Expected Loss vs Unexpected Loss

Key takeaways

• Expected loss = PD x LGD x EAD, and it goes into your rate.
• Unexpected loss is the tail, and it is covered by capital, not price.
• Provisions cover expected loss; capital absorbs unexpected loss.
• A low-risk loan is cheap because both numbers are small.

What is expected loss?

Expected loss is the product of three estimates a lender makes about a loan: the probability that it defaults, the share of exposure that would be lost if it did, and how much would be outstanding at that point.

EL = PD x LGD x EAD. On a $500,000 loan with a 1% probability of default and a 20% loss given default, the expected loss is $1,000 a year - 0.2% of the exposure. That figure has to be recovered in the interest rate, alongside funding cost, operating cost and profit.

This is why a well-secured, low-LVR home loan is priced far below an unsecured personal loan. It is not a judgement about the borrower's character; it is arithmetic about recovery.

Why is unexpected loss different?

Expected loss is an average, and averages are not what destroys a bank. What destroys a bank is a year in which losses come in far above average - a recession, a regional employment shock, a property downturn concentrated in the segment it lent into.

That variability cannot be recovered through pricing, because a lender charging enough to cover the worst plausible year would be uncompetitive in every normal year. Instead, the lender holds capital: shareholder funds that absorb the excess when it arrives.

Both reach your rate, but by different routes. Expected loss is a direct cost. Unexpected loss shows up because equity capital is expensive, so a loan requiring more capital must earn more to deliver the same return.

How does correlation make the tail fat?

If defaults were independent, a large portfolio would have almost no unexpected loss - the law of large numbers would smooth it away. They are not independent. Mortgage defaults cluster, because the things that cause them - unemployment, rate rises, falling property values - hit many borrowers at once.

That correlation is what creates the tail, and it is why regulatory capital models include an explicit asset correlation assumption. It is also why concentration matters: a portfolio spread across one industry town is far riskier than the same number of loans spread nationally, even with identical individual PDs.

For a borrower, the useful takeaway is that your rate is set partly by what your loan does to the lender's portfolio, not only by your own credit quality.

Frequently asked questions

What is the formula for expected loss?

Expected loss equals probability of default multiplied by loss given default multiplied by exposure at default (EL = PD x LGD x EAD). Each component is an estimate produced by the lender's credit models.

Why do banks hold capital instead of just charging more?

Because pricing for the worst plausible year would make a lender uncompetitive in every normal year. Capital absorbs the variability instead, which is why prudential regulators set minimum capital requirements rather than minimum pricing.

Does unexpected loss affect my interest rate?

Indirectly. Loans that attract higher capital requirements need to earn more to produce the same return on equity, so capital-intensive lending is priced higher. That is one reason high-LVR and investor lending typically cost more.

What is the difference between a provision and capital?

A provision is an accounting charge against expected credit losses that reduces profit. Capital is shareholder funds available to absorb losses beyond what was provisioned. Provisions handle the average; capital handles the surprise.

Related reading

• PD, LGD and EAD: The Three Numbers That Price Your Loan
• Risk-Based Pricing: Why Two Borrowers Get Different Rates
• The Taylor Rule Applied to Australia

Sources

• Prudential Standard APS 110 Capital Adequacy — APRA
• Financial Stability Review — Reserve Bank of Australia