This is the most depressing time to do research. This is the most exciting time to do research.Many academics complain that the current environment is not conducive to fundamental research. This is the most depressing time to do research. At the same time, this is the most exciting time to do research. Because of the stifling academic and social environment, few are wiling to touch fundamental problems. Great many of important problems are left unresolved. Anyone who want to accomplish great research works can actually accomplish great research works. 
Recent years, I have been working on the foundation of finance theory. The foundation of mainstream finance theory is quite simple. Finance roughly consists of two parts, invest theory and corporate finance.  Investment theory is established on two papers, Markowitz’s 1952 paper on portfolio and Sharpe’s 1964 paper on CAPM. Corporate finance is even simpler. It is established on the single paper by Modigliani and Miller in 1958, which is often referred as MM. 

The MM paper stated that company value is independent of financing structure. The proportion of debt and equity doesn’t affect company value. They proved the case when the expected return on investment is constant to perpetuity. But the statement of irrelevance of financing structure is applied to general cases in the textbooks and literature. Miller also provide an argument for general cases. It is the conservation of risk. No matter how one distributes risk, the total risk is conserved. The financing structure doesn’t affect company values.

In reality, financing structures do affect company values. This is often attributed to “market imperfection”. 

I read MM paper about twenty years ago. One can’t help but notice that MM proved only a very special case mathematically. I was busy developing my own theory. I didn’t have much time. But I have to teach MM theory again and again. I was feeling increasingly uncomfortable teaching something that I am not sure. Finally I sat down to do the math work. It shows that when the cashflows become more general, MM’s statement is no more valid. 

In other words, the differences of valuation of investments are not due to “market imperfection”, but due to theory imperfection. 

I also wrote a paper on CAPM. The empirical record of CAPM is very poor. Many revisions have been proposed, mostly empirically motivated. I was thinking if CAPM has any theoretical flaws. In CAPM, it is assumed that investors maximize their utilities. I construct a simple investment world where people maximize their utility. I derive the return distributions of assets from utility theory. They are different from CAPM predictions and they are more consistent with empirical data.

This shows that the mismatch between CAPM and empirical data is due to imperfect theory, not “imperfect market”. 

I have somewhat retreated from my earlier research. I try to do research in the framework of the mainstream theory. I discuss the papers that mainstream academics are most familiar with. I don’t use any new knowledge or ideas. I am not developing a new theory. I simply extend the mathematical derivation to a more general case or derive concrete results mathematically from the theoretical foundations people all agree with. I show that the foundations of the mainstream theory are internally inconsistent. Hopefully these results would have easier reception. Some related papers:

The Scope of Validity of Modigliani and Miller Propositions, Working paper 

On the Inconsistency between CAPM and the Utility Theory, Working paper