About the simple (two variable) regression function and its notation
The bivariate normal distribution (common in credit risk) gives the joint probability for two normally distributed random variables
The factors that impact the cost of asset liquidation: Market microstructure (dealership structure and temporal aggregation), time horizon, asset type (simple vs. complex), and asset fungibility
A securitization is a structured finance with three ingredients: 1. Pooled credit-sensitive assets; 2. Transfer of credit risk; 3. Tranched liabilities
The capital market line is determined by a mix of: the riskfree asset and the market portfolio. The market portfolio, in turn, consists of all risky assets (this example has only two assets).
08:20
Risk contribution of credit to portfolio unexpected loss
Risk contribution is analogous to systematic risk in single-factor (capital asset pricing model): as Ong says, it is a measure of the âundiversified risk of an asset in the portfolio. It is the amount of credit risk which cannot be diversified away by placing the asset in the portfolio.â
Yesterday I reviewed the beta distribution used to characterize the LGD random variable (recovery/loss conditional on default). According to de Servigny (Chapter 4), the key determinants of recovery are: Seniority, Industry, Business cycle, Collateral, Jurisdiction, and Bargaining power.
Under the corporation, the original credit-sensitive assets serve as collateral for the asset-backed securities issued to investors. Under the trusts, as the Master Trust deposits assets into the Grantor trust in exchange for a beneficial interest, the beneficial interest serve as the collateral.
09:15
Basel internal ratings-based (IRB) risk weight function
Basel's IRB determines a capital charge (K) = Credit Value at Risk (CVaR) @ 99.9% – Expected Loss (UL). This function is estimating an unexpected loss (UL).
In subprime securitization, seven frictions are identified, but the key frictions are the five represented by the red line that runs from friction #1 (borrower and originator) to friction #6 (the principal-agent problem between investor and asset manager). The essential problem (though several factors contribute) is that the originator and arranger were able to arbitrage the rating agency models.
09:28
Expected default frequency (EDF, PD) with Merton Model
A visual and Excel-based review of the Merton model used to estimate EDF (or probability of default). This is a structural approach; i.e,. default is predicted by the firm's balance sheet properties
08:42
Unexpected loss (UL) of a portfolio of credit assets
The unexpected loss (UL) of a portfolio of credit assets incorporate individual asset ULs and pairwise default correlations
INTERNAL enhancements include subordination (a feature of tranching; a senior tranche is protected by subordinate tranches), overcollateralization (which includes direct equity, holdback and cash collateral account) and an excess spread. EXTERNAL refers to enhancement provided by banks outside the structure (e.g., letter of credit) or counterparties outside the structure (e.g., basket credit default swap)
An attempt to review the justification for Adjusted Risk-adjusted Return on Capital (ARAROC) which is a "second generation" RAROC. Spreadsheet can be downloaded at my website.
The security market line (SML) plots the expected return of an asset (or portfolio) as a function of the asset's beta.
Quick overview of Basel II framework that sets capital requirements for banks. Three pillars contains the rules & support (supervisor review, market discipline) that say how much eligible regulatory capital must be held against risk-weighted assets.
There are three approaches to operational risk in Basel II: basic indicator (BIA), standardized (SA), and advanced measurement approach (AMA). BIA is alpha (15%) of the bank’s total gross operating income (GOI). SA weights the charge by business line (12%, 15% or 18% depending on the business line)
RAPMs are variations of: return per unit of risk. Treynor and Sharpe are similar: both are excess return per unit of risk. Treynor defines risk as systematic risk (beta) and is therefore appropriate to well-diversified portfolios (i.e., into such portfolios idiosyncratic risk is eliminated); Sharpe defines risk as total risk (volatility). Jensen’s alpha is outperformance relative to expected performance under CAPM.
Beta is covariance (x,y)/variance(y). It has many applications. Including, for example, the minimum hedge ratio for a future hedge on a commodity, the capital asset pricing model (CAPM), cash flow beta, and marginal value at risk (marginal VaR).
Adjusted Exposure (AE) is a component of credit portfolio expected loss (EL). The adjusted exposure is only the risky portion of the loan asset. It consist of: 1. All outstanding (OS) and 2. Usage given default (UGD) multiplied by commitments. Usage given default (UGD) parameterizes credit optionality: with a commitment, the bank grants a âcredit optionâ to the borrower.
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