Interest Rate Risk and Bank Hedging
Abstract:
How do banks hedge their business risk due to interest rate fluctuations, which naturally drive both cash-flow risk an d discount rate risk simultaneously? To answer this question we build a mod el where a bank’s profitability is determined by the spreads on its loans a nd deposits, while its balance sheet growth is governed by equity and depos it flows, both of which depend on interest rates. Furthermore, the balance sheet growth is also affected by a maximum leverage ratio — defined using e ither accounting-based or market-based measures — imposed by a regulator. I nterest rate movement affects the tightness of this leverage constraint thr ough 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 w ith 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 po licy trades off these two discount and cash-flow effects. We show that a ba nk optimally hedges away the entire interest rate risk — so that the result ing equity value is independent of interest rate — when its deposit rate be ta, loan rate beta, and deposit growth beta are zero. Otherwise, the bank r etains some optimal net exposure to interest rate risk, aiming to stabilize its leverage ratio to avoid regulatory intervention versus exploiting a sh ifting investment opportunity set driven by the interest rate environment.< /p> DTSTAMP:20260416T125019Z DTSTART:20260309T163000Z DTEND:20260309T180000Z SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR