Credit Risk Measurement and Management Flashcards
Approaches to Fixed-Income Analysis
Fixed-income analysis can be divided into fundamental analysis and technical analysis
- Fundamental analysis explores many of the same issues that are undertaken when engaging in credit analysis for risk management purposes; that is, default risk.
- Technical analysis looks at market timing issues, which are affected by the risk appetite of institutional investors and market perception, as well as pricing patterns.
The 3 components of expected losses (EL)
- The probability of default (PD)
- The exposure amount (EA) of the loan at the time of default
- The loss rate (LR), that is, the fraction of the exposure amount that is lost in the event of default
Expected loss formula
Expected loss tree
Unexpected loss formula
Variance of the probability of default
Expected loss of a portfolio
Unexpected loss of a portfolio
Marginal contribution of asset i to the unexpected loss of a portfolio
Amount of economic capital needed
- Is the distance between the expected outcome and the unexpected (negative) outcome at a certain confidence level
- Cm = Capital Multiplier
Economic capital formula
The ‘company game’ according to Wilcox
- CN/U is the inverse of the return on equity ratio (ROE)
The no return point
- OF - Operational flow of funds (industrial margin plus net investments or divestments)
- D - Debt
The cumulated default rate expressed by the survival rates
Annual default rate formula
Example of Default Frequencies for a Given Rating Class
Chaining
- ‘Forward chaining’ starts with available data. Inference rules are used until a desired goal is reached.
- ‘Backward chaining’ starts with a list of goals. Then, working backwards, the system tries to find the path which allows it to achieve any of these goals.
Debt is equal to the payoff of risk-free debt minus the payoff of a put option on the firm with exercise price equal to the face value of the debt
- D(V, F, T, t) the value of debt
- V the value of the firm
- F the face value of the firm’s only zero-coupon debt maturing at T
- Pt(T) the price at t of a zero-coupon bond that pays $1 at T
- p(V, F, T, t) is the price of a put with exercise price F on firm value V
Vasicek model
- Is a model describing the evolution of interest rates
- rt is the current spot interest rate and Ɛt is a random shock.
- When λ is positive, the interest rate reverts to a long-run mean of k
- The Vasicek model incorporates mean reversion. The flexibility of the model also allows for risk premium, which enters into the model as constant drift or a drift that changes over time. In a model with mean reversion, shocks to the short rate affect shortterm rates more than longer-term rates and give rise to a downward-sloping term structure of volatility.
Vulnerable call option payoff
- V is the firm value of the call writer
- S is the stock price
- K is the exercise price
The Merton model
- The Merton model allows us to price risky debt by viewing it as risk-free debt minus a put written on the firm issuing the debt.
- The Merton model is practical mostly for simple capital structures with one debt issue that has no coupons.
Yield spread
Yield spread is the difference between the yield to maturity of a credit-risky bond and that of a benchmark government bond with the same or approximately the same maturity. The yield spread is used more often in price quotes than in fixed-income analysis.
i-spread
The i-(or interpolated) spread is the difference between the yield of the credit-risky bond and the linearly interpolated yield between the two benchmark government bonds or swap rates with maturities flanking that of the credit-risky bond. Like yield spread, it is used mainly for quoting purposes.
z-spread
The z-(or zero-coupon) spread builds on the zero-coupon Libor curve. It is generally defined as the spread that must be added to the Libor spot curve to arrive at the market price of the bond, but may also be measured relative to a government bond curve.
spread01
Measures the change in the value of a credit-risky bond for a one basis point change in spread
The default time distribution function or cumulative
default time distribution F(t)
Is the probability of default sometime between now and time t
The default time density function or marginal default probability
Is the derivative of the default time distribution
Conditional default probability over some horizon (t, t + τ) given that there has been no default prior to time t
z-spread relation to the hazard rate
- R = recovery rate
The conditional default probability at time t, the probability that the company will default over the next instant, given that it has survived up until time t, is denoted λ(t), t ∈ [0, ∞)
Joint default probability of two Bernoulli variables
Securitizations levels
- Asset-backed securities(ABS)
- Mortgage-backed securities (MBS)
- Collateralized loan obligations (CLOs)
- Securitizations that repackage other securitizations are called collateralized debt obligations (CDOs)
- CDOs, issuing bonds against a collateral pool consisting of ABS, MBS, or CLOs, collateralized mortgage obligations (CMOs), or collateralized bond obligations (CBOs)
Weighted average life (WAL)
The weighted average of the number of years each dollar of par value of the bond will remain outstanding before it is repaid or amortized
The waterfall
Refers to the rules about how the cash flows from the collateral are distributed to the various securities in the capital structure.
Settlement and Pre-settlement risk
- Pre-settlement risk. This is the risk that a counterparty will default prior to the final settlement of the transaction (at expiration). This is what “counterparty risk” usually refers to.
- Settlement risk. This arises at settlement times due to timing differences between when each party performs on its obliga-tions under the contract.
Types of CSA
- Counterparty risk (CVA)
- Funding (FVA)
- Collateral terms (ColVA)
- Capital requirements (KVA)
Netting factor
- n represents the number of exposures
- ρ is the average correlation
- Lower is better
Credit Value Adjustment (CVA) Formula
CVA example
CVA and DVA
- DVA is a component of counterparty credit risk arising from a party’s ability to value the potential benefits they make from defaulting.
BCVA = Bilateral CVA - NEE (Sometimes ENE) = Negative expected exposure
BCVA as a function of expected exposures and spreads
- EPE - Expected positive exposure
- ENE - Expected negative exposure
CVA conditional on Wrong Way Risk (WWR)
CVA to a counter-party that omits wrong-way risk
BCVA complete formula
- S = The probability that the counterparty has survived until time t - 1
Debt service coverage ratio (DSCR)
Net operating income/Debt payments
Constant Prepayment Rate (CPR)
- SMM - single monthly mortality is the single-month proportional prepayment.
- A SMM of 0.65% means that approximately 0.65% of the remaining mortgage balance at the beginning of the month, less the scheduled principal payment, will prepay that month.
Public Securities Association (PSA)
- m = number of months since origination
Loan Originator
The loan originator is the original lender who creates the debt obligations in the collateral pool. This is often a bank, for example, when the underlying collateral consists of bank loans or credit card receivables
Underwriter or Arranger
The underwriter or arranger is often, but not always, a large financial intermediary. Typically, the underwriter aggregates the underlying loans, designs the securitization structure and markets the liabilities.
Collateral Loan types of frictions
- Friction between the asset manager and the investor is a principal-agent problem.
- Friction between the arranger and originator is a predatory borrowing and lending problem.
- Friction between the investor and credit rating agencies is a model error problem.
- Friction between the servicer and the mortgagor is a moral hazard problem.
Hazard rate
λ = spread / (1 - recovery rate)
Distance to Default
- F is the debt Face value
- V is the firm’s asset value
Credit Support Annex (CSA) collateral posting requirement
Credit Support Annex (CSA) threshold
- Threshold is the amount of uncollateralized exposure. A lower threshold value means a larger portion of exposure is protected by collateral.
- In contrast, a lower independent amount means a smaller initial margin is posted.
Payment and Close-Out Netting
- Payment netting. This gives a party the ability to net cashflows occurring on the same day sometimes even if they are in different currencies. This typically relates to settlement risk.
- Close-out netting. This allows the termination of all contracts between an insolvent and a solvent counterparty, together with the offsetting of all transaction values (both in a party’s favour and against it). This typically relates to counterparty risk.
Counterparty exposure mitigation
Counterparty exposure, in theory, can be almost completely neutralized as long as a sufficient amount of high-quality collateral, such as cash or short-term investment grade government bonds, is held against it. If the counterparty were to default, the holder of an open derivative contract with exposure to that counterparty would be allowed to receive the collateral.
Probability and joint probability of survival
Marginal and cumulative probability of default
Calculating net exposure per counterparty
When net exposure is negative, use $0
Implied default correlation for a pair of credit asssets
The average spread of a company’s bond
Credit spread = RD - Rf = -(1/T) * ln(D/F) - Rf
- RD = yield of the debt
- Rf = risk-free rate
- D = value of debt
- F = face value of debt
- T = maturity
