Cost of debt & credit risk (F)

What is the cost of debt formula?

ANSWER: rD = YTM = rf + (credit) spread + CRP
• rf = YTM of US/German 10Y Treasury.
• It's a market rate, not the coupon.
• Know by heart.

What is the yield to maturity (YTM)?

ANSWER: The discount rate that equates the PV of coupons + repayments to today's bond price
• P = Σ (coupon_t + repayment_t)/(1 + YTM)^t.
• Price < par → YTM > coupon.
• Often published per rating class.

What is a credit spread?

ANSWER: YTM − risk-free rate
• Compensation for default risk (PD, LGD), unexpected losses (capital cost) and liquidity.
• Strongly tied to rating and maturity.

What is the yield to worst (YTW)?

ANSWER: For callable bonds: compute yield-to-call for every call date plus the YTM, and take the lowest
• Conservative yield measure: the issuer calls when it's bad for the investor.

What is the option adjusted spread (OAS)?

ANSWER: Spread after removing all embedded options from the bond
• Pure pricing of credit risk and liquidity ('effective YTM').
• Raw spread mixes credit risk with option value.

How do high-yield spreads compare to investment-grade spreads?

ANSWER: HY spread ≈ 4× IG spread
• Normal times EUR IG ~100bp, HY ~400bp; crisis peaks ~400 vs ~1600bp.
• Both move with the credit cycle.

Where is the investment-grade boundary?

ANSWER: BBB− (Moody's Baa3) or better = investment grade; BB+ (Ba1) or worse = speculative / high yield
• Below it spreads jump and covenants get stricter.

What is PD?

ANSWER: Probability of default, usually annual
• Driven by business risk + financing risk; estimated via ratings or credit scoring models.

What is LGD?

ANSWER: Loss given default = 1 − recovery rate
• Typical assumption 40–45% (banking spread uses 40%).
• Driven by seniority and collateral.

What is EAD?

ANSWER: Exposure at default
• Amount outstanding (incl. interest) when default happens.

What is the expected loss formula?

ANSWER: EL = PD × LGD (× EAD)
• First component of the bank spread.
• Small for IG (≈ 0), large for B ratings.
• Orchard: security lowers LGD → lower EL.

What drives PD?

ANSWER: Business risk + financing risk
• Main structure of the S&P methodology, so a credit scoring model needs proxies for both.
• Exam Q EXAM4 Q8b.

What drives LGD?

ANSWER: Seniority (subordination) + tangibility of collateral (linked to sector)
• Exam Q EXAM4 Q8a.

What does the LGD distribution look like?

ANSWER: Bimodal: high probabilities at the edges (≈ 0% or ≈ 100% recovery)
• Loans: ~66% recover 100% (senior, secured).
• Bonds: ~34% recover only 0–9%.
• Average LGD poorly describes individual cases → hard to model.

How are PD and LGD related?

ANSWER: Individual (cross-section): NOT related. Annual averages (time series): slightly correlated
• Different drivers; but in crisis years many defaults AND low recovery prices (distressed asset market flooded).

What are typical recovery rates by seniority?

ANSWER: 1st lien loan ~65%, 2nd lien ~32%, senior unsecured bond ~38%, senior subordinated ~31%, junior subordinated ~22%
• Recovery falls with lower priority in the waterfall.

What are typical 1-year default rates by rating?

ANSWER: AAA 0%, A ~0.05%, BBB ~0.2%, BB ~0.5%, B ~3%, CCC ~27%
• Rises roughly exponentially down the scale; biggest jump below investment grade.

What are the average default rates for IG and speculative grade?

ANSWER: IG ≈ 0.08% per year, speculative grade ≈ 3.6% per year
• Spec grade is cyclical: ~1–2% in good years, peaks 10–12% in crises (1991, 2001–02, 2009).

What is the 1st order analysis in the S&P methodology?

ANSWER: CICRA (country + industry risk) combined with competitive position → business risk profile; cash flow/leverage → financial risk profile; matrix of both → anchor rating
• Main drivers of PD.
• Lower business risk allows more financial risk for the same rating.

What is the 2nd order analysis in the S&P methodology?

ANSWER: Modifiers (diversification, capital structure, financial policy, liquidity, management/governance, comparable ratings) → stand-alone credit profile → group/government support → issuer rating
• Fine-tuning.
• Then debt instrument analysis gives the issue/recovery rating (LGD).

What is CICRA?

ANSWER: Country and industry risk assessment combined
• First step of S&P methodology; combined with competitive position into the business risk profile.

What is the difference between issuer rating and issue rating?

ANSWER: Issuer rating = PD of the company. Issue/recovery rating = adds instrument-specific LGD (seniority, collateral)
• A secured loan can be rated above the issuer, a subordinated bond below.

What is the typical Debt/EBITA per rating?

ANSWER: Aaa 0.6, Aa 1.8, A 2.0, Baa 2.7, Ba 3.5, B 5.1, Caa–C 7.3
• Conditional on average business risk and market circumstances; standards change over time.
• Used in Imtech case: Debt/EBITDA 3.5 → non-investment grade.

What is the size rule of thumb for credit ratings?

ANSWER: > 1bn: BBB or higher; < 1bn: BB or lower; < 100m: B or lower
• Size is a strong business risk proxy.

What is a credit scoring model?

ANSWER: Logit regression: log(PD/(1 − PD)) = α + β × ratios, trained on historical defaults
• Variables: business risk (WC/TA, RE/TA, size) + financing risk (ME/BL, Debt/EBITDA, Int/EBIT).
• Gives PD directly.

What is the accuracy ratio (ACR)?

ANSWER: Measure of default-prediction power of a rating scale: 0 = random, 1 = perfect
• Area between the rating's cumulative accuracy curve and the diagonal, relative to a perfect model.

What is a bond equivalent rating (BER)?

ANSWER: A credit score converted into a rating, with the same distribution as actual S&P ratings
• Makes a fair contest between credit scores and agency ratings possible.

How do credit scores compare to agency ratings?

ANSWER: Credit scores predict defaults better, especially at short horizons (< 2–3 years); agency ratings are more stable
• Agencies trade accuracy for stability.

Why do rating agencies want stable ratings?

ANSWER: 1) investors want stability 2) timely ratings could deepen crises (procyclicality) 3) reputation: better late and right than fast and wrong 4) lower review costs
• Stability and accuracy are conflicting objectives.

What is the main role of rating agencies?

ANSWER: Certification, not information
• Standardized widely accepted scale, stability, dominance of few agencies → hard entry; S&P dominance lasts unless regulators intervene.

What is the bank credit spread formula?

ANSWER: Spread = RL − RF = PD × LGD + K × 15% + operational costs
• Expected loss + cost of equity buffer for unexpected losses (shareholders want ~15%) + operating costs.
• Course version: PD × 40% + K × 15% + 30bp.
• Know by heart (exam Q EXAM1 Q8).

What is K (bank capital) under Basel I, II and III?

ANSWER: Basel I: flat 8%. Basel II: depends on loan quality (PD, LGD, ρ). Basel III: Basel II + extra capital
• K is the equity buffer for UNEXPECTED losses.

What is RAROC?

ANSWER: (net interest income − expected loss − operating costs) / economic capital
• Risk-adjusted return on the capital a loan consumes; banks want ≥ ~15%.

What is the Basel II capital concept?

ANSWER: Value-at-Risk at C = 99.9%: K is set so losses exceed K only in 0.1% of years
• 'A bank may fail once in 1000 years'.
• Assumes binomial loss distribution, no fat tails.

What does the Basel II capital requirement K depend on?

ANSWER: PD, LGD, EAD, asset correlation ρ and confidence level C
• K = N[(N⁻¹(PD) + √ρ·N⁻¹(C))/√(1−ρ)] × LGD × EAD (interpret, don't memorise).

What is asset correlation ρ and its effect?

ANSWER: How much borrowers' defaults move together; higher ρ → defaults cluster → fatter right tail → higher K
• Expected loss unchanged.
• Basel: ρ from 24% (low PD) to 12% (high PD).

What is the SME correction in Basel II?

ANSWER: Asset correlation for SMEs assumed ~20% lower (up to −4pp at €5m turnover) → lower K
• Partly politically driven (keep SME lending cheap).

What is the typical range of Basel II capital requirements?

ANSWER: From ~1.2–2% for AAA up to ~30% for CC
• Rises steeply below BB.

What are the capital requirements in the Basel II standardized approach?

ANSWER: 2% (AAA/AA), 4% (A), 8% (BBB–BB), 12% (B and lower)
• Based on external ratings; less risk-sensitive than the advanced (IRB) approach.

What was the problem with Basel I?

ANSWER: Flat 8% capital → spread too high for highly rated borrowers (≈185bp vs market ~40bp) and too low for junk
• Banks couldn't compete with the bond market for good firms; incentive to take riskier loans.

How does the Basel II banking spread compare to market spreads?

ANSWER: Almost an exact match per rating class
• Expected loss alone is far too small for IG; the capital cost explains most of the IG spread.