Dynamic loan portfolio management in a three time step model

TL;DR

This paper models a three-time-step dynamic decision process for banks managing loans, debt, and equity, analyzing how raising new funds impacts returns and compliance with capital requirements.

Contribution

It introduces a theoretical framework for bank decisions over three periods, including effects of raising equity and debt, with bounds and constraints on capital and returns.

Findings

Raising equity and debt can both increase or decrease return on equity depending on circumstances.

The model provides bounds on the amount of capital that can be raised.

An equity holder constraint prevents bank default at the final time.

Abstract

This paper studies the bank dynamic decision problem in the intermediate time step for a discrete-time setup. We have considered a three-time-step model. Initially, the banks raise money through debt and equity and invest in different types of loans. It liquidates its assets and raises new funds at the intermediate-time step to meet the short-term debt holders claim. Further, it has to meet specific capital requirements given by the regulators. In this work, we have theoretically studied the effect of raising new equity and debt. We show that in some cases, raising equity and debt may increase the return on equity, and in some cases, it may decrease the return on equity. We have discussed several cases and given a bound on the capital that can be raised. We have added an equity holders constraint, which ensures the return on equity and desists the bank from defaulting at the final time point.