Justification of Per-Unit Risk Capital Allocation in Portfolio Credit Risk Models

Abstract

Risk capital allocation is based on the assumption that the risk of a homogeneous portfolio is scaled up and down with the portfolio size. In this article we show that this assumption is true for large portfolios, but has to be revised for small ones. On basis of numerical examples we calculate the minimum portfolio size that is necessary to limit the error of gradient risk capital allocation and the resulting error in a portfolio optimization algorithm or pricing strategy. We show the dependence of this minimum portfolio size on different parameters like the probability of default and on the credit risk model that is used.

Paralyzed by shock: the portfolio formation behavior of peer-to-business lending investors

“…In the context of our analysis, we do not have information on the overall investor portfolio. However, even with significant investments in other asset classes, the overall VaR can still be decreased as long as the peer-to-business loan portfolio, which is at the center of our analysis, is not fully diversified (Dorfleitner and Pfister 2014). Moreover, from a behavioral finance perspective, investors might view their peer-to-business loan portfolio as part of one mental account and other asset classes as part of a different mental account.…”

“…Using numerical examples,Dorfleitner and Pfister (2014) show that to obtain constant per unit risk, which can be interpreted as having a well-diversified portfolio, the minimum number of loans ranges from approximately 200 (VaR at 95% level and loan probability of default of 5%) to more than 500 (VaR at 99.9% level and loan probability of default of 10%).…”

Paralyzed by Shock and Confused by Glut: The Portfolio Formation Behavior of Peer-to-Business Lending Investors

“…Dorfleitner and Pfister (2014) show that in order to have constant per unit risk, which can be interpreted as having a well diversified portfolio, the minimum number of loans ranges from roughly 200 (VaR at 95 % level and loan default probability of 0,5 %) to more than 500 (VaR at 99.9 % level and loan default probability of 10 %).…”