Investors’ heterogeneity and tranching

ABSTRACT

The article presents a theoretic model of tranching in asset securitization. When potential buyers are heterogeneous in the constraint on their portfolios, we find that senior tranche, which is less risky and created by tranching, will introduce more investors and thus reduce risk exposure to investors. Thus, tranching helps improve the sale’s revenue. We also find that the portfolio constraints of investors are always binding at optimum, which is called marginal rating.

KEYWORDS:

• Tranching
• portfolio constraint
• marginal rating
• heterogeneity

JEL CLASSIFICATION:

• D52
• G12
• G21

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ All the results still hold when type I investors are more risk averse than type II investors, but it becomes more complicated, all proofs will be provided on request.

² Short sale is implicitly allowed here, and we discuss this issue in next section.

³ Formally, let $D=\hat{D}+\epsilon$, where $\epsilon$ is a positive number. Provided $\epsilon$ is small enough, we have $P_S^{\prime }\left(\hat{D}+\epsilon \right)<P_S\left(\hat{D}\right)$ since $P_S^{\prime }\left(\hat{D}\right)<P_S\left(\hat{D}\right)$ by Equation 9 and the function $P_S^{\prime }\left(\cdot \right)$ is continuous.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China for Young Scholar [grant number.71403051], [grant number 71403306] and the Humanities and Social Science Research Projects of the MOE in China [grant number.13YJC790153].