Ch6 Applications of Portfolio Approaches (1)

1. Diversification & Risk-Neutral Pricing
- Mrkowitz's Efficient Frontier: difficulty to apply to fixed income securities: fat-tailed asymmetric (limited upside & greater amounts of downside)
- Merton: equity & debt prices modeled with options => Moody's KMV model
DD(distance to default) & EDF(expected default frequency)
**Moody's KMV Model: applying asset correlations to credit quality correlations
- Risk Neutral: fixed income investors require risk-free rate plus some return to cover expected losses based on the true probability of default
- Difference between risk-neutral & true probability of default used to assess the difference between expected & unexpected losses

** CreditMetrics Model: modeling credit quality transitions


2. CreditMetrics Framework
**video clips: http://www.youtube.com/watch?v=CMn3q9gO3tM
http://www.youtube.com/watch?v=gyy0lXlXpCU

2-1. CreditMetrics Four Building Blocks by JP Morgan
i. VaR due to Credit: Credit Rating, Migration Likelihoods, Seniority, Credit Spreads, Recovery Rate, PV Bond Revaluation => Standard Deviation of value due to credit quality changes for a single exposure
ii. Portfolio Value due to Credit
iii. Exposures: User Portfolio, Market Volatilities, Exposure Distributions (support ii)
iv. Correlations: Rating-Equity Series, Models, Joint Credit Migrations (support ii)


2-2. Four steps for measuring credit risk
i. Specify one-year transition (migration) matrix
ii. Specify an appropriate time horizon
iii. Specify forward-pricing model (one-year forward zero curves): calculating possible one-year forward values for the bond
iv. Specify forward distribution of bond (portfolio) changes:
Probability Weighted Value = Probability of State x P.V. of Bond
Delta = Probability Weighted Value - Mean Value
Variance = Delta ^ 2 x Probability of State

2-3. Transition Matrix
- Rating categories & the probabilities of credit risk migrating from one risk-rating category to another over a given credit risk horizon
- Historical averages for a broad sample of loans & bonds => it is necessary to adjust a transition matrix to be consistent with prevailing economic conditions and the composition of the loan or bond portfolio.

2-4. Forward Pricing Model
A bond or loan is valued at the end of the year in each of the credit categories in the transition matrix. Based on the forward values, the percentage change in value as a result of rating changes can be calculated.

2-5. Distribution of the Changes in Portfolio Value
A distribution for the changes in the value of a bond or loan over the credit horizon can be generated using the transition matrix and end-of-year value changes for a bond or loan.


3. Portfolio Credit VaR
3-1. CreditMetrics Joint Migration Probability
i. One-year transition matrix
ii. Specify horizons
iii. Calculate cumulative probabilities using transition probabilities & threshold values (=NORMSINV(.))
iv. Calculate correlation between asset returns (=BIVAR(threshold vlaueA, threshold valueB,rho)) <- multivariate distribution

e.g.) joint migration prob. that AA-rated will be AA-rated & BB-rated will be BB-rated at year-end => 0.9065 x 0.8053 = 0.73

3-2. assumption:
- zero correlation among rating changes
- equity returns are an appropriate proxy for asset returns

***cons
- assumed zero correlation => accurate estimation of rating change correlation among assets
- industry & state of the economy influences defaults & defualt correlations => migration probabilities do not remain stable over time
- asset values are not directly observable
- equity returns are an appropriate proxy for asset returns => suspect for high leveraged firms

***Monte Carlo Simulation