For deciding on which performance evaluation measures will be more appropriate to be used for investigating the funds' performance, Fama and French (1993) three-factor model is used as follows:
Corporate Ownership & Control / Volume 13, Issue 4, Summer 2016
 Rpt -Rft = ?The index is constructed to include stocks from selected listed companies in the Gulf Cooperation Council region Source www.globalinv.net.The alpha of Mamoghli and Daboussi
A third performance measure, in the downside framework that is similar to the Jensen alpha, utilizing Estrada's beta, was presented by Mamoghli and Daboussi (2008) as follows:

?DP (RP -RF -?DP(RM -RF)

The adjusted Jensen alpha based on the Estrada downside beta calculates the return of the portfolio in excess of its required rate of return calculated according to the D-CAPM of Estrada 2002.For evaluating the funds' performance, the methodology based on the classical CAPM model along with its based performance evaluation measures are applied as follows:
Treynor's coefficient Reward-to-Volatility or RVOL is used to measure the excess return of a fund, over the risk free rate, per unit of systematic risk as suggested by Treynor (1965).Survivorship bias was cited in literature as in Brown et al. (1992) and Otten and Bams (2004) highlighting the fact that if funds which are unable to survive for the whole sample period are eliminated from the sample, the performance measurement can be upwardly biased.The Sortino ratio: Sortino and Price (1994) ratio is presented as follows:

SOR=RP-RF /?DP

where
RP is the portfolio's return, RF is the risk-free rate which here represents the minimum acceptable return or MAR and ?DP of the portfolio returns.The latter part of the study explores the aggregate performance by forming two fund portfolios; one representing the average Islamic mutual fund and the other is the average conventional fund, to examine the performance of the Islamic mutual funds portfolio compared to its conventional peers and to the overall market.In this framework, Estrada downside beta with respect to the risk free rate is determined as follows:

Estrada
?Di= ?T, t=1[Min(RPt - RFt ),0}*[Min(RMt - RFt ,0]/
[Min(RMt - RFt ),0]^2

Then, three performance measures in the downside risk framework are applied.It is an all share absolute market capitalization index that does not include dividends www.tadawul.com.sa and the GCCI Islamic index, issued by Global Investment House Company; a well- recognized investment company located in Kuwait.Our choice of portfolio evaluation measures generalises the studies of Grinblatt and Titman (1989) and Mansor and Bhatti (2011) by including a wider set of measures.As presented in Estrada (2002, 2007), in the alternative mean semi- variance framework, the investor's utility will depend on the downside variance of returns semi-variance of the investor's portfolio.Quarterly rate of returns of individual stocks were manually copied from the Saudi exchange official website as prior to 2006, quarterly data was unavailable.Sharpe ratio Reward-to-Variability: As suggested by Sharpe (1966), measures the average excess returns of a fund, over the average risk free rate, per unit of total risk of the fund

sharpe=Ri-Rf/?var(Ri-Rf)=Ri-Rf/?The index of Mishra and Rahman
Similar to the Treynor ratio but only replacing traditional beta by the downside beta was presented.Then, for the Saudi funds data: out of 240 mutual funds dominated in different currencies and with different objectives, only 21 equity funds, 10 Islamic and 11 conventional equity funds, dominated in local currency, in existence from June 2005 were chosen.p +?0p(Rmt -Rft)+?1pSMBt +?2pHMLt +ept (1)
where:

* Rpt -R ft is the average excess return of the fund p .The CAPM is given by:

E(Ri)=Rf +?(E(Rm-Rf))

Where ERi is the expected return on the asset; Rf the risk-free rate; ERm-Rf the market premium; ?The new ratio is written as follows:

MR=RP-RF /?DP

where 

RP is the return of portfolio, RF is the risk-free rate
 where
and ?DP is the downside beta.by Mishra and Rahman (2002) in Mamoghli and Daboussi (2008).