# Expected loss (Ofer Abarbanel online library)

Expected loss is the sum of the values of all possible losses, each multiplied by the probability of that loss occurring.

In bank lending (homes, autos, credit cards, commercial lending, etc.) the expected loss on a loan varies over time for a number of reasons. 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.

Three factors are relevant in analyzing expected loss:

• Probability of default (PD)[1]
• Loss given default (LGD)[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

Recalculating expected loss

Expected loss is not time-invariant, but rather needs to be recalculated when circumstances change. Sometimes both the probability of default and the loss given default can both rise, giving two reasons that the expected loss increases.

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]

References

1. ^“Basel Glossary PD”. Basel. Retrieved 2 February 2013.
2. ^“Basel Glossary EAD”. Basel. Archived from the original on 5 July 2012. Retrieved 2 February 2013.
3. ^“Basel Glossary LGD”. Basel. Archived from the original on 21 April 2013. Retrieved 2 February 2013.
4. ^“Regulatory use of system-wide estimations of PD, LGD and EAD” (PDF). BIS. Retrieved 2 February 2013.
5. ^“QIS 3 FAQ: I. IRB-inputs: PD, LGD and EAD”. BIS. Retrieved 2 February 2013.
6. ^“Implications of PD-LGD Correlation in a Portfolio”. Moodys. Retrieved 2 February 2013.
7. ^“Expected loss (EL) on credit asset if PD, LGD are correlated”. bionicturtledotcom. Retrieved 2 February 2013.
8. ^Schuermann, T. “What Do We Know About Loss Given Default?” (PDF). Wharton. Archived from the original (PDF) on 13 March 2012. Retrieved 2 February 2013.
9. ^“Expected Loss”. World Bank. Retrieved 2 February 2013.

Ofer Abarbanel online library