns of the considered funds actually reinforce thebenefits of this study.

3.4 Empirical resultsThe second step of the investigation consists of calculating the out-sample andin-sample periods for each of the considered styles. One statistic, which summarizesthe M-DRM performance of each style, and another risk statistic that summarizes therisk measures under each of the aforementioned definitions are reported in Table III.

The six considered risk measures are two for the conventional MVB framework(the conventional SD and b), two for the MSB framework (the semi-deviation and bD ),and two for the alternative MDB framework (the M-DRM and bM�DRM ). The evidenceof Table III reports that the null hypothesis for all of the out-sample styles is rejectedat the significant level of 5 percent. Moreover, the last row of the panels A and B of thetable reports the M-DRM of KLCI index with the numerical values of 0.156 and 0.126,respectively. The average of the b, downside b, and M-DRM values for the in-sample

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periods is larger than the out-sample periods which shows the financial crisis impactover the period. In addition, the higher magnitude of the drawdown risk of KLCI indexfor the in-sample periods is also another reason for undesirable effects of the crisis onthe risk levels. Another remarkable finding is that the DRM risk for the out-sampleperiod is lower than two other risk measures, except three sub-classes, while this riskfor the in-sample periods is larger than others. It may be because the M-DRM usuallyconsiders the loss maximum to compute the risk, thus when computing this risk undercrisis condition (which usually faces more loss), the risk levels show higher magnitude.It implies that the M-DRMs in the crisis condition are more compatible to aggressive(risk-loving) investors.

A correlation matrix concerning six risk measures is reported in Table IV andexplains a significant correlation in more detail. As reported in panels A and B of the

Management stylesNo.

fundsMeanreturn SD Skewness Kurtosis

Jarque-Bera( JB) p-value

Panel A: Out-sample (2000-2005)Blend 12 �1.36e-16 0.078893 0.234401 1.860808 3.857065 0.145361Contrarian 10 �1.27e-16 0.037001 1.959162 6.793252 75.59429 0.000000Emerging markets 12 �7.12e-17 0.031928 0.115527 2.130430 2.057575 0.357440Equity income 8 �1.46e-16 0.070509 0.699319 3.770618 6.481348 0.039138Geographicallyfocused 14 �2.26e-17 0.060368 0.546678 3.344721 3.340407 0.188209Growth 6 �1.16e-16 0.081047 0.053030 2.207792 1.623724 0.444030Growth and income 8 �1.17e-16 0.066136 0.638754 3.466558 4.701326 0.095306Index fund 7 �2.14e-17 0.095624 0.260904 2.230611 2.196617 0.333435Long-short 6 �7.14e-17 0.056022 0.502335 3.061397 2.575039 0.275954Market neutral 4 �2.32e-17 0.082442 0.181464 2.062873 2.566892 0.277081Value 5 �7.48e-17 0.064537 0.281942 2.814631 0.895496 0.639066KLCI index – 0.004286 0.057887 0.209327 4.372040 5.230148 0.073162MSCI index – 0.000285 0.050806 �0.460383 4.358167 6.843250 0.032659S&P index – 0.004542 0.061938 0.161278 2.693170 0.503726 0.777351Panel B: In-sample (2006-2011)Blend 69 �4.83e-17 0.098246 �0.264090 2.220180 2.291658 0.317960Contrarian 59 �2.42e-17 0.042559 �0.136949 2.133586 2.133041 0.344204Emerging markets 42 �7.48e-17 0.055803 �0.163198 1.662179 4.898772 0.086347Equity income 30 9.31e-17 0.064392 �0.101275 1.759895 4.078794 0.130107Geographicallyfocused 35 3.31e-17 0.106848 �0.237102 1.670775 5.145249 0.076335Growth 40 9.40e-17 0.102578 �0.117450 1.750245 4.177420 0.123847Growth and income 41 1.26e-16 0.113552 �0.155535 1.723548 4.459073 0.107578Index fund 15 3.58e-17 0.072490 �0.082933 1.978322 2.767621 0.250622Long-short 10 4.70e-17 0.078684 �0.444390 2.701098 2.271448 0.321189Market neutral 9 4.23e-17 0.054885 0.174913 2.874666 0.356726 0.836639Value 9 1.51e-18 0.041068 �0.222468 2.802542 0.612140 0.736335KLCI index – 0.009928 0.050623 �0.612932 4.064030 6.806832 0.033259MSCI index – 0.007570 0.067862 �0.560985 3.410854 3.688016 0.158182S&P index – 0.010953 0.046707 �0.315015 3.359708 1.359677 0.506699

Notes: The Jarque-Bera ( JB) is estimated as JB¼N [s2/6þ (k�3)2/24], where s, k, N are the value ofskewness, the value of kurtosis, and the number of data applied for the test, respectively. The JB testuses a w2-distribution with two degrees of freedom

Table II.Descriptive statistics

of normality test

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table, the drawdown risk measures (the M-DRM and the drawdown b) outperform theconventional risk measures (the SD, b, and downside risks).

To compare the risk measures, Figure 1 displays the risks dispersion generated bythe M-DRM, the conventional SD, and the downside risk.

The theoretical quantile-quantile (QQ) plot is utilized to investigate whether thedata in a single series follow a specified theoretical distribution; e.g. whether the dataare normally distributed (Chambers et al., 1983; Cleveland, 1994). Figure 1 displays thatthe M-DRM has a closer distribution than two other risk measures to the QQ plot,which shows this statistic has a better data distribution in comparison with others.

More specifically, detailed analysis concerning the relationship between risk andexpected return across funds can be concluded by regression analysis. This study runsa cross-sectional simple linear regression model to investigate the relationship betweenmean returns with each of the six considered risk variables. Equation (32) is run forthis mean:

MRi ¼ g0 þ g1RMi þ ui ð32Þ

Statistics of the bM�DRM

Management styles M-DRM SD DR b bD bM�DRM t-statistic R2 p-value

Panel A: Out-sample (2000-2005)Blend 0.101 0.033 0.029 0.50 0.47 0.28 10.90 0.82 0.000Contrarian 0.065 0.029 0.028 0.25 0.23 0.13 5.93 0.68 0.000Emerging markets 0.069 0.028 0.027 0.35 0.34 0.23 14.01 0.75 0.000Equity income 0.121 0.042 0.035 0.61 0.48 0.47 25.59 0.65 0.000Geographically focused 0.113 0.041 0.035 0.65 0.63 0.58 28.24 0.48 0.000Growth 0.113 0.037 0.031 0.58 0.62 0.43 10.93 0.53 0.000Growth and income 0.114 0.044 0.036 0.64 0.61 0.51 21.29 0.48 0.000Index fund 0.122 0.043 0.034 0.63 0.60 0.70 32.05 0.70 0.000Long-short 0.114 0.040 0.034 0.63 0.67 0.80 27.37 0.67 0.000Market neutral 0.110 0.041 0.034 0.50 0.56 0.89 10.95 0.33 0.000Value 0.114 0.043 0.035 0.64 0.63 0.96 70.68 0.92 0.000Average 0.11 0.04 0.03 0.54 0.53 0.54Drawdown risk of KLCI index 0.126Panel B: In-sample (2006-2011)Blend 0.051 0.025 0.024 0.64 0.59 0.50 9.44 0.90 0.000Contrarian 0.043 0.026 0.026 0.19 0.21 0.83 123.19 0.87 0.000Emerging markets 0.060 0.027 0.026 0.34 0.36 0.84 101.25 0.85 0.000Equity income 0.068 0.027 0.026 0.58 0.52 0.67 11.52 0.81 0.000Geographically focused 0.086 0.031 0.026 0.53 0.55 0.86 87.11 0.89 0.000Growth 0.094 0.031 0.026 0.86 0.83 0.91 8.34 0.97 0.000Growth and income 0.102 0.034 0.028 0.63 0.63 0.89 101.06 0.92 0.000Index fund 0.132 0.042 0.032 0.57 0.62 1.11 2.14 0.97 0.032Long-short 0.117 0.035 0.030 0.61 0.59 0.91 49.29 0.89 0.000Market neutral 0.214 0.075 0.050 0.56 0.58 0.95 50.12 0.90 0.000Value 0.118 0.049 0.041 0.68 0.65 0.84 41.26 0.86 0.000Average 0.10 0.04 0.03 0.56 0.56 0.85Drawdown risk of KLCI index 0.156

Notes: M-DRM, Maximum drawdown risk; SD, standard deviation; DR, downside risk;b, conventional b; bD , downside b; bM�DRM , the b estimated by the M-DRM

Table III.The results of computedrisk measure

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where MRi, RMi, g0, g1, ui, and i are mean return, risk measure, a constant, regressioncoefficient, an error term, and funds (styles), respectively. The regression results of thesix models (one for each of the six considered risk measures) are reported in panels Aand B of Table V.

Panel A displays the result of OLS linear regressions out of sample and panel B alsodisplays the results of OLS regressions for the in-sample styles. The evidence showsthe same results in both panels, in which all six considered risk measures are explicitlysignificant due to differentiation in their explanatory power. In addition, Table Vdetects that M-DRM outperforms the conventional SD and semi-SD (D-SD) due to its

MEAN SD SEMI DRM b D-b DD-b

Panel A: Out-sample (2000-2005)MEAN 1SD �0.75 1SEMI �0.95 0.91 1M-DRM �0.21 0.06 0.16 1b �0.19 0.09 0.16 0.53 1D-b �0.26 0.19 0.24 0.19 0.32 1DD-b 0.03 �0.12 �0.07 0.05 0 0.32 1Panel B: In-sample (2006-2011)MEAN 1SD �0.83 1SEMI �0.96 0.95 1M-DRM �0.05 0.09 0.06 1b �0.03 0.01 0.02 0.10 1D-b �0.60 0.59 0.63 �0.15 �0.04 1DD-b 0.12 �0.07 �0.09 �0.13 �0.02 �0.07 1

Notes: M-DRM, maximum drawdown risk; SD, standard deviation; SEMI, downside risk(semi-standard deviation; b, conventional systematic risk; D-b, downside systematic risk; DD-b,maximum drawdown risk systematic

Table IV.Correlation matrix

of full sample

–0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Quantiles of OD

Qua

ntile

s of

Nor

mal

OptimizedDrawward Risk

–0.2

0.0

0.2

0.4

0.6

0.0 0.2 0.4 0.6 0.8

Quantiles of SD

Qua

ntile

s of

Nor

mal

Standard Deviation

0.35

0.40

0.45

0.50

0.55

0.60

0.40

0.45

0.50

0.55

0.60

0.65

0.70

Quantiles of DSD

Qua

ntile

s of

Nor

mal

Downside Risk

Figure 1.Volatility around

quantiles of normal

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explanatory power. The significant coefficient of the M-DRM and its relevant b in theout-sample funds is greater than the other risk measures. This superiority can alsobe found in the in-sample funds, where two measures of M-DRM and its relevant bhave significant coefficients equivalent to 0.47 and 0.53, respectively. These values aregreater than the conventional measures, which implicate the superiority of the twoproposed measures, the M-DRM and its b, in comparison with the conventional ones.

3.5 Funds rank using the modified measuresAs a brief conclusion at this point, the results discussed and reported reveal twoconsiderable findings in which, when comparing the M-DRM and MD-b with theconventional SD and b, the M-DRM outperforms the conventional SD and alsosemi-SD; the risk measure that best describes the relationship between the expectedreturn and market return is the MD-b.

Panel A of Table VI reports details of the rank for the whole sample, in which nineconventional measures are modified using the M-DRM to compare and rank each of themutual funds together with respect to the two benchmark indexes of Malaysian S&Pand MSCI. The highest modified Sortino measure for the whole sample belongs toContrarian with the numerical value of 8.61. The evidence shows that the ranking offive measures of Treynor, M2, IR, MSR, and FPI is also similar to the rank of Sortinomeasure in which Contrarian dominates the other styles. The highest numerical valueof the modified Jensen’s a measure over the whole sample is associated with the marketneutral style with a numerical value of 0.36. Among the management styles of mutualfunds, the rank of S&P index over the whole sample of the modified measures is 13thfor four measures of Treynor, M2, IR, and FPI, while the rank for the two measuresof Sortino and MSR is 12th, and for the Jensen’s a and URP measures is fourth andninth, respectively. Among the management styles of mutual funds, the rank of MSCIindex over the sample of the modified measures is 11th for three measures of Treynor,M2, and URP, while the rank for other five measures is 13th, 12th, and second.

MRi¼ g0þ g1RMiþ ui,MV g0 t-statistics g1 t-statistics R2 Adj-R2

Panel A: Out-sample (2000-2005)SD 0.040 45.43 �1.06 �54.42 0.34 0.34b 0.0002 0.36 �0.22 �1.81 0.0005 0.0004D-SD 0.031 62.67 �11.18 �84.66 0.46 0.46bD 0.004 7.08 �0.121 �15.55 0.041 0.041M-DRM 0.020 12.19 �0.11 �12.66 0.59 0.58bM�DRM 0.036 11.38 �0.051 �11.37 0.62 0.61Panel B: In-sample (2006-2011)SD 0.018 0.58 �0.59 �7.68 0.36 0.35b 0.010 3.51 �0.11 �4.81 0.14 0.14D-SD 0.021 0.68 �0.27 �4.17 0.10 0.10bD 0.022 8.01 �0.102 �12.55 0.19 0.18M-DRM 0.025 4.21 �0.14 �6.29 0.47 0.47bM�DRM 0.033 10.26 �0.064 �10.21 0.54 0.53

Notes: MR, mean return; SD, conventional standard deviation; b, conventional b; D-SD, semi-standarddeviation; bD, downside b; M-DRM, maximum drawdown risk measure; bM�DRM, maximumdrawdown b

Table V.Simple regression analysisupon full sample

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(con

tinu

ed)

Table VI.Rank of the modified

measures in the M-DRMframework

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Mea

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Table VI.

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Panels B and C of Table VI report details of rank for the out-sample and in-sampleperiod. The panels display the numerical values of these nine modified measures,where five modified measures of Sortino, M2, IR, MSR, and FPI have same rank witheach other. Similar to the whole sample, the highest modified Sortino measure for theout-sample and in-sample period belongs to Contrarian with the numerical value of4.26 and 18.96, respectively. The evidence shows that the in-sample periods under-perform the out-sample periods. In addition, the ranking of five measures of Treynor,M2, IR, MSR, and FPI is also similar to the rank of Sortino measure in which Contrariandominates the other styles and also the in-sample period under-performs the out-sample one. The highest numerical value of the modified Jensen’s a measure over theout-sample period is associated with the value style with a numerical value of �0.01,while this rank for the in-sample periods is related to the index fund style.

Among the management styles of mutual funds, the rank of S&P index over theout-sample period of the modified measures is 12th for six measures of Sortino,Treynor, M2, IR, MSR, and FPI, while the rank for the two measures of Jensen’s a andURP is second and first, respectively. The rank of this index is different over the in-sample periods in which it is second for Sortino, Treynor, M2, Jensen’s a, IR, MSR, andFPI. UPR is in first rank for this index. This is another reason which the in-sampleperiods, due to the existence of financial crisis, under-perform the out-sample ones.

Among the management styles of mutual funds, the rank of MSCI index over theout-sample period of the modified measures is 13th for six measures of Sortino,Treynor, M2, IR, MSR, and FPI, while the rank for two measures of Jensen’s a andURP is first. The rank of this index is different over the in-sample period in which it isseventh, for five measures of Sortino, M2, IR, MSR, and FPI. This index for Treynor,Jensen’s a, and UPR is 11th, 9th, and 1st, respectively. The better rank of the out-samplefunds than the benchmark indexes indicates the better performance of the funds ratherthan the in-sample ones.

As reported in panel B of Table VI, four out-sample styles of contrarian, emergingmarkets, equity income, and value have a modified leverage factor greater than one.This implies that the M-DRM of the fund is less than the M-DRM of the market index.Therefore, investors should consider levering the fund by borrowing money andinvesting in the certain fund. This implication can also be followed by the six in-samplestyles of contrarian, emerging markets, geographically focussed, growth and income,long-short, and index fund in panel C of the table. It means that we experience morevolatilities of the funds return below the market index over the crisis period (in-sampleperiod), thus it is natural which a more number of the sub-classes follow a leveringpolicy in the in-sample periods rather than the out-sample ones.

The majority of the styles in the in-sample period underperform the selectedbenchmarks, as reported in panel C of table. In contrast, all of the styles in the out-sample period over-perform the benchmarks. This again shows the inappropriateeffect of financial crisis in funds’ performance over the in-sample period.

In addition, seven out-sample styles – index fund, growth, market neutral, blend,growth and income, long-short, geographically focussed – of the mutual funds have amodified leverage factor lower than one. This means that the M-DRM of the fund isgreater than the M-DRM of the market index. Therefore, it implies that investorsshould consider un-levering the fund by selling out part of holding in the fund andinvesting the proceeds in a risk-free security such as a Treasury bill. This implicationcan also be applied for the in-sample styles of blend, growth, equity income, marketneutral, and value in panel C of Table VI.

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3.6 A final digression: why do the M-DRM and its relevant b work?The superiority of the M-DRM and MD-b upon conventional measures of SD, semi-SD,b, and downside b in evaluating the performance of Malaysian mutual funds can be asomewhat attractive result to some. In this section, we provide an attempt todescribe and justify empirically the plausibility of this finding. First, as describedabove, a certain fund manager does not dislike volatility per se; rather he only dislikesdrawdown volatility. He does not shy away from funds that explain large andconsiderable jumps greater than the mean; he shys away from funds that explainfrequent and large jumps less than the mean.

In fact, investors are not worried about getting greater than their minimumacceptable return; rather they are worried about getting lower than their minimumacceptable return. Moreover, aversion to the M-DRM is compatible to both the theoryand results in the literature of finance. Finally, the superiority of M-DRM and MD-b canbe associated with the contagion impacts in fund markets. Note that in theconventional MV framework, the suitable measure of risk is the conventional bwhen markets are integrated, and the conventional SD when markets are segmented.The superiority of the MD-b can then be described by the fact that markets are moreintegrated upon the M-DRM than upon the upside returns due to the contagionimpacts, something that data upon most markets seem to propose.

4. ConclusionThe conventional SD, b, semi-variance, downside b and their behavioral model(MVB and MSB) have been extensively utilized but also extensively debated over thepast 40 years. Most of the debates against conventional risk measures haveconcentrated on whether these measures evaluate more appropriately the performanceof mutual funds. This study reports and provides evidence that the data supports theM-DRM and MD-b upon conventional risk measures. In this paper, we have generateda parallel between the conventional framework in terms of MVB, MSB, b, downside b,CAPM, and D-CAPM and a replacement framework in terms of the M-DRM; that is,upon MDB, MD-b, and the alternative model based on it. Moreover, we have proposedthe appropriate method to estimate and test the MD-b and a, the measure of risksuggested in this study, and how to extend it into the replacement pricing modelsuggested in this paper to replace the CAPM.

The evidence described supports the M-DRM upon the conventional risk measures,and, in particular, the MD-b. The empirical evidence also indicates that mean returnsare much more sensitive to differences in MD-b than to equal differences in theconventional and downside b.

More specifically, this study improves and provides suggestions for therisk-adjusted performance measures of the management styles of Malaysia mutualfunds. The appraisals are based on the modified performance measures grounded inthe modern portfolio theory. Using the MDB framework, this study modified ninemeasures of Sortino, Treynor, M2, Jensen’s a, IR, MSR, UPR, FPI, and leverage factordeveloped by Treynor (1965), Jensen (1968), Sortino and Price (1994), Modigliani andModigliani (1997), Sortino et al. (1999), Pedersen and Rudholm (2003), and Ferruzand Sarto (2004). The evidence shows that the in-sample periods under-perform theout-sample ones, because the in-sample funds’ (styles’) performance were reported aslower than the performance of the benchmark indexes which is due to inappropriateeffects of recent financial crisis. It also develops some implications based on themodified leverage factor to invest in the funds.

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Finally, this paper questions the deficient frameworks in terms of MVB, MSB, b,downside b, CAPM, and D-CAPM and suggests replacing them with a replacementand more efficient framework in terms of MDB, the MD-b, and the maximumdrawdown CAPM.

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Corresponding authorMohammad Reza Tavakoli Baghdadabad can be contacted at: [email protected]

To purchase reprints of this article please e-mail: [email protected] visit our web site for further details: www.emeraldinsight.com/reprints

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This article has been cited by:

1. Mohammad Reza Tavakoli Baghdadabad. 2014. Average drawdown risk reduction and risk tolerances.Research in Economics . [CrossRef]

2. Mohammad Reza Tavakoli Baghdadabad. 2014. Traditional beta, average drawdown beta and market riskpremium. Journal of Asset Management . [CrossRef]

3. Mohammad Reza Tavakoli Baghdadabad, Paskalis Glabadanidis. 2014. An extensile method on thearbitrage pricing theory based on downside risk (D-APT). International Journal of Managerial Finance10:1, 54-72. [Abstract] [Full Text] [PDF]

4. Mohammad Reza Tavakoli Baghdadabad, Paskalis Glabadanidis. 2013. Average Drawdown Risk and CapitalAsset Pricing. Review of Pacific Basin Financial Markets and Policies 1350028. [CrossRef]

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