When it comes to value-at-risk, Kamakura Risk Manager (KRM) includes three popular methodologies:

• Variance-covariance (matrix) value-at-risk, as popularized by JP Morgan
• Historical value-at-risk, using historical market values
• Full option-adjusted, credit adjusted Monte Carlo simulation driven value-at-risk

Variance-Covariance Value-At-Risk

• KRM can generate a variance-covariance matrix internally from historical risk factor data

• KRM can also acquire third-party sources of variance-covariance matrix data on a fully automated basis using standard data mapping tools
• KRM can process risk factor shifts of any user-desired magnitude
• KRM allows rich web-based or Excel-based reporting using KRMs standard third party reporting tool Crystal Reports
• KRM supports a single enterprise-wide portfolio VAR run, while simultaneously producing fully consistent VAR for one or more cuts of the portfolio by organizational unit, customer category, product category
• KRM processes the entire portfolio on a transaction by transaction basis, even if it includes millions of transactions

Historical Value-At-Risk

• KRM produces historical value-at-risk measures both for use in their own right and as a back-testing methodology
• KRM can produce historical volatilities and covariances automatically in KRM format for processing
• KRM supports a single enterprise-wide portfolio VAR run, while simultaneously producing fully consistent VAR for one or more cuts of the portfolio by organizational unit, customer category, product category
• KRM processes the entire portfolio on a transaction by transaction basis, even if it includes millions of transactions

Credit-adjusted and Option-adjusted Value-At-Risk in KRM

Market participants are well aware that both variance-covariance VAR and historical VAR grossly underestimate the risk in almost every portfolio. There are many common sense and analytical reasons why this is true:

• Portfolio value changes are not normally distributed. As bankers know, lenders have almost no upside and and 100% downside. Historical and variance-covariance VAR ignore this simple truth, assuming symmetrical gains and losses
• Both historical and variance-covariance VAR methods ignore cash flows between now and the value at risk date
• Both methods ignore embedded optionality and other financial options that may be exercisable between now and the value at risk date. When value at risk is being used to determine loan loss reserves, capital adequacy, and internal capital allocations, the value at risk date is commonly many months in advance. That leads to a value at risk calculation on the portfolio the firm has now, not the portfolio the firm will have on the value at risk date
• Both methods tend to ignore the risk of default, modeling at best variations in credit spreads. This ignores the fact that a default the day before maturity can still result in the loss of 20 or 30% of the principal on the bond. Moving credit spread in a simulation from 5% to 30% on the day before maturity only reduces the bonds present value (5% coupon, 100 principal) from 104.99 to 104.92. Explicitly modeling the loss given default would recognize the real possibility of a major reduction in value from default. Historical value at risk and variance co-variance value at risk ignore this risk and dramatically understate credit risk
• Both methods suffer from survival bias. They use historical data on the risk of counterparties that the firm has now, none of which (by definition) would be in the portfolio if they had gone bankrupt during the historical period the special asset division has the bad credits! Again, this results in the dramatic understatement of measured risk

Kamakura Risk Manager has been carefully designed to avoid these pitfalls. Full credit-adjusted and options-adjusted Monte Carlo driven VAR is the only methodology for doing this successfully.

Advantages of KRMs Option-adjusted and Credit-adjusted Value-At-Risk

Kamakura Risk Manager has a number of very significant advantages which we believe result in the most accurate value at risk technology in the industry:

• KRM features explicit transaction by transaction valuation in every scenario using derivatives analytics by Dr. Robert Jarrow.
• KRM explicitly models all cash flows between now and the value at risk date and reinvests them in user-specified investment vehicles
• KRM explicitly models the impact of default, not just movements in credit spreads, using state of the art credit models developed by Dr. Robert Jarrow and others.
• KRMs random number generation is completely consistent and fully integrated whether the purpose is valuation and value at risk or net income and balance sheet projection on a financial accounting basis. The risk factor engine is the same.
• Kamakura can provide credit risk and risk factor data in a KRM compatible format via Kamakura Risk Information Services
• Kamakura can provide full value at risk processing via Kamakura On-Line Processing Services