Ch6 Extending VaR to Non-Tradable Loans (1)

1. Traditional Approaches to Measuring Credit Risk
1-1. Traditional Approaches
- Expert Systems
- Rating Systems
- Credit Scoring Models

1-2. Features
- focus only on the probability of default => they do not address the amount of loss in the event of default
- ignore losses incurred from credit downgrades or upgrades for which mark to market models measure


1-3. Expert Systems
based on the opinions of experts
=> not a precise methodology for assigning weight or ranking the five Cs

**five Cs of credit
- Character(reputation): management's integrity & its commitment to repay the loan
- Capital(amount): relationship between equity and debt
- Capacity(earnings volatility): corporate borrower's ability to generate cash flow or liquidate short-term assets to repqy its debt obligation
- Collateral: assets offered as security for the debt as well as other assets controlled by the issuer
- Cycle(economic cycle): how the current state of the economy will impact exposure to credit risk


**Neural Network:
- One way to remove some of the subjectivity
- Flexible & adaptable systems that incorporate changing conditions in a systmatic way into the decision-making process
- Drawback: costly to implement & maintain, overfitting



1-4. Rating System
1-4-1. External rating system: e.g.) Moody's, S&P
- Through-the-cycle assessments: They provide the probability of default at the worst point in the business cycle and are more appropriate for lending decisions
- At-the-point (point-in-time) assesments: The relate to changes in cyclical condition and are more appropriate for capital allocation.

1-4-2. Internal rating system



1-5. Credit Scoring Models
It assign a Z-score that classifies a borrower as good or bad, and the Z-score can then be translated into a probability of default measure.
- Strengths: lower cost, less subjectivity than the expert systems approach
- Drawbacks: data limitations (from B/S => not updated frequently), linear models (some of the relationship - nonlinear), only explanation of 2 stay (default or no default), static betas, only consideration of 5 fundamental variables (do not consider non-quantifiable variables)


Ref video clip: http://www.youtube.com/watch?v=tnADtb-BfFI
- Variables:
X1 = Working Capital / Total Assets
X2 = Retained Earnings / Total Assets
X3 = EBIT / Total Assets
X4 = Market Value of Equity / Book Value of Total Liability
X5 = Sales / Total Assets


- Altman's Z function:
Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5

- Interpretation


2. Estimating Default Probabilities
Two approaches for measuring the risk-neutral default probabilities
- options-theoretical structure approach: equity prices & risk-free debt prices; Endogenous(Asset/Liability); Merton's & KMV --> A firm defaults if its assets are insufficient and a corporate liability characterized as an option on the firm's assets
- reduced form approach: risky debt prices; Exogenous(Debt Prices); tractability & empirical fit --> silent about why a firm defaults. Prices of credit-sensitive securities can be canclulated as if they were default-free using an interest rate that is the risk-free rate adjusted by the intensity
- incomplete-information approach

Probability of default => VaR computes estimates of loss
Either approach can be used to estimate the possibility of each credit event occuring (e.g., upgrades, downgrades, defaults)



2-1. Merton Model

Merton models equity in a levered firm as a call option on the firm's assets with a strike price equal to the debt repayment amount.

2-1-1. Firm's Equity Value

where:
A = M.V. of the firm's assets
StdDev A = standard deviation of the firm's M.V. of assets
r = risk-free rate
T = time to expiration
B = expected price, face value of the firm's debt

**volatility & M.V. of assets are unknowns
StdDev(E) estimated from a time series of equity prices
=> using two equations, two unkowns can be solved. These values are combined with the amount of debt liabilities B to calculate the firm's current Distance to Default (the number of standard deviations between current asset values and the debt repayment amount). The greater the Distance to Default, the lower the PD (or expected default frequency, EDF)
==> N(-d2) = NORMSDIST(-d2) = probability of default or EDF