In a paper Sovereign Wealth - No Fund: The Decisive Role of Domestic Veto Players, Bernhard Reinsberg offers an explanation in political economy for the lack of an SWF in India. Here is the abstract:
Sovereign Wealth Funds (SWFs), government-owned investment funds, are of growing importance in international finance. They are a vehicle to manage foreign exchange reserves and wealth which have been accumulating in the emerging world, particularly in the BRICs. However, while China and Russia set up SWFs over the last decade, India and Brazil still lack such funds. In analysing thoroughly the Indian case, this paper seeks to contribute to recent literature on the determinants of SWFs with two main findings: First, it confirms conventional economic theory which shows the requirement of excessive foreign reserves for the set-up of SWFs. Second, it suggests that political systems matter, as demonstrated by the lively debate in India on whether that country should have such a fund. In this way, influential societal actors, in particular the central bank and regulating agencies as well as business associations, have dominated the public discourse and successfully lobbied the government to waive initial plans in support of an alternative wealth management scheme.