Expected loss

Expected loss is the value of a possible loss times the probability of that loss occurring. (see: Loss function#Expected loss)

In banking lending (homes, autos, credit cards, commercial lending, etc.) a third concept is introduced to emphasize that most loans are repaid over time and therefore have a declining outstanding amount to be repaid. Additionally, loans are typically backed up by pledged collateral whose value changes differently over time vs. the outstanding loan value. In banking the three factors are:

• Loss given default (LGD)
  • "magnitude of likely loss on the exposure, expressed as a percentage of the exposure"^[1]

• Probability of default (PD)
  • "probability of default of a borrower"^[2]

• Exposure at default (EAD)
  • "amount to which the bank was exposed to the borrower at the time of default, measured in currency"^[3]

Simple example

• Original home value $100, loan to value 80%, loan amount $80
  • outstanding loan $75
  • current home value $70
  • liquidation cost $10

• Loss given default = Magnitude of likely loss on the exposure / Exposure at default
  • -$75 loan receivable write off Exposure at default
  • +$70 house sold
  • -$10 liquidation cost paid =
  • -$15 Loss
  • Express as a %
  • -15/75 =
  • 20% Loss given default

• Probability of default
  • Since there is negative equity 50 homeowners out of 100 will "toss the keys to the bank and walk away", therefore:
  • 50% probability of default

• Expected loss
  • In %
    • 20% x 50% =10%
• In currency
  • currency loss x probability
  • $15 * .5 = $7.5
• check
  • loss given default * probability of default * Exposure at default
• 20% * 50% * $75 = $7.5

PD & LGD may be correlated?

The above assumes probability of default (PD) and Loss given default LGD are in no way correlated. If there is any degree of correlation the expected loss goes up.

For example, over a 20-year period only 5% of a certain class of homeowners default. However, when a systemic crisis hits, and home values drop 30% for a long period, that same class of borrowers changes their default behavior. Instead of 5% defaulting, say 10% default, largely due to the fact the LGD has catastrophically risen.

To accommodate for that type of situation a much larger expected loss needs to be calculated. This is the subject to considerable research at the national and global levels as it has a large impact on the understanding and mitigation of Systemic risk.^{[4][5][6][7][8][9]}

See also

• Loss given default
• Exposure at default
• Probability of default
• Systemic risk
• Loss function#Expected loss
• Loss function

References