Discussion Papers 2023


"Optimal Loan Portfolio under Regulatory and Internal Constraints"

Author Name

Okawara, Makoto and Akihiko Takahashi


May 2023

Full Paper PDF file

Revised in July 2023

Forthcoming in International Journal of Financial Engineering.


The environment surrounding banks is becoming increasingly severe. Particularly, to prevent the next financial crisis, Basel III requires financial institutions to prepare higher levels of capitals by January 1st, 2028, and the financial stability board (FSB) suggests the risk appetite framework (RAF) as their internal risk management. Hence, efficient usage of their own capitals for banks is more important than ever to improve profitability. Under such circumstances, this paper is the first to consider an optimization problem for a typical loan portfolio of international banks under comprehensive risk constraints with realistic profit margins and funding costs to achieve an efficient capital allocation. Concretely, after taking concentration risks on large individual obligors into account, we obtain a loan portfolio that attains the maximum profit under Basel regulatory capital and loan market constraints, as well as internal management constraints, namely risk limits on business units and industrial sectors. Moreover, we separately calculate credit risk amounts of the internal constraints in terms of regulatory and economic capitals to compare the optimized profits. In addition, considering sharp increases in default probabilities of all obligors as in the global financial crisis, we perform a stress test on the optimization results to investigate the effects of changes in risk amounts and profits. As a result, we propose to unify risk constraints on the business units and industrial sectors by using credit risk amounts in terms of economic capitals.

Keywords: regulatory capital, economic capital, risk appetite framework(RAF), granularity adjustment, constrained optimization