Essays on Risk Measurement and Fund Separation

Download or read book Essays on Risk Measurement and Fund Separation written by Fang Liu and published by . This book was released on 2015 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1 extends Cass and Stiglitz's analysis of preference-based mutual fund separation. We show that high degrees of fund separation can be constructed by adding inverse marginal utility functions exhibiting lower degrees of separation. However, this method does not allow us to find all utility functions satisfying fund separation. In general, we do not know how to write the primal utility functions in these models in closed form, but we can do so in the special case of SAHARA utility defined by Chen et al. and for a new class of GOBI preferences introduced here. We show that there is money separation (in which the riskless asset can be one of the funds) if and only if there is a fund (which may not be the riskless asset) with a constant allocation as wealth changes. Chapter 2 generalizes the concept of "systematic risk" to a broad class of risk measures potentially accounting for high distribution moments, downside risk, rare disasters, as well as other risk attributes. We offer two different approaches. First is an equilibrium framework generalizing the Capital Asset Pricing Model. Second is an axiomatic approach resulting in a systematic risk measure as the unique solution to a risk allocation problem. Both approaches lead to similar results extending the traditional beta to capture multiple dimensions of risk. The results lend themselves naturally to empirical investigation. Chapter 3 proposes a regression approach to recovering the return distribution of an individual asset conditional on the return of an aggregate index based on their marginal distributions. This approach relies on the identifying assumption that the conditional return distribution of the asset given the index return does not vary over time. I show how to empirically implement this approach using option price data. I then apply this approach to examine the cross-sectional equity risk premium associated with systematic disaster risk, to estimate the exposure of banks to systemic shocks, and to extend the Ross (Journal of Finance, 2014) recovery theorem to individual assets.