لخّصلي

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 = α p +β0p(Rmt -Rft)+β1pSMBt +β2pHMLt +ept (1)
where:

• Rpt -R ft is the average excess return of the fund p .


• SMB is the difference in return between a small cap portfolio and a large cap portfolio and


• HML is the difference in return between a portfolio of high book-to-market ratio and a portfolio of low book-to-market ratio.
  Given the complexity of the issues involved, it is not surprising that there is no single universally accepted asset pricing model, but there is a wide choice of models each with its own merits. 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.

The CAPM is given by:

E(Ri)=Rf +β(E(Rm-Rf))

Where ERi is the expected return on the asset; Rf the risk-free rate; ERm-Rf the market premium; β is the sensitivity of asset returns to market returns.

E(Ri)=Rf +β−(E(Rm-Rf))

Where

β−=Σ T,t=1 [min(Ri,t-Rf,t),0]*[min(Rm,t-Rf,t),0]/ Σ T,t [min(Rm-Rf,t,0)]^2

Contrary to the CAPM that uses variance to measure risk, the D-CAPM uses the semi-variance. Therefore the D-CAPM penalizes the downside return potential of the asset.
In both the CAPM and the D-CAPM the beta and downside-beta may be estimated with a regression of the asset’s excess return on the market’s excess return. A restriction is applied for the D-CAPM case so that market excess return is only taken into account if it falls below its mean value.

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).

Treynor Ratio =(RP-RF)/ βp

where (RP -RF )is the average excess return and βp is the fund’s beta.

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/σ

(RP - RF ) is the average excess return and σ is the total volatility of the fund.

Jensen’s Alpha: Measures the Funds’ excess returns, over and above those of the benchmark. The alpha measure as suggested by Jensen 1968 is:

Jensen's α = RP -RF -βp(RM -RF)

where
α is the fund excess returns over and above those of the benchmark, RP is the average return of the fund over the measurement period, βP is the sensitivity of the fund excess returns, over the risk free rate, to the excess returns of the benchmark and RM is the average market return over the measurement period.
The second part of the study then applies the capital asset pricing model in the downsid framework. 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. In this framework, Estrada downside beta with respect to the risk free rate is determined as follows:

Estrada
βDi= ΣT, 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.

The Sortino ratio: Sortino and Price (1994) ratio is presented as follows:

SOR=RP-RF /σDP

where
RP is the portfolio’s return, RF is the risk-free rate which here represents the minimum acceptable return or MAR and σDP of the portfolio returns.

The index of Mishra and Rahman
Similar to the Treynor ratio but only replacing traditional beta by the downside beta was presented.

by Mishra and Rahman (2002) in Mamoghli and Daboussi (2008). The new ratio is written as follows:

MR=RP-RF /βDP

where

RP is the return of portfolio, RF is the risk-free rate
where
and βDP is the downside beta.

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:

αDP (RP -RF -βDP(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.
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. Only TASI local all share index is used in these tests. GCCI index was excluded because of its zero values for the coefficient of determination.
The research data is a unique data set. First, for the construction of Fama and French three- factor model, the variables were calculated based on the data of companies listed on the Saudi stock exchange for the period from December 2006 to September 2011. Out of 156 Saudi listed companies only 89 were included in the construction of the benchmarks. Quarterly rate of returns of individual stocks were manually copied from the Saudi exchange official website as prior to 2006, quarterly data was unavailable. Book values and market capitalization values for the selected companies were manually copied from the quarterly reports issued on the official Saudi exchange website for the entire sample period. Quarterly data were used since many of the data values were not available on monthly basis.
All of the stocks on December 2006 are ranked on size and split into two groups small and big. Then all the stocks are also ranked on the basis of book to market ratio and broken into three groups 30% each for high and low and 40% medium, resulting in six value-weighted portfolios S/L, S/M, S/H, B/L, B/M, B/H. The SML variable is constructed by the average of 3 small cap stock portfolios minus the average of 3 big cap stock portfolios. The HML is the average of the two high book to market stock portfolios minus the average of the two low book to market stock portfolios.
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. Monthly net asset values were collected from Bakheet Investment Company a service for a fee. Missing monthly net asset values were collected manually from the interactive chart available on the official Saudi exchange website.
Two indices are used: The Saudi Tadawul all- share index. 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. The index is constructed to include stocks from selected listed companies in the Gulf Cooperation Council region Source www.globalinv.net.
The risk free rate is taken to be the 1-month Saudi interbank offered rate SIBOR, obtained from the National commercial Bank. 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. This data set is not subjected to survivorship bias, since no open-end mutual fund dropped out of sample.