Imagine you’re running a bank. But instead of coffee and pens, you’re serving loans — and you want to make sure your kitchen doesn’t catch fire when borrowers can’t pay. Basel II offers three recipes for how much capital you should set aside in case that happens.
Let’s dig into each one — starting with the simplest and gradually moving to the gourmet-level “chef’s tasting menu” used by sophisticated banks.
1. Standardized Approach – The Fast Food Version of Basel
This is the McDonald’s of capital calculation — it’s fast, uniform, and doesn’t require deep culinary skill (aka risk modeling).
Under this method, each asset $($loan, bond, etc.$)$ gets a risk weight based on external credit ratings. For example:
- An AAA-rated country bond? Risk weight = 0% $($yum, risk-free!$)$
- A corporate bond rated BB? Risk weight = 150% $($aka, spicy!$)$
If the borrower is unrated, you still assign weights based on predefined categories. Banks with less developed risk systems use this method — easy to apply, not so personalized.
Why does this matter? Because your capital requirement is simply 8% of your risk-weighted assets-RWA. So if your RWA is \$100 million, you need to hold \$8 million in capital.
💡 But what if your loan is backed by something like gold bars or government bonds? Shouldn’t that reduce your risk?
Exactly! This brings us to collateral adjustments under two approaches:
2. Simple vs. Comprehensive Collateral Approaches
🍰 Simple Approach $($Dessert Tray Method$)$
Here, you replace the borrower’s risk weight with the collateral’s risk weight.
🧮 Example:
You lend \$100 million to a company rated B $(risk\ weight = 150\%)$, secured by \$80 million in AAA-rated government bonds $(risk\ weight = 20\%)$.
So:
- 80 million × 20% = 16 million $(collateral \ portion)$
- 20 million × 150% = 30 million $(unsecured\ portion)$
- ✅ Total RWA = $46 million
This is like saying: “I don’t fully trust you, but your jewelry box makes me feel better.”
🍽 Comprehensive Approach $($Michelin-Star Risk Math$)$
Instead of swapping risk weights, you adjust both exposure and collateral for volatility — like preparing for stormy weather.
🧮 Example:
- Original loan = $100 million
- Add 15% for exposure risk → \$100M × 1.15 = \$115M
- Reduce collateral value by 20% → \$80M × 0.80 = \$64M
- Net exposure = \$115M − \$64M = \$51M
- Apply borrower’s risk weight: 150% of $51M = $76.5M RWA
It’s more complex but better reflects reality — like a chef who adjusts their seasoning for humidity.
3. Foundation IRB Approach – The Sous-Chef’s Toolkit
Now we let banks use their own estimates — sort of.
They must estimate:
- PD = Probability of Default
But Basel provides:
- LGD = Loss Given Default
- EAD = Exposure at Default
- Maturity (M) = Typically set at 2.5 years
📉 Example:
- \$150M loan, PD = 0.1%, LGD = 45$\%$, DR $\\($explained below$\\)$ = 3.4%
- Capital = \$150M × 0.45 × (3.4% − 0.1%) = $2.24M
Pretty neat, right? But some banks want to go full MasterChef mode…
4. Advanced IRB Approach – The Risk Gourmet Special
This is the big league. Banks estimate everything: PD, LGD, EAD, and Maturity.
But wait — what the heck is DR99.9?
🧪 What Is DR99.9? AKA “Default Rate at the 99.9th Percentile”
It’s the worst-case probability of default, assuming a once-in-a-thousand-year financial apocalypse.
DR99.9 is calculated using:
- A copula model $($fancy talk for “what if everyone fails together?”$)$
- PD and correlation (\rho) between borrowers
- A normal distribution $($because banks love bell curves$)$
🧮 The formula: $\text{DR}_{99.9} = \Phi \left( \frac{ \Phi^{-1}(PD) + \sqrt{\rho} \cdot \Phi^{-1}(0.999) }{ \sqrt{1 – \rho} } \right)$
This gives us a “tail-end” estimate of how bad things can get. Think of it as the “meteor hit the economy” scenario. It’s trying to compute the default rate under severe stress — specifically, at a 99.9% confidence level.
This means:
“What’s the proportion of obligors we expect to default in an extremely bad year — one that occurs once in 1,000 years?”
🌪 The Final Recipe for Capital Requirement:
Once we have $DR_{99.9}$, we compute: $Capital=EAD×LGD×(DR_{99.9}−PD)×MA$
Where MA = Maturity Adjustment — which accounts for the longer exposure window.
Finally: RWA=12.5×Capital
Why 12.5? Because 1/0.08 = 12.5. The Basel committee loves this little trick.
So What’s the Difference Between These Approaches?
| Approach | Who Estimates What? | Customization | Complexity |
|---|---|---|---|
| Standardized | Basel gives you everything | Low | Easy |
| Foundation IRB | Bank estimates PD only | Medium | Moderate |
| Advanced IRB | Bank estimates PD, LGD, EAD, M | High | Complex |
🎯 Final Thoughts: Why This All Matters?
Because banks don’t just want to survive — they want to thrive without blowing up. And how they estimate and hold capital defines how much risk they can take, and what kind of loans they can afford to make.
So what’s next after we know the capital to hold?
Well… how do we monitor, validate, and backtest these capital models? What if things go wrong — or worse, we assumed they were right when they weren’t?
Stay tuned. That’s where model validation and stress testing come in.