In this article, I propose an extension of the Treynor-Black model to a case where the investor is not fully invested in the stock market at the outset and there is no need to explicitly specify securities' expected returns. I derive explicit tangent portfolio weights based on a factor model of...

I propose a novel investment objective for portfolios fully invested in risky assets only. The new objective is based on achieving the highest possible excess return per unit of variance. The optimal portfolio is a linear combination of the tangent portfolio and the minimum variance portfolio...

We examine how extreme market risks are priced in the cross-section of asset returns at various horizons. Based on the decomposition of covariance between indicator functions capturing fluctuations of different parts of return distributions over various frequencies, we define a \textit{quantile...

This paper suggests incorporating investor probability weighting and the default risk of individual firms into a consumption-based asset pricing model. The extended model provides a unified solution for several anomalous patterns observed on financial markets. The analysis addresses not only...

In the finance literature, a common practice is to create characteristic portfolios by sorting on characteristics associated with average returns. We show that the resulting portfolios are likely to capture not only the priced risk associated with the characteristic, but also unpriced risk. We...

This study documents annual returns of the invested global multi-asset market portfolio, using a newly constructed unique dataset which basically covers the whole invested market. We analyze returns as well as risk over the period from 1960 to 2017. The market realizes a compounded real return...

We derive the equilibrium asset expected returns when there is ambiguity in asset expected returns, as well as ambiguity in asset return variances. In our model, ambiguity risk is systematic in nature and is non-diversifiable. Under regularity conditions, expected asset returns are linearly...