Ch6 Loss Given Default

1. Suboptimal Loan Recovery Rates
1-1.LGD (Loss Given Default)


**Definition: http://investopedia.com/terms/l/lossgivendefault.asp
The amount of funds that is lost by a bank or other financial institution when a borrower defaults on a loan.

1-2. Factors that lead to suboptimal(inefficient) behavior and to suboptimal loan recovery rates (IAW researchers)
- debt structure -> inefficient behavior; a risk of creditors' run in the absence of creditors' coordination
- bargaining power of debtor who tries to extract concessions from creditors
- senior debt: excessive right or control -> lazy banking
- house banks





2. Recovery Rates of Traded Bonds
***recovery rate = PV(CF after default) / exposure-at-default

**Determinants or Key drivers
*video clip: http://www.youtube.com/watch?v=4rMxLgOEZ-U
2-1. By Seniority
- Bank debt(70-80%)
- Bank Secured notes (45-70%)
- Bank unsecured notes (35-50%)
- Senior subordinated notes (20-40%)
- Subordinated notes (15-30%)
- Junior Subordinated notes (2.5-20%)
* The more senior, the higher recovery rate

2-2. By Industry
- Public Utilities: ~70%
- Lodging: ~26%
**Creteria: physical asset obsolescence
**Industry growth
**Industry concentration: lower concentration -> higher recovery

2-3. Business Cycle
- Peak Cycle: 65%
- Recession: 30%

2-4. Collateral
- PD vs. Recovery: inversly correlated
- PD vs. LGD: positively correlated

2-5. Jurisdiction

2-6. Bargaining Power


**Demand for bonds in default: A large number of vulture funds, buyers of bonds in default, would increase the recovery rate

**Distressed firm: informal reorganization -> lower costs & increase recovery rates





3. Recovery Functions
- Credit VaR computed -> incorporating an accurate representation of recovery rates
- Constant recovery rate: underestimation of a firm's true credit VaR (large StdDev associated with recovery rates)

3-1. Modeling LGD
Fitting the recovery function: estimating how much the holder of the debt will get in the event of default


3-2. Beta Distribution
A parametric statistical distribution that depends on two inputs for calibration, mean & variance. Most portfolio credit risk models, including Portfolio Manager, Portfolio Risk Tracker, and CreditMetrics, assume that the recovery rate follows a beta distribution. The beta distribution is particularly convenient for modeling recovery rates because the support of the distribution lies in the interval between 0 and 1.

3-2-1. Video clips: http://www.youtube.com/watch?v=yQn_dD85pNw

3-2-2. Expected Loss Expression:
EL = AE x EDF x LGD
where:
AE = Adjusted Exposure
EDF = Expected Default Frequency (probability of default)

**LGD
- hard to parameterize
- uncertainty of the average value of LGD becaue of the following factors
---cyclical: sensitive to macroeconomic
---variable mean (seniority, industry, collateral) -> average recovery rate are variable
---volatile (hidg std. dev.)

The parameter alpha and beta enable the calibration of the mean and the variance of the distribution.

**alpha (centre) = steepness of HUMP
**beta (shape) = Fatness of Tail


e.g.) Junior: alpha = 2.0, beta = 6.0 -> Mean recovery = alpha / (alpha + beta) = 2.0 / (2.0 + 6.0) = 25%
Senior: alpha = 4.0, beta = 3.3 -> Mean recovery = 55%


3-2-3. Common for LGD
Virtue
- Compact (two parmas) and bounds [0,1]
- Flexible (alpha = centre, beta = shape)
Drawbacks
- Only unimodal not bimodal
- Cannot cope with point masses at 0 and 100%


3-3. Kernel Estimation
Beta distribution does not necessarily ensure a good of fit of the true recovery distribution.
Standard kernel estimators use probability density functions and have nonbounded support, which will lead to density estimates that ranges [- infinity, + infinity]. We can perform the estimation using a standard kernel on the transformed data. We then apply the inverse transformation to obtain a [0, 1] density as desired.

Kernel estimators allocated differenct weights to each observation. A kernel estimator of a density at a given point x will allocate weight to all observations in the sample.

The density estimate at x is:

where:
K(.) = symmetric probability density function
h = bandwidth (window width) -> degree of smoothness of the estimation - the larger the
bandwidth, the smoother the estimation

3-4. Conditional Recovery Modeling
An alternative parametric methodology to estimate the optimal probability density functions for ultimate recovery conditional on several explanatory variables.
**commonly used explanatory variables:
- Collateral quality
- Debt below class
- Debt above class
- Aggregate default rate

***Advantage
- A large concentration of occurrences at 0% & 100% recovery while computing a continuous probability density function for the range [0, 120 percent].