Paper: arXiv 2501.07856

Authors: Deb Narayan Barik, Siddhartha P. Chakrabarty

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.

Complexity vs Empirical Score

  • Math Complexity: 6.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a formal discrete-time mathematical optimization framework for bank portfolio rebalancing and dynamic capital structure decisions. However, it is purely theoretical with no empirical data, backtesting, or empirical validation provided in the excerpt.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimize bank dynamic decisions & Return on Equity ROE across 3 time steps] --> B[Inputs: Initial capital debt/equity, short-term debt claims, regulatory capital ratios]
    B --> C[Intermediate Step Decision: Asset liquidation vs. Raising new debt & equity]
    C --> D[Optimization Model: Integrate regulatory capital rules & equity holder non-default constraints]
    D --> E[Theoretical Analysis: Derive capital raising bounds & evaluate ROE impact]
    E --> F[Findings: Raising capital conditionally increases/decreases ROE; bounds prevent default]

Cited References (18)

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  2. A dynamic model of optimal capital structure (2007)
  3. A dynamic model of bank behaviour under multiple regulatory constraints (2019)
  4. The leverage ratio, risk-taking and bank stability (2020)
  5. Loan portfolio management and Liquidity Risk: The impact of limited liability and haircut — → 2308.06525
  6. Deposits and bank capital structure (2015)
  7. Derivative pricing in discrete time (2012)
  8. BASLE COMMITTEE ON BANKING SUPERVISION (1988)
and 10 more
  1. BASLE COMMITTEE ON BANKING SUPERVISION (2006)
  2. Basel III: A global regulatory framework for more resilient banks and banking systems (2010)
  3. The leverage ratio: A new binding limit on banks (2009)
  4. Why ‘ B asel II ’may need a leverage ratio restriction (2008)
  5. Is Basel II enough?: The benefits of a leverage ratio (2008)
  6. Limited liability (1998)
  7. Risk taking, limited liability and the competition of bank regulators (2001)
  8. Large risks, limited liability, and dynamic moral hazard (2010)
  9. Does limited liability reduce leveraged risk?: The case of loan portfolio management (2022)
  10. How have banks adjusted to higher capital requirements? (2013)

1 of 18 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.