TITLE:
Robust Portfolio Allocation for a Bank under Inflation
AUTHORS:
Ryle S. Perera
KEYWORDS:
Basel III Capital Accord, Capital adequacy Ratio (CAR), HJBI Equation, Monotone Preferences, Inflation. Stochastic Differential Game
JOURNAL NAME:
Theoretical Economics Letters,
Vol.8 No.15,
November
26,
2018
ABSTRACT: In this study, we develop a robust portfolio allocation model for a bank in an
incomplete market with inflation (a non-tradeable stochastic factor). The optimality criterion of the investments is established on a
functional via a modified version of the monotone mean-variance preferences. An increase in anticipated inflation will increase the
interest rate, while reducing the expected net stream of dollar receipts in the
loan portfolio. Eventually whilst existing loans mature and are re-negotiated
(at the higher interest rate), the interest rate is earned by the bank on
existing loans are locked up. Under such explicit risk aggregation paradigm, we formulate this problem as a stochastic differential game (SDG) and apply the Hamilton-Jacobi-Bellman-Isaacs
(HJBI)-equation to derive the optimal investment strategy. We discuss
the dynamics of myopic optimal portfolio and the intertemporal hedging demand
portfolio of the optimal portfolio holdings. We
describe the dynamics of the total capital ratio under Basel III regulations.
Finally, we show that our solution coincides with the solution to classical
Markowitz optimization problem with risk aversion coefficient depends on
stochastic factor. Our results confirm that the banker’s optimal holdings and
the trade-off between holding a myopically optimal portfolio and intertemporal
hedging demand are determined by the derivatives of marginal utility
with respect to the state variable.