FC2Video

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

SaR is value at risk (VaR) for a pension fund.

The best hedge is based on portfolio volatility in the mean-variance framework. Specifically, 1. Given a current portfolio with value (W), and 2. Given an asset (A) with correlation (rho) to the portfolio, 3. What is the trade that produces the minimum volatility for the new portfolio (W+a)?

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.

The security market line (SML) plots the expected return of an asset (or portfolio) as a function of the asset's beta.

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).

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.

The very traditional (mean-variance) two asset portfolio volatility is largely a function of asset correlation/covariance.

The next building block is mapping transitional probabilities to standard normal variables; then using a bivariate normal to capture joint probabilities of default

The bivariate normal distribution (common in credit risk) gives the joint probability for two normally distributed random variables

A review of the method used in the first building block of CreditMetrics, a ratings-based credit risk portfolio model

The key idea in valuing a CDS is a fair deal: the (probability-adjusted) expected PAYMENTS (i.e., made by protection buyer) should equal the expected PAYOFF (contingent, made by seller)

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)

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).

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).

The standard approach is a lookup table based on (i) external credit rating and (ii) the type of counterparty.

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.

A brief review of Crouhy’s approach to setting the internal capital charge for market risk. Internal means to distinguish from regulatory (external) capital requirements such as Basel II.

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.

RAROC is a risk-adjusted performance measure (RAPM): risk-adjusted return divided by economic capital (i.e., the capital reserved to cover unexpected losses).

Liquidity adjusted value at risk (LVaR)adjusts (increases) VaR as a function of the bid-ask spread.

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

This continues to follow the subprime securitization case study by Aschraft. There are two steps: 1. Specify the loss distribution; and 2. Map the target credit rating to the implied credit enhancement

This reviews the definition of subprime and highlights the startling trends in subprime MBS origination from 1999 to 2006.

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.

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.

Internal liquidity support includes: Liability design (e.g., time tranching) or a Liquidity Reserve. External support includes: Lines of credit (LOC) and asset swaps

The net excess spread is a type of internal credit enhancement in a securitization. In this simple structure, $100 million in loan assets are securitized by way of two bond class issuances (senior and subordinated debt). The excess spread can be diverted on a post or pre-loss basis (pre-loss: deposited into cash collateral account).

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)

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.

In a securitization, we can take a balance-sheet perspective: on the left-hand side, credit-sensitive assets (collateral) have value, create cash flow, and contain risk; on the right, liabilities (tranches issued to investors) IN TOTAL must preserve value, cash flow and risk.

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

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).

Risk contribution is analogous to systematic risk in single-factor (capital asset pricing model): as Ong says, it is a measure of the “undiversified 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.”

The unexpected loss (UL) of a portfolio of credit assets incorporate individual asset ULs and pairwise default correlations

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?

A review of Michael Ong’s unexpected loss (UL) for a single credit-asset. First, I briefly compare the various definitions of unexpected loss we encounter in the FRM; they are not so different. Ong’s UL is a single standard deviation (i.e., low confidence) while economic and regulatory capital (reflecting high confidence levels) are some multiple of Ong’s UL.

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.

The beta distribution is typically used for modeling loss given default (1 - recovery rate).

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

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 “credit option” to the borrower.

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.

How the RSS is calculated (test of FLV format)

About the simple (two variable) regression function and its notation