Interest Rate Risk and Bank Hedging

How do banks hedge their business risk due to interest rate fluctuations, which naturally drive both cash-flow risk and discount rate risk simultaneously? To answer this question we build a model where a bank’s profitability is determined by the spreads on its loans and deposits, while its balance sheet growth is governed by equity and deposit flows, both of which depend on interest rates. Furthermore, the balance sheet growth is also affected by a maximum leverage ratio — defined using either accounting-based or market-based measures — imposed by a regulator. Interest rate movement affects the tightness of this leverage constraint through its impact on profitability, on balance-sheet growth, and even on the (endogenous) discounted value of bank equity. Ultimately, a bank’s optimal hedging strategy stabilizes the marginal value of cash for bank equity. On one hand, a bank would like to allocate an additional dollar to the state with higher interest rate if that state has a greater profitability and/or a higher balance sheet growth, which concerns the cash-flow effect. However, that state is also with a higher discount rate, and the optimal hedging policy trades off these two discount and cash-flow effects. We show that a bank optimally hedges away the entire interest rate risk — so that the resulting equity value is independent of interest rate — when its deposit rate beta, loan rate beta, and deposit growth beta are zero. Otherwise, the bank retains some optimal net exposure to interest rate risk, aiming to stabilize its leverage ratio to avoid regulatory intervention versus exploiting a shifting investment opportunity set driven by the interest rate environment.