Dear Toumi Kaother.

I found a few articles that may provide some answers to your question.

Regards.

http://www.emeraldinsight.com/doi/abs/10.1108/08288660810876831

http://jibfnet.com/journals/jibf/Vol_2_No_1_March_2014/11.pdf

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1961660

http://www.kantakji.com/media/3072/v119.pdf

thanks a lot dear Moh Halim Kadri!

In my view, one way to answer your question is to think of a portfolio of Islamic financial product that is independent from the market equity portfolio and replace its return in  place of the risk free rate return in the standard CAPM formula.

You can use Islamic market index for market portfolio and Islamic treasury sukuk for risk free rate.

Thanks dear yasser..I have already used this method in one of my papers

But with regard to the answer given by Yaser, I do not think the Islamic treasury sukuk is a risk free portfolio, as a result it can not just be replaced in the place of the risk free rate in CAPM.

Thanks Dear Mo Sherif..I'm surprised as for using of zakat as a proxy for risk free rate..

Zakat is not a return from investment financing, it is a charity donation to  specific group in the society.

I know..but why is used as a proxy for risk free ..i will read about that

In reality, there is no 'risk free rate'. The rate of return on US Treasuries is used as a proxy. In Islamic finance, the rate of return on AAA-rated Sukuk (e.g. IsDB) could equally be used as a proxy. 

Thank you Prof Simon Archer for sharing your nice answer!  I was also looking for the answer of this question!

thanks prof. Archer.

Hello and good time

I’ve invented a new and sophisticated asset pricing model based on Islamic criteria titled ”SPFO” and I’ve proposed it to government for crude oil pre-sale via Sukuk.

You can find it in my page.

Risk and Returns of Sharīʿah Compliant Stocks on the Karachi Stock Exchange – A CAPM and SCAPM approach

📷SourceRisk and Return Under Sharia Framework: An Attempt to Develop Sharia Compliant Asset Pricing Model-SCAPM