CAIA L2 - 3.2 - Credit Risk Models Flashcards
List
5 Credit Events
3.2 - Credit Risk Models
- Bankruptcy
- Credit downgrade
- Failure to make payments
- Corporate events
- Government actions
3.2 - Credit Risk Models
Define
Adverse Selection
3.2 - Credit Risk Models
= BEFORE TRANSACTION =
Borrowers often have more information than lenders - it raises a lender’s risk
- lenders raises rates
- credit risk is increased
How to offset => include collateral (or limit loan)
3.2 - Credit Risk Models
Define
Moral Hazard
3.2 - Credit Risk Models
= AFTER TRANSACTION =
borrower takes on more risk knowing that the counterparty (lender) bears the risk of the transaction
How to offset => monitoring or limit loan
3.2 - Credit Risk Models
Formula
Expected Loss E[Loss]
Loss Given Default LGD
Recovery Rate RR
3.2 - Credit Risk Models
E[Loss] = LGD × PD
LGD = EAD × (1 – RR)
RR = present value of recovered sum / EAD
3.2 - Credit Risk Models
Compare + State most famous
Structural credit risk models
Reduced-form models
Empirical models
3.2 - Credit Risk Models
Structural credit risk models
* Explicit relationship between capital structure and default from the perspective of the equity owner.
* Equity = call option on entity’s assets + strike = face value of bonds
* Famous: Merton and KMV (Kealhover, McQuown, and Vasicek)
Reduced-form models
* Default = random event that can be quantified (with economic and statistical models)
* assumes default = exogenous factor and don’t consider causes of default
* Famous: ‘Jarrow-Turnbull model’ and ‘Duffie-Singleton model’ (Dica “J” depois de “D” - recovery at maturity and any time, respectivamente)
Empirical models
Produce a credit score that is used to rank entities by creditworthiness.
* Famous: Altman’s Z-Score
3.2 - Credit Risk Models
Formula
Equity Value of
Merton Model
3.2 - Credit Risk Models
E’t’ = A’t’×N(d) − K×e^(−r×t) × N(d−σ’A’√τ)
r = annualized short-term interest on risk-free debt
τ = T – t (i.e., time left to debt maturity)
σ’A’ = annualized volatility of the asset rate of return
N (⋅) = cumulative probability function
d = standard normal distribution
A = value of firm’s assets
K = Face value of the debt
3.2 - Credit Risk Models
Formula
Debt Value of
Merton Model
3.2 - Credit Risk Models
D’t’ = K × e^(–(r + s’t’)×τ)
s’t’ = annual spread due to credit risk
s’t’ = −(1/τ) × ln[ N(d−σ’A’√τ) + (A’t’/K) × e^(r×τ) × N(−d) ]
3.2 - Credit Risk Models
Evaluate
Usefulness and shortcomings
of the
Merton model
3.2 - Credit Risk Models
Useful:
- initial assessment before looking at more complex models. It does not look at the true PD, but instead, it looks at the probability implied by market prices determined by risk-neutral investors
Shortcomings:
- assume the value of company assets (V t) and the respective volatility (σt) as parameters of input to the model, since they are not directly observable in the market.
- does not explain the credit spreads on short-term securities well
3.2 - Credit Risk Models
Evaluate
4 Properties of the Merton Model
(PD sensitivity)
3.2 - Credit Risk Models
PD sensitivity to:
- Maturity - Direct relationship - decreasing rate
- Asset volatility - Direct relationship
- Leverage - Direct relationship
- Risk-free rate - Inverse relationship
The Merton model is sensitive to both maturity and volatility with respect to credit spreads. However, the slope of the change declines as time progresses.
3.2 - Credit Risk Models
Formula
KMV credit risk model
3.2 - Credit Risk Models
calculates the volatility of equity through a structural relationship between the market values of a firm’s equity and its assets, as well as the relationship between the volatilities of the firms equity and its assets.
σ’E’ = (A’t’ / E’t’) Δ σ’A’
σ’A’ = asset volatility
3.2 - Credit Risk Models
Formula
Distance to Default (DD)
(KMV Model)
3.2 - Credit Risk Models
percentage difference between a firm’s assets and its default trigger relative to asset volatility.
measures the number of standard deviation decline in assets that will cause the firm to enter default territory.
DD’t’ = (A’t’ − K) / (A’t’ × σ’A’)
K = default trigger
σ’A’ = asset volatility
3.2 - Credit Risk Models
Formula
Expected Default Frequency (EDF)
(KMV Model)
3.2 - Credit Risk Models
EDF = PD of loans with certain characteristics
EDF = DD’n,default’ / DD’n,total’
DD’n,default’ = the percentage of firms that defaulted within a one-year time horizon when their asset values were within n standard deviations away from default
DD’n,total’ = the percentage of total firms with n standard deviations away from default this represents
3.2 - Credit Risk Models
Formula
P’t’ - probability that a firm can survive for t years
(Reduced-form models)
3.2 - Credit Risk Models
p’t’ = e^(–λ×t)
λ = default intensity
(1/λ) = expected time until default (usually in years)
Probability that default could occur between time s and t, and assuming no default until time s:
p(s) – p(t) = e^(–λ ×s) – e^(–λ ×t)
Obs: Probability of surviving after year “t” = 1 - [ p(s) – p(t) ]
3.2 - Credit Risk Models
Formula
D’0’ - Risky Debt With Default Intensity
and
D’0’ - Risky Debt With Default Intensity + Recovery Rates
(Reduced-form models)
3.2 - Credit Risk Models
D’0’ = e^(−(r+λ)×T) × K
λ = default intensity
(1/λ) = expected time until default (usually in years)
D0≈ e^{−[r+λ×(1−RR)]×T} × K
s’t’ = λ × (1 – RR)
3.2 - Credit Risk Models
Formula
Altman’s Z-Score Model
3.2 - Credit Risk Models
Z =
(1.2 × X1) + (1.4 × X2) + (3.3 × X3) + (0.6 × X4) + (1 × X5)
- Default (or distressed) group: Z < 1.81
- Gray zone: 1.81 ≤ Z ≤ 2.99
- Nondefault (or safe) group: Z > 2.99
- X1: working capital/total assets. The ratio is a measure of liquid assets to total capitalization and is an indicator of liquidity. A firm with operating losses will see declining working capital.
- X2: retained earnings/total assets. The ratio is a measure of cumulative profitability and measures the relative size of the amount of a firm’s reinvested earnings, losses, or both. The ratio also indirectly measures leverage because high ratios may be indicative of more profit retention and less use of debt.
- X3: earnings before interest and taxes/total assets. The ratio is a measure of productivity independent of leverage and taxes. It is most appropriate for measuring corporate failure.
- X4: market value of equity/book value of total liabilities. Solvency. The ratio measures the magnitude of decline in a firm’s assets before they are exceeded by the value of liabilities and the firm becomes insolvent.
- X5: sales/total assets. The ratio is a measure of activity (turnover) by looking at the ability of a firm’s assets to generate sales.
3.2 - Credit Risk Models
