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80/20 Golden Rule · Pareto Optimality

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TheronGroup · RSK4804Integrated Professor's Notes

4.3Expected loss on a revolving facility

Expected loss is the amount a lender should provide for in advance, not the loss it fears in a bad year. The three components answer three separate questions — how likely is default, how much will be owed when it happens, and how much of that is unrecoverable — and the maturity adjustment scales the answer for the time the exposure stays open. Each is estimated independently, and a candidate who blends them loses the marks allocated to the separation.

Kgothalo Steel Processors (Pty) Ltd, a steel service centre in Ekurhuleni, has applied to your bank for a revolving working-capital facility. You sit on the credit committee, which has asked for the expected loss to be priced before the facility is approved.

ItemFigureSource
Approved facility limitR18 000 000Credit application, para 4.2
Expected drawn exposure at default82%Bank's internal EAD model
One-year probability of default2,40%Grade 6, internal masterscale
Loss given default45%Secured on plant, after haircut
Maturity adjustment1,15Basel adjustment at M = 2,5 years

Required (8)

Calculate the expected loss on the facility, expressed in Rand and as a percentage of the exposure at default.

Step 1 — Establish the exposure the calculation runs on

The limit is not the exposure. A revolving facility is drawn in part, so the exposure at default is the modelled draw against the approved limit, and every later component is applied to that figure rather than to the limit.

EAD = 82% × R18 000 000 = R14 760 000

Step 2 — Apply the expected-loss identity

The probability of default, the loss given default and the maturity adjustment are multiplied onto the exposure established in step 1. The maturity factor multiplies forward here because the question asks for expected loss; it divides only when a probability is being backed out of a given expected loss.

EL = PD × EAD × LGD × M = 0,0240 × R14 760 000 × 0,45 × 1,15 = R183 319,20

Step 3 — Express the answer as a proportion of the exposure

The committee prices in basis points, so the Rand figure is returned to the exposure it was computed from. The limit plays no part in this ratio.

R183 319,20 ÷ R14 760 000 = 0,01242 = 1,242% of exposure at default
Professor's Note

The maturity adjustment is where this question is most often lost. Candidates who have learned the identity as PD × EAD × LGD either omit the factor or, having noticed it in the data, divide by it. Read the requirement: where the expected loss is being computed forward, the adjustment multiplies. It divides only when the expected loss is given and a probability is being recovered from it.

80/20 Golden Rule · Pareto OptimalityPage 47

One page of 368. The RSK4804 module runs to 45 documents across notes, solution packs, a revision reference and a formula sheet.

How to read the page

  • The question stem — the pale-blue block — is reproduced exactly as it would be set, with its source table and mark allocation. A set question is never parted from its answer.
  • Each numbered step is headed by what it does, not by a number alone, and every substitution is shown in its own tinted block, so a marker can follow the method line by line.
  • The Professor's Note — the gold-edged block — names the point where candidates most often lose the marks on this question type.
  • Every figure is computed in code, never typed. A figure that does not carry through fails the document's build.

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