The profitability of a bank is determined by the behaviour of its future expected cash flows.
The BB contains held-to-maturity instruments. Their future CFs are accrued to P&L on a straight-line basis prior to the CF date. Interest received minus interest paid = Net Interest Income. In the TB, the process is different. The future CFs, both +ve and –ve, are transformed each day into present values and netted. Changes in the net PV = trading P&L. The PV of each CF is calculated by multiplying it by a discount factor derived from a YC. YC models such as bootstrappers or Nelson-Siegel convert market interest rates observable at various maturities into a smooth continuous curve of rates or DFs. Where a financial instrument is traded, its market price = the market’s view of the PV of its future CFs. Under both the TB and BB approaches, when the CF date is reached; the accrued or unrealized net income is re-labelled realized P&L.
In the TB, all future CFs are converted into PVs. The TB is therefore highly sensitive to changes in the YC. Risk sensitivity measures such as IR delta and PV01 were developed in the 1970s and 80s to determine the change in $value of the TB for a 1 bps shift of the YC. They were used by market risk departments and codified as regulation in Basel I in 1996.
While the BB does not discount its future CFs to PV, it is nonetheless still sensitive to changing IRs. E.g. fixed rate loans are more valuable to the bank when rates fall. Banks traditionally used measures such as duration and gap analysis to determine the impact of IR changes on its BB. Basel II in 2004 formalized the IRRBB approach by introducing the concept of Economic Value of Equity. EVE is equivalent to the PV01 concept in the TB but applies larger, less frequent IR shifts.
In 2016, Basel III introduced a more specific approach to calculating EVE. It is shown in the diagram below. Six YC shift scenarios are applied to the BB: parallel up, parallel down, steepener, flattener, short rate up, and short rate down. The maximum loss of the six YC shift-impacts is captured. This max loss number should not be > 15% of Tier 1 capital.
Traded instruments are also allowed in the BB. But only if their future CFs are exactly equal and opposite to those of a designated hedging derivative. The diagram below shows a bond being hedged with an IR swap. If the hedge is effective, then the two instruments’ PVs will move each day in equal and opposite direction – allowing daily monitoring of hedge effectiveness – taking account of any curvature in the rate-change -> P&L relationship. The BB borrows systems and methodology from the TB when calculating PVs for hedge effectiveness tests.
