Overview
This work focuses on the calculation of fair profit-sharing ratios and the expected payoffs at maturity for partners involved in Islamic investment contracts. These contracts, specifically mudarabah and musharakah, are based on profit and loss-sharing (PL-sharing) principles. The study establishes a method for determining these quantities, drawing a comparison between these Islamic financial instruments and conventional finance arrangements such as limited partnerships and joint ventures.
Research Context
Islamic investment contracts, including mudarabah and musharakah, operate on a profit and loss-sharing framework. The research notes their functional comparison to types of ventures found in conventional finance, such as joint-stock companies and partnerships. The objective is to define a methodology for equitable profit distribution within these specific contractual structures.
Approach
To compute fair profit-sharing ratios and expected payoffs, the research introduces the concept of c-fair profit-sharing ratios, denoted by $c = (c_1, \ldots,c_d) \in (\mathbb R^{\star})^d$, where $d$ represents the number of partners. This constitutes an equilibrium approach designed to account for the contributions made by contracting parties in terms of both capital and labor. The method extends to mixed contracts which incorporate one or both of the aforementioned Islamic contracts with an agency contract (known as wakalah).
Findings
- The $c$-fair profit-sharing ratio for each partner is determined to be the sum of their individual contributions to capital and labor.
- These contributions are weighted by identified economic factors: investment risk and opportunity.
- In the $c$-fair model, the expected investment profit is distributed among contract partners according to shares $\varpi_{\ell} = c_{\ell} \, / \, (c_1 + \ldots + c_d)$.
- These shares correspond to the partners' respective contribution weights to the venture's overall success.
- The results are extended to apply to mixed contracts that combine mudarabah or musharakah, or both, with a wakalah (agency) contract.