Trade Recommendations

riskDistance

As noted in the glossary, "riskDistance" is

a calculated value used subsequently in the calculation of totalRequiredPickup and is dependant upon the relative values of riskUp and riskDown.

• If riskUp exceeds riskDown
  totalRiskDistance = 1 + (riskUp - riskDown)^(1/RISK_DISTANCE_EXPONENT)
• If riskUp is equal to riskDown
  totalRiskDistance = 1.0
• If riskUp is less than riskDown
  totalRiskDistance = 1 - TRADE_RISK_ASYMETTRY * (riskDown - riskUp)^(1/RISK_DISTANCE_EXPONENT)

The risk distance attempts to quantify the degree of similarity between two issues: issues that are very similar in risk profile will have a smaller "riskDistance" between them than issues that will react very differently under various market scenarios. Note that the factors inherent in the calculation of riskUp and riskDown are optimized through simulation. Note also that riskDown, the reduction of risk through trading, is only valid and calculated when trading by the portfolio method, in which trades which increase the similiarity of the risk profile of the portfolio to that of the index are considered risk-decreasing. When optimizing by the issue method, all components of the "risk distance" are added to riskUp.

Values of "riskDistance" for all trades examined may be viewed on the tradeReport via the "View|Risk Distances" selection on the tradeMenu.

"Risk Distances" are also reported in the tradeEvaluationReportBox.

The calculation of "riskDistance" is shown in the riskMeasurementCalculationBox.

The calculation of "riskDistance" may be reviewed in the riskMeasurementCalculationBox:

The riskMeasurementCalculationBox

The following table of attributes is adapted from the glossary:

Attribute	Binary?
retractibility	True
split share corporation	True
cumulative dividends	True
interest income	True
Credit Class 2	True
macaulayDurationPortBid	False
pseudoModifiedDurationPort	False
pseudoConvexityPort	False
macaulayDurationCostBid	False
pseudoModifiedDurationCost	False
pseudoConvexityCost	False
pseudoModifiedDurationWorstBid	False
Credit Class 3	True
Floating Rate	True
Credit Class High	True
Credit Class Low	True
ytwModifiedDuration	False

The first figure reported in each line of the riskMeasurementCalculationBox is the current value of the riskAttribute. When examining a trade prepared by the issueMethod, the "current value" is the value of that attribute for the issue sold.

If the value of this attribute is different for the issue to be purchased, the difference is reported as "Change".

The last item reported on each line in the main body of the report is the multiplier, which is obtained from the systemConstantsRecord. These are optimizableParameters and are also reported in the "RISK PARAMETERS" section of the analyticalParametersReportBox

The final section of the report shows the calculations and constants used to derive a "riskDistance" from these individually measured distances in "Risk Space", as noted in the glossary:

• Risk Reduction Asymmetry Factor : TRADE_RISK_ASYMETTRY
• Risk Distance Exponent : RISK_DISTANCE_EXPONENT
• Risk from Credit Change : riskCreditTrade
• Risk of current holdings : riskCreditHoldings
• Risk Increasing Distance (^RISK_DISTANCE_EXPONENT) : riskUp
• Risk Decreasing Distance (^RISK_DISTANCE_EXPONENT) : riskDown
• A choice of three options, depending upon the sign of (riskUp - riskDown)
  • If negative: riskDistance = (1 - (TRADE_RISK_ASYMETTRY * (riskDown - riskUp)^(1 / RISK_DISTANCE_EXPONENT))) = riskDistance
  • If zero: riskDistance = 1 since risks are balanced
  • If positive: riskDistance = (1 + (riskUp - riskDown)^(1 / RISK_DISTANCE_EXPONENT))

By way of example, let us consider a trade examined in accordance with the issueMethod. We shall assume that the only measured risk attribute difference between the two issues is that one is a split share corporation while the other is not (this is at least a possibility! Most other differences will have a "knock-on" effect on other risk attributes, perhaps most obviously "retractibility" and any of the duration measures). Recall, from the glossary, that the value of riskUp is calculated as:

Each component, i, of the tradeRawRisk vector is examined. If

• the sign of the tradeRawRisk is the same as the sign of holdingsRiskDifference or
• the trade weight of the trade being examined is 1.0 (that is, the trade is a swap

then "riskUp" is incremented by
tradeWeight * (tradeRawRisk[i] * riskMultiplier[i])^RISK_DISTANCE_EXPONENT

According to the optimized parameterization in effect on November 17, 2005, the value of riskSplitShareCorp is 3.588, while the value of RISK_DISTANCE_EXPONENT is 2.000. Therefore, the increment to riskUp contributed by the RISK_AXIS_SPLITSHARECORP axis is calculated according to the table:

Since this is the only difference between the two issues, riskUp = 21.050 for this trade and since:

riskDistance = (1 + (riskUp - riskDown)^(1 / RISK_DISTANCE_EXPONENT))