3-3-1. Definition: http://www.investopedia.com/terms/e/economic-capital.asp
3-3-2. Economic Capital Calculation
Economic Capital = EV - P(c)
where:
EV = Expected Portfolio Value = V0(1 + ER)
V0 = Prevailing Mark to Market Portfolio Value
ER = Expected Portfolio Return
P(c) = Portfolio Value in the worst-case scenario at the (1 - c) confidence level
EL (Expected Loss) = FV - EV
FV = Forward Portfolio Value = V0(1 + PR)
PR = Promised Portfolio Return
*CreditMetrics => Standard Deviation Estimates for each loan or bond in a portfolio & Change to an exisiting portfolio's Standard Deviation => assessing the Diversification Effects
3-4. Asset Correlations
- Mulifactor Analysis based on the country & industry -> manageable correlation matrics
- Country & industry weights to each borrower along with uncorrelated unique risks
3-5. Exposures
- Future CF at risk beyond the one-year horizon <-> Derivatives: exposure dependent on future interest rates
- Forward Price & Exposure Distribution for interest rate swaps
3-6. Credit Risk Portfolio Approaches
3-6-1. Moody's KMV Portfolio Manager
- default probabilities are estimated using an option-based Merton model approach
- structural model (default probability is endogenous)
- default probability: a function of firm asset growth & the level of debt; the higher the growth & lower the debt level -> the lower the default probability
- default probability correlations are measured using equity correlation
3-6-2. JP Morgan CreditMetrics
- historical data -> historical transition migration matrics
- correlations in changes in credit ratings are modeled
*assumption: firms within the same credit rating have the same default probabilities
- measuring marked-to-model losses
**marked to model: the pricing of a specific assets or portfolio based on internal assumptions or financial models <-> mark-to-market valuation
- LGD is taken into account using beta distribution
- equity correlations are utilized for default probability correlations
- incorporating B/S to differentiate credit risk of issuers within the same rating
3-6-3. Kamakura Risk Manager
- reduced form model
- default probability: exogenous based on equity prices
- default probability and recovery rates are correlated within rating categories
3-6-4. Credit Suisse Financial Products (CSFP) CreditRisk+
- default probabilities & default probability correlations by sector
- derault rate = continuous random variable
- pairwise correlation of defaults
- conceptually similar to Term Structure Models of the yield curve -> appropriate for a buy-and-hold strategy
- the number of default events approximated by a Poisson distribution
- assumption: the exposure to systematic risk are the same within sectors
**term-structure: a function that relates a certain financial variable or parameter to its maturity. e.g.) term-structures of option = volatilities, credit spreads, variance swaps, etc
Term structures often are not directly observable
**term-structure model: Lattice models, Stochastic calculus, Short-rate Models, Heath-Jarrow-Morton models, Market models
3-6-5. McKinsey CreditPortfolioViewTM
- macroeconomic factors: unemployment rates, rates of growth in GDP, long-term interest rate levels, foreign exchange rates, aggregate savings rates
- multifactor model for simulating joint conditional distributions of credit migration & default probabilities (for different country and industry)
- simulating joint conditional distributions of credit migration and default probabilities
- a regression approach
**correlation between recovery rates & default probabilites
- traditionally ignored by credit risk models: recovery rate regarded as constant or a stochastic value independent of default probaility
- during recessions, negatively correlated
3-6-6. Altman's Portfolio Approach
- applying the portfolio optimization techniques to fixed income securities using a variant of the Sharpe ratio
EAR = YTM - EAL
where:
EAR = Expected Annual Return
YTM = Yield to Maturity
EAL = Expected Annual Loss
- EAL based on historic mortality rates & losses for specific bond ratings
e.g.) BB-rated bond, promised yield of 9.0% with a spread of 2.0% over 7.0% risk-free T-bond, expected annual loss of 91 basis points
=> EAR = 9.0% - 0.91% = 8.09% or risk-premium of 109 basis points over risk-free rate
- commercial loans: no explicit risk rating => linking with the public rating system => utilizing credit migration, default, recovery experience from a large database of debt securities
- Expected Portfolio Return:
where:
Xi = weight of bond of loan i to the value of the portfolio
VP = portfolio variance
***Sharpe ratio of optimized bonds portfolio is greater than that of an equally weighted portfolio
3-6-7. Z'-Score Model
**video clip: http://www.youtube.com/watch?v=tnADtb-BfFI
- modified z-score: the higher the z'-score, the higher the credit rating
z'-score = 6.56 X1 + 3.26 X2 + 6.72 X3 + 1.05 X4 + 3.25
where:
X1 = WC/TA
X2 = RE/TA
X3 = EBIT/TA
X4 = B.V. of Equity/Total Liabilities
- Portfolio risk using unexpected losses:
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