A simple (two-variable) regression has three standard errors: one for each coefficient (slope, intercept) and one for the predicted Y (standard error of regression). While the population regression function (PRF) is singular, sample regression functions (SRF) are plural. Each sample produces a (slightly?) different SRF. So, the coefficients exhibit dispersion (sampling distribution). The standard error is the measure of this dispersion: it is the standard deviation of the coefficient.
The bivariate normal distribution (common in credit risk) gives the joint probability for two normally distributed random variables
About the simple (two variable) regression function and its notation
A securitization is a structured finance with three ingredients: 1. Pooled credit-sensitive assets; 2. Transfer of credit risk; 3. Tranched liabilities
Review of key players including special originator, purpose entity, custodian, underwriter, investors, legal, and credit rating agencies
How the RSS is calculated (test of FLV format)
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.
This is a review which follows Jorion's (Chapter 7) calculation of marginal value at risk (marginal VaR). Marginal VaR requires that we calculate the beta of a position with respect to the portfolio.
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).
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
In MG, the underlyings were short positions in long-term forward contracts to deliver oil. The hedge was a stack-and-roll hedge: long positions in short-term futures contracts that were rolled over consecutively. The strategy depended on the continuation of (i) stable or gently increasing spot oil prices and (ii) backwardation
Liquidity adjusted value at risk (LVaR)adjusts (increases) VaR as a function of the bid-ask spread.
RAROC is a risk-adjusted performance measure (RAPM): risk-adjusted return divided by economic capital (i.e., the capital reserved to cover unexpected losses).
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).
For secured (collateralized) exposures, the simple approach to CRM substitutes the risk-weight of the collateral (i.e., it operates on the risk-weight term of the formula). For secured (collateralized) exposures, the comprehensive approach adjusts the net exposure (i.e., it operated on the exposure term of the formula).
ABX introduced a means for the transparent pricing of subprime risk (where previously there was none). In the second part of this briefcast, I show how the authors instructively calculate the implied spread given the index price.
07:58
Expected loss (EL) on credit asset if PD, LGD are correlated
Expected loss (EL) calculations typically assume no correlation (i.e., they assume independence) between probability of default (PD) and loss given default (LGD). Basel II internal ratings-based (IRB) approach to a capital charge assumes independence between PD & LGD. How can we compute expected loss (EL) if there is correlation between EDF/PD and LGD/recovery?
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)
The security market line (SML) plots the expected return of an asset (or portfolio) as a function of the asset's beta.
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