This notebook compares the risk weight the two approaches produce for the same exposure, as its PD varies. The FIRB weight moves with the PD; the STD weight does not, so it stands as a fixed level for each credit quality step. Plotting them together shows which approach is the more conservative, and where. It is the last post in the series, and the one that puts a number on a question the fifteen scenarios could only answer anecdotally. Across the worked examples Foundation

The maturity factor scales the risk weight up as an exposure runs for longer. A loan that matures in five years ties up capital, and stays exposed to a downturn, for far longer than one that matures in a year, so the formula charges more for it. The factor is what applies that charge. It has two drivers. The first is , the exposure maturity in years, which the earlier notebooks derived from the cash-flow schedule and can run from 1 to 5 years. The second is , the maturity a

The conditional PD is a borrower's probability of default under a severe, economy-wide downturn, rather than in a normal year. It is what the capital formula measures the risk weight against, and it is always higher than the ordinary PD that goes into it.

Loan 1 and Loan 2 are the same loan to the same counterparty, differing only in that Loan 2's obligor has defaulted. This comparison is about unexpected loss and expected loss, and how the two approaches treat a defaulted exposure differently. A bank expects to lose a certain amount on its lending, and it covers that expected loss through provisions. Capital is held for the loss above that expectation, the unexpected loss, and this is what the risk weight measures. Foundatio

Loan 1 and Loan 2 isolate the performing versus defaulted treatment of the same loan: same counterparty, same amortisation schedule. The only thing that changes between them is whether the obligor is in default. Loan 2 is identical to Loan 1 in every fact except that the obligor is in default. That one fact does not move a driver inside the risk-weight formula; it replaces PD with a 100% override and, with it, the risk weight itself. A defaulted Foundation IRB exposure does

Loan 1 and Loan 2 isolate the performing versus defaulted treatment of the same loan: same counterparty, same amortisation schedule. The only thing that changes between them is whether the obligor is in default. Loan 1 and Loan 2 isolate the performing versus defaulted treatment of the same loan: same counterparty, same amortisation schedule. The only thing that changes between them is whether the obligor is in default.

Like the DRT comparison, this notebook puts SFT 1 and SFT 2 side by side to isolate what actually drives the difference between them. Here that means PD and maturity, moving together in opposite directions: SFT 1 (AA+) pairs a floored PD with a longer maturity, SFT 2 (A+) pairs an unfloored, higher PD with a shorter maturity. Neither set is simply worse on both counts, so the risk weight has to weigh both drivers rather than read off either one alone.

DRT 3 and DRT 4 moved one thing at a time: counterparty type, then PD alone, on a weak BB/B pair of ratings. SFT 1 and SFT 2 move to a much stronger pair of ratings, AA+ and A+, and this time PD and maturity move together, in opposite directions, to see how the two interact rather than in isolation.

DRT 3 and DRT 4 moved one thing at a time: counterparty type, then PD alone, on a weak BB/B pair of ratings. SFT 1 and SFT 2 move to a much stronger pair of ratings, AA+ and A+, and this time PD and maturity move together, in opposite directions, to see how the two interact rather than in isolation.

Across DRT 1 to DRT 4 we ran the same netting set four times, changing just one thing between each run. DRT 1 and DRT 2 showed what securing an exposure does to the maturity factor. DRT 3 showed what happens when the counterparty is financial rather than non-financial, and DRT 4 showed what happens when that counterparty is then on a weaker grade. The first two runs were about the maturity factor and the last two were about the probability of default, and because only one inp

DRT 1 and DRT 2 were about the maturity factor. DRT 3 and DRT 4 shift the focus to the probability of default. DRT 3 already brought in the higher LGD and correlation multiplier through the switch to a financial counterparty; DRT 4 keeps that counterparty type fixed and moves to a weaker rating grade instead, so PD is the only input left to change.

DRT 1 and DRT 2 were about the maturity factor. DRT 3 and DRT 4 shift the focus to the probability of default. Alongside that shift, the counterparty changes from non-financial to financial – a single change with two consequences: LGD moves from 40% to 45%, and correlation picks up the 1.25x scalar that applies to financial counterparties.

DRT 1 and DRT 2 isolate the secured versus unsecured treatment of the same netting set. The counterparty, PD, LGD, trade notionals and maturities are identical across the two. The only thing that changes is whether daily margining is in place, and that decides which maturity floor applies.

DRT 1 and DRT 2 isolate the secured versus unsecured treatment of the same netting set. The counterparty, PD, LGD, trade notionals and maturities are identical across the two. The only thing that changes is whether daily margining is in place, and that decides which maturity floor applies.

The risk weight calculation has many moving parts. To understand what each one contributes, we need scenarios that show how the risk weight changes when a single component moves at a time. This post sets out the scenario design used throughout the course, organised by product: derivatives, secured financing trades, and loans. Each set of scenarios below identifies which parameter changes from one scenario to the next. The design is a controlled experiment rather than a portf

The Standardised Approach is the default way to calculate risk-weighted exposure amounts for credit risk: an institution uses it automatically for any exposure type it does not hold IRB permission for, and every institution is free to use it everywhere even if it could use IRB instead. Where Foundation IRB converts a borrower's own PD and LGD into a risk weight through a formula, the Standardised Approach does no conversion at all. The institution places each exposure into a

Under the Standardised Approach, every institution applies the same supervisory risk weights to the same exposure type, regardless of how well or badly that particular institution actually understands its own borrowers. The IRB Approach exists because that is wasteful: an institution that has spent years building a credit risk model for, say, mid-sized corporates, has real information about how likely those borrowers are to default and how much would be lost if they did. It l

The Standardised Approach (SA) is the default. Every institution can use it, and it applies a supervisory risk weight to each exposure based on the counterparty's external credit rating, with no institution-specific modelling involved. The Internal Ratings Based Approach (IRB) is the alternative available to an institution that has built and had approved its own model of how likely a given borrower is to default. Under its Foundation variant, the institution supplies its own