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Set out what loan loss provisions and loan loss reserves are and how they work.

FRM® Part II · Credit Risk Measurement and Management · Credit Risk Management · FRM2.CR.3.e

The idea

A loan loss provision is the income statement expense recognised in a period for expected credit losses. The loan loss reserve, or allowance, is the cumulative balance on the balance sheet, deducted from gross loans. They link through a roll-forward. Write End and Begin for the ending and beginning reserve, CO for gross charge-offs and NCO for net charge-offs, which are charge-offs less recoveries. For the balance at the end of the period, the roll-forward is End = Begin + Provision − CO + Recoveries. Rearranged to find the expense recognised for the period, the result is Provision = End − Begin + NCO. A write-off uses up the reserve and reduces gross loans, with no new expense if the loan was fully reserved, so net loans do not change. Specific provisions cover individually identified impaired loans. General or collective provisions cover losses in the performing portfolio. Reserves absorb expected loss, and capital absorbs unexpected loss. The common mistake is to treat a write-off as a second expense.

Formulas

Loan loss reserve roll-forward

ending reserve = beginning reserve + provision − charge-offs + recoveries

beginning reserve
the allowance at the start of the period
provision
the expense charged in the period
charge-offs
gross loans written off
recoveries
cash recovered on loans previously written off

Solve it for the provision when the target reserve is known. A write-off uses up the reserve; it is not a second expense.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which statement correctly describes the loan loss reserve (allowance)?

  1. An income statement expense recognised each period for expected losses.Why not: Describes the provision, not the reserve.
  2. A balance sheet account, deducted from gross loans, that accumulates provisions net of write-offs. - correct
  3. A pool of cash held separately to repay depositors if loans default.Why not: The reserve is an accounting valuation allowance, not segregated cash.
  4. A regulatory capital buffer meant to absorb unexpected losses.Why not: Reserves cover expected loss; capital covers unexpected loss.

The provision is the income statement expense in a period; the reserve is the stock on the balance sheet. The reserve is a contra-asset, not cash and not capital.

A harder one

A bank's loan loss reserve was USD 300 million at the start of the year and USD 330 million at year-end. During the year gross charge-offs were USD 140 million and recoveries on loans previously charged off were USD 25 million. The provision expense for the year was:

  1. USD 170 millionWhy not: Ignores the recoveries; only net charge-offs reduce the reserve.
  2. USD 30 millionWhy not: Uses only the change in the reserve and ignores charge-offs.
  3. USD 145 million - correct
  4. USD 195 millionWhy not: Adds recoveries to charge-offs instead of subtracting them.

Ending reserve = beginning + provision - net charge-offs, where net charge-offs = 140 - 25 = 115. Provision = 330 - 300 + 115 = 145.

The hardest tier

A bank keeps its reserve at 2.5 percent of gross loans. Gross loans at year-end are USD 12,400 million. The reserve was USD 270 million at the start of the year, with gross charge-offs of USD 110 million and recoveries of USD 30 million. The tax rate is 25 percent. The provision needed lowers net income after tax by:

  1. USD 120 millionWhy not: Gives the pre-tax provision and ignores the tax shield.
  2. USD 90 million - correct
  3. USD 112.5 millionWhy not: Ignores recoveries, so net charge-offs are overstated.
  4. USD 30 millionWhy not: Uses only the change in the reserve and ignores net charge-offs.

Target reserve = 2.5% x 12,400 = 310. Provision = 310 - 270 + (110 - 30) = 120. After tax at 25%, net income falls by 120 x 0.75 = 90.

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