In addition to analyzing individual companies and agencies it is also necessary to review the credit risk of a single obligor over a length of time, the credit risk of the daily and long-term trading activity (equities, debt, commodities, derivatives),

and the credit risk of managing a portfolio of investments (debt and / or equity securities and related derivative instruments). Measurement At the most basic measurement, loan counterparty / credit default increases with the existence and depth of an economic recession when profitability is under pressure. Essentially, an individual company is not earning enough (nor has sufficient equity) to cover its operating expenses or cover interest and principal repayment of borrowed funds. Thus, the "quality" of the present business / economic cycle is a possible predictor of default. |

However, the basic model does not take into account for additional business ventures or acquisitions a company may engage in during ideal economic conditions. Nor does it consider the level of sophistication companies and financial institutions engage in to purchase financial products or utilize methodologies to manage and mitigate risk. It does not recognize the risk of managing a portfolio of assets (and corresponding liabilities). Nor does it consider the sophistication of markets and exchanges or electronic / telephonic communications and payments systems or computer database systems that respond immediately to market, social and political volatility.

Thus, quantitative measurement tools and methodologies are used to determine the value of an asset in response to market volatility or the likelihood of incurring a loss related to the predicted value of an asset over time in response to market volatility or default risk, and what value may be recovered from an impaired asset.**Beta (ß) Portfolio Measurement**

Beta (ß): is a gauge of sensitivity to market moves; if one invests in many stocks across a wide sector of services, industries and geographic location, then one is considered to have a portfolio that matches the market and is well diversified as a decline in some stocks will be offset by the increase in value of other stocks, thus beta equals 1.0 (or the market). Stocks are measured relative to their historical movement in relation to the market (a well diversified portfolio or benchmark such as the S&P 500). Thus, a stock with a Beta over 1.0 will move further, either positively or negatively in value, in relation to market movements, while a Beta less than 1.0 will not move/fluctuate as much as the market. Beta is historical and may not accurately reflect a portfolio/stock's present volatility.

Before drawing any conclusions from a fund's beta, it is a good idea to find out the R2 associated with the beta. R2 is a measurement of how well the portfolio's performance correlates with the performance of the benchmark index measured over three years. An R2 of 1.0 indicates a perfect correlation, while an R2 of 0.00 indicates no correlation

**Options Measurement**

Delta: how the price of an option will change as the price of the underlying asset/index will change.

Delta hedging: hedging of option positions.

Kappa: how the value of an option changes as interest rates change.

Theta: how fast an options value will decline as expiration approaches?

Vega: Coefficient measuring the sensitivity of an option value to a change or undervaluation of volatility.

**Portfolio Measurement**

< The of assets on option put as valued be can company any debt that proposes Model>

Monte Carlo method: random path generating as a simulation method to depict a wide range of potential market outcomes (parametric probability model).

MPT: Modern Portfolio Theory, an investor looks at expected returns and the standard deviations (volatility of returns) thereof to construct an efficient portfolio.

Sharpe Ratio: A measure of risk adjusted return, this ratio compares the reward for pure risk-taking with the volatility of the investment. The formula is the annual rate of return minus the rate of a risk-free (T-bill) investment divided by the annualized standard deviation. The larger the figure the better the investment. It can also be determined as a Monthly figure:

Monthly Sharpe Ratio = Average Monthly Return - Risk Free Return

Monthly Standard Deviation

RAROC (Risk-Adjusted Return On Capital) was originally developed by Banker's Trust for the allocation of capital.

**Standard Deviation: **quantitative measurement of the historical volatility of an asset/portfolio's returns in terms of the dispersion of returns (independent of some benchmark). The purpose is to determine how much fluctuation there has been around the average annual return. Example: if the average annual return is 12%, and the standard deviation is 10%, then that means the asset/portfolio's return could have been as high a 22% (12% + 10%) or as low as 2% (12% - 10%). However, as a statistical analysis tool, one standard deviation indicates that there is only a 68% chance that the return will be within this range. Two standard deviations give us a 95% confidence level that the range of return will be between -8% (2% - 10%) and 32% (22% + 10%).**Stress testing**: constructing possible scenarios/paradigms, everything from market to political changes, and how it may affect the value of the asset. Calculates what will happen to the value of a particular derivative or an entire portfolio if certain events occur.

Volatility: is a statistical measure of the tendency of the price of a share, commodity or bond to vary over time. It is one of the most important components in pricing options and other derivatives. Volatility increases with time.**Basel I Accord and Basel II Accord**

The 1988 Basel I Accord required banks to do a better job at evaluating the real risk of their various businesses and how much capital should be reserved for various financial transactions. Many of the credit risk measurement methodologies were developed in response. Basel II will allow banks to have more flexibility in measuring credit risk by allowing them to be able to select among three regulatory frameworks to calculate capital requirements for credit risk:

Standard

Internal ratings based (IRB)

Advanced IRB (approved by U.S. regulators) **VaR (Value at Risk)**

VaR does not predict market volatility. Rather, it is a statistical measure / model (at 95% to 99% confidence level) that can be used to determine the maximum potential future one-day loss in the fair value of interest rate, foreign exchange and certain equity market sensitive financial instruments that may result from market volatility based on the current exposure the firm has. The VaR acronym itself has become somewhat generic and VaR is calculated several different ways by either proprietary models at financial institutions or commercially offered packages (Credit Metrics, Credit Risk+, Risk Metrics, Algologist from Algorithmic, SunGard Data systems offers Credient and Banc ware through its subsidiary Trading and Risk Systems). However, the result is an industry standard and is used and reported widely to estimate the potential decline in the value of a position or a portfolio, under normal market conditions, again over a one-day holding period with a statistical 95% / 99% confidence level, by subjecting the position or portfolio to certain previously observed and recorded volatilities and correlations / sensitivity to the volatility.

**Risk Metrics (Credit Metrics)**

Some of the original development of the VAR concept and one of the first commercially available VAR packages was the Credit Metrics package developed by J.P. Morgan. In 1988, JP Morgan spun-off its Risk Management Products Group and Risk Metrics was created. The company offers several quantitative credit analysis products such as Risk Metrics™, Credit Metrics™, Data Metrics™, Corporate Metrics™ and Risk Grades™. In August 2000, Risk Metrics and Moody's Risk Management Service (MRMS) formed a strategic alliance and Moody's RiskCalc™ default prediction models were integrated with Risk Metrics' Credit Manager™ product (the software package of Credit Metrics methodology). RiskCalc™ / Credit Manager™ is used to measure total portfolio (bonds, loans and derivatives) VaR / credit exposure, especially in response to credit events such as Moody's credit upgrades and downgrades.

Credit Metrics VaR can be measured as a Variance / Covariance model in which each instrument is associated with some market factors that determine the variance of the instrument's value. For instance, a single basis point change in market interest rates can be used to measure the variance of the price of a bond. Thus, there are a range of prices for the bond as market interest rates increase by one basis point at a time above the coupon interest rate and a range of prices as market interest rates decline one basis point at a time below the coupon interest rate. The sophistication and complexity of VAR becomes evident if an additional hedging instrument for the bond is included in the equation and a portfolio of bonds is considered rather than a single bond (variance/covariance matrix model).

With regard to loans, the methodology allows for a review of loan portfolios to determine how concentration of loans to a particular country or industry will affect the portfolio if there is widespread downgrade or default; and what the correlation might be between various concentrations within the portfolio. The analysis requires that the institution know how much it will earn if the loan matures, how likely the borrower will default, and how much the institution can expect to get back after default (weak point in the equation).

Difficult to measure credit risk within the context of a portfolio as one finds less correlation in a credit portfolio as opposed to an equity portfolio as the chances of two individual entities defaulting simultaneously is remote.

The model attempts to calculate a Credit VAR for the portfolio through:

Calculate exposure to a specific credit (loans and/or market-sensitive products)

Probability of each credit being subject to a credit event over a given time horizon, such as an upgrade, downgrade (migrations) or default, and calculates a distribution of values for each potential migration.

Individual value distributions for each credit are assimilated through a portfolio to give an overall VAR statement.

An attempt to express counterparty default probabilities as options. The default probabilities can be estimated using S&P and Moody's ratings and apply VAR calculations. The options can be sold as derivatives based on whether a trader thinks the credit rating of a company is about to go up or down.

VaR (Value at Risk) looks at historical data (daily, weekly or monthly price data; daily volatility is also derived from the weekly or monthly data by dividing by the square root of the number of trading days in the period) for any asset class, and reduces the risk to its common measure: the standard deviation of changes in value of the portfolio or asset over the course of a specified time period, or the time period required to sell or hedge the portfolio or asset. It considers "two sigma," or two standard deviations from the mean in order to obtain a 99% confidence level of the value of the asset (thus we will know that there is only a 1% chance that change in the value of the asset or yield of the asset will be greater than this maximum in either direction). [From statistics we know that 90% of the area under the normal distribution is to be found within + and - 1.65 standard deviations from the mean, i.e., 1.65s]. For instance, if we determine that the VaR of an asset is 2%, than the potential downside loss on a $1,000 investment in the asset is $20. Secondly, VAR also considers the covariance of how assets move against each other thus, how is the risk profile of the portfolio actually lowered through diversification. The value at risk approach is based on a forecast of the potential worst case estimate of what the actual mark-to-market could equal over a pre-determined time period.

Historical simulation: this technique calculates the change in value of the current portfolio that would have occurred over a set of previous periods, given the actual changes in the market price indices. The standard deviation of the simulated changes is to a 65% confidence level and is limited to those observed values.

Variance/Covariance technique involves calculating the standard deviations of changes for a variety of relevant price indices and generating a matrix of correlations among pairs of indices. The sensitivity of the portfolio instruments to these underlying indices is derived, and the standard deviation of the entire portfolio can be calculated. However, it cannot measure non-linear price sensitivities for instruments to given changes in market indices.

Monte Carlo simulation is a form of stochastic simulation. On the basis of a matrix of variances and covariance’s of market price indices, a large number of values for the indices are generated randomly and used to calculate a range of values for the portfolio. This method is the most complex and computation intensive; however, it is probably the most reliable and can capture non-linear risks (gamma, Vega) in options portfolios.

RIFLE (Risk Identification For Large Exposures)

Risk Identification For Large Exposures (RIFLE) is another risk measurement statistical model.

KMV (Moody's)

Moody's KMV (named after the gentlemen who developed the model, Messer. Kealhofer, McQuown, & Vasicek) is an international database (Credit Research Database / CRD) of records (approximately 30 years compilation) of loan defaults by publicly traded and private corporations. The database is utilized to develop a group of products offered by Moody's to analyze single obligor and portfolio credit quantitative default models. The purpose of the group of products is to develop a more systemic approach to credit analysis compared to a subjective review process. KMV is used by the credit analyst to determine the implied probability of the default of the counterparty.

Expected Default Frequency™ (EDF) is the measurement of the probability of default.

Financial Analyst™ is one of the key components of KMV for considering publicly traded companies with syndicated facilities in the market. The accessed database allows the credit analyst to analyze of cash flows and create customizable ratios for the subject company, and compare it to an industry peer benchmark.

Credit Edge™ (a web browser-based analysis product) utilizes KMV EDF Credit Measure (Expected Default Frequency) measurement of publicly traded companies to predict the likelihood of default risk on a day-to-day basis. The Portfolio Tracker option of Credit Edge produces a quantitative EDF rating, which corresponds to Moody's standard debt rating system (for instance 3.5 / B+). The EDF Analyst option allows one to change variables (capital structure, equity market price, financial statements) of the subject company to determine how it may affect the EDF rating.

Credit Risk+

Credit Risk+ was developed by Credit Suisse First Boston (CSFB) and is a model for determining credit losses in a portfolio.**Operational Risk Measurement**

The Basel II Accord requires that banks set aside capital against operational risk (defined as the risk of direct or indirect loss resulting from inadequate or failed internal processes, business practices, people and systems, or from external events). The measurement of operational risk requires that financial institutions track transactions and measure the failure rate of reconciliation with counterparties. The measurement system must be able to model a probability of events that could occur and may result in an operational loss.

Basel II will allow banks to have some flexibility in measuring operational risk by allowing them to be able to select among three regulatory frameworks to calculate capital requirements for operational risk:

Basic Indicators Approach

Standardized Approach

Advanced Measurement Approach (AMA, which is a financial institution developed proprietary internal capital model; approved by U.S. regulators)

There are some commercially available software packages available such as OpData from Algorithmic

Proprietary systems are in operation with the large banks. J.P. Morgan Chase's has an operational risk measurement system that incorporates the measurement of operational errors by the name of Horizon. Citigroup utilizes EDCS (Events Data Capture System) system to capture historical operational loss data (minimum 3 years as per the Basel II regulation) across the company's entire operations and a probability of events model is based on that historical and present EDCS data.**Management**

Regulatory Capital Adequacy mandates that there is sufficient capital and liquidity to cover short-term and / or unexpected on- and off-balance sheet credit risk and market risk for both financial institutions and broker / dealers.

Utilize a professional portfolio default risk measurement tool (KMV, Credit Metrics), which is designed to correlate a portfolio to real world variable and will calculate the probability of default and the percentage gross lost, and then set VAR limits.

Establish a Daily Settlement Limit with counterparty. This represents the aggregate par value of contracts maturing on any one day.

Execute ISDA Master Trading & Netting Agreements with every counterparty and utilize novation netting (the sum of all trades between parties are added up on both sides and a single net number is transferred between the parties rather than many individual transfers).

Base point value hedge (BPV): longer-term bonds with a maturity of more than 3 years can be hedged comparatively simply by taking an opposite position in futures.

Hedge Ratio = Face Vale Bond x Price Factor CTD x BPV Bond

Face Value Future BPV CTD

Margin limits: subjective, depending on the volatility and liquidity of the assets, its trading styles, depth and breath of the market (one never wants to end up owning the market), performance history, reputation and relationship with the institution, length of track record of the subject;

Initial margin is up-front prior to any trading or at the time of the trade

Call margin or top up margin or variation margin or maintenance margin is to cover actual or continued losses

close-out margin terminates the losing position with any surplus returned to the counterparty

unsecured mark-to-market threshold is when one the losses exceed a certain level, the counterparty is required to deliver margin to cover the MTM losses

Laddering: a portfolio of various issues that mature at different dates rather than a portfolio consisting of one large issue.