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Fund Returns | Base Return Fund
Local Return Fund
See Detecting Inconsistent Returns in Appendix C for details on using the Base Return Fund to identify inconsistencies in performance data. |
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Index Returns | Base Return Index
Local Return Index
See Detecting Inconsistent Returns in Appendix C for details on using the Base Return Index to identify inconsistencies in performance data. |
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Weights | Base Weight Fund
Base Weight Index |
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Fund Returns | Accret Amort Return Fund
Base Return Fund
Convexity Return Fund
Coupon Return Fund
Cross Product Return Fund
Currency Return Fund
Duration Matched Excess Yield Change Fund
Duration Matched Price Return Fund
Duration Matched Total Return Fund
Duration Matched Yield Change Fund
Duration Matched Yield Return Fund
Key Rate Duration Return Fund
Option Adjusted Begin Spread Fund
Option Adjusted End Spread Fund
Option Adjusted Spread Change Fund
Option Adjusted Yield Change Fund
Parallel Shift Return Fund
Pivot Yield Change Fund
Price ExConvexity Return Fund
Price Return Fund
Price Spread Return Fund
Reshape Return Fund
Rolldown Return Fund
Total Residual Return Fund
Total Spread Return Fund
Yield Return Fund
Yield Spread Return Fund
See Detecting Inconsistent Returns in Appendix C for details on using the Base Return Fund to identify inconsistencies in performance data. |
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Fund Contributions | Base Contribution Fund
Cross Product Contribution Fund
Currency Contribution Fund
Duration Matched Price Contribution Fund
Duration Matched Total Contribution Fund
Duration Matched Yield Contribution Fund
Key Rate Duration Return Contribution Fund
Local Contribution Fund
Parallel Contribution Fund
Price Spread Contribution
Reshape Contribution Fund
Residual Return Contribution Fund
Roll Contribution Fund
Total Spread Contribution
Yield Spread Contribution |
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Index Returns | Accret Amort Return Index
Base Return Index
Convexity Return Index
Coupon Return Index
Cross Product Return Index
Currency Return Index
Duration Matched Excess Yield Change Index
Duration Matched Price Return Index
Duration Matched Total Return Index
Duration Matched Yield Change Index
Duration Matched Yield Return Index
Key Rate Duration Return Index
Option Adjusted Begin Spread Index
Option Adjusted End Spread Index
Option Adjusted Spread Change Index
Option Adjusted Yield Change Index
Parallel Shift Return Index
Pivot Yield Change Index
Price ExConvexity Return Index
Price Return Index
Price Spread Return Index
Reshape Return Index
Rolldown Return Index
Total Residual Return Index
Total Spread Return Index
Yield Return Index
Yield Spread Return Index
See Detecting Inconsistent Returns in Appendix C for details on using the Base Return Index to identify inconsistencies in performance data. |
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Index Contributions | Base Contribution Index
Cross Product Contribution Index
Currency Contribution Index
Duration Matched Price Contribution Index
Duration Matched Total Contribution Index
Duration Matched Yield Contribution Index
Key Rate Duration Return Contribution Index
Local Contribution Index
Parallel Contribution Index
Price Spread Contribution Index
Reshape Contribution Index
Residual Return Contribution Index
Roll Contribution Index
Total Spread Contribution Index
Yield Spread Contribution Index |
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Relative Returns | Accret Amort Return Difference
Base Return Difference
Base Return Fund In-Out Difference
Base Return Index In-Out Difference
Convexity Return Difference
Coupon Return Difference
Cross Product Return Difference
Currency Return Difference
Duration Matched Excess Yield Change Difference
Duration Matched Price Return Difference
Duration Matched Total Return Difference
Duration Matched Yield Change Difference
Duration Matched Yield Return Difference
Key Rate Duration Return Difference
Local Return Difference
Option Adjusted Begin Spread Difference
Option Adjusted End Spread Difference
Option Adjusted Spread Change Difference
Option Adjusted Yield Change Difference
Parallel Shift Return Difference
Pivot Yield Change Difference
Price ExConvexity Return Difference
Price Model Return Difference
Price Return Difference
Price Spread Return Difference
Reshape Return Difference
Residual Return Difference
Rolldown Return Difference
Total Spread Return Difference
Yield Return Difference
Yield Spread Return Difference
See Detecting Inconsistent Returns in Appendix C for details on using the Base Return Fund In-Out Difference and Base Return Index In-Out Difference to identify inconsistencies in performance data. |
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Attribution Effects | Allocation
Allocation Interaction
Cross Product Effect
Currency Effect
Duration Matched Price Effect
Duration Matched Total Return Effect
Duration Matched Yield Effect
Interaction
Key Rate Duration Effect
Parallel Shift Effect
Price Spread Effect
Reshape Effect
Residual Effect
Rolldown Effect
Selection
Selection Interaction
Total Attributed
Total Key Rate Duration Effect
Total Spread Effect
Yield Spread Effect
Note: These options display the effects before the multiple-period smoothing algorithm is applied. |
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Smoothed Attribution Effects | Smoothed Allocation Interaction
Smoothed Allocation
Smoothed Cross Product Effect
Smoothed Currency Effect
Smoothed Duration Matched Price Effect
Smoothed Duration Matched Total Effect
Smoothed Duration Matched Yield Effect
Smoothed Fund Base Contribution
Smoothed Index Base Contribution
Smoothed Interaction
Smoothed Key Rate Duration Effect
Smoothed Parallel Shift Effect
Smoothed Price Spread Effect
Smoothed Reshape Effect
Smoothed Residual Effect
Smoothed Rolldown Effect
Smoothed Selection Interaction
Smoothed Selection
Smoothed Total Attributed
Smoothed Total Key Rate Duration Effect
Smoothed Total Spread Effect
Smoothed Yield Spread Effect
Note: These options display the effects after the smoothing algorithm is applied.
Eagle recommends choosing smoothed attribution effects regardless of the number of time periods. In the case of a single time period, no smoothing is applied. The effects are only smoothed for multiple time periods. This allows you to use the smoothed effects in all cases. |
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Weights | Average Base Weight Difference
Average Base Weight Fund
Average Base Weight Index
Base Weight Difference |
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About Key Rate DurationsDuration of a bond is the sensitivity of an instrument's value to interest rate changes across the yield curve. It does not capture the impact of yield change at a particular point on the curve. Key rate duration (KRD) is the interest rate sensitivity of the bond's value to interest rate change at a particular point on the yield curve.
Mathematically, the sum of the key rate duration is equal to the duration of the bond. Eagle supports an extension of its Fixed Income Attribution model to support key rate duration decomposition so that the duration matched risk-free price return is decomposed into roll and a set of key rate durations effects.
To quantify the yield curve sensitivity of each bond in a portfolio, you can define a series of key rate durations relative to specific yield curve points. The key rate duration is the percentage price response per 100 basis point movement in a particular risk-free rate ─ while the rest of the yield curve remains constant. By defining many points along the yield curve, key rate durations provide an accurate representation of the sensitivity of each bond in a portfolio to changes of the yield curve.
Key rate durations can play a key role in portfolio management by quantifying the exposure of a portfolio to each section of the yield curve. Using these measures, portfolio managers who deliberately want to express a view about yield curve reshaping structure their portfolio to have different key rate duration exposures from those of their benchmark. Alternatively, investors who want to immunize their portfolios to yield curve reshaping structure a portfolio with the same key rate duration exposures as their benchmark.
To calculate each of the key rate duration returns, you multiply the observed yield change at each of the key rate duration points by -1 times the key rate duration of that point. The following table lists the return for key rate durationi.
Return | Formula | Description |
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Key Rate Durationi | ( – (OADiBeg * YieldChgDuri) ) | The sum of the reshape and parallel decomposition factors is equal to the sum of all of the key rate return factors. |
Where
OAD = effective duration (standard or option adjusted)
i = ith of n key rates
For Key Rate Duration (KRD) analysis, Eagle calculates an average yield change of the curve weighted by the key rate duration points. The average yield change is used instead of pivot point yield change to calculate price return due to parallel shift and reshape. The sum of KRD effects is equal to the sum of the Parallel and Reshape effects. For more information about parallel shift and reshape, see Portfolio and Benchmark Return Decomposition.
Edit the Default Number of Key Rate DurationsYou can have as many key rate durations as you like. The default number is 10. Performance System Parameter 11 allows you to edit the default number.
To edit the default number of key rate durations:
...
- Edit the value in the Item Value text box and click Save.
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Specify Optional Fields Such as Par Value, Coupon, and ConvexityYou can use the Optional Fields tab on the Creating Fixed Income Options & Field Map Field dialog box to specify additional fields. These additional fields are optional. That is, they are not required for the standard portfolio and benchmark return decomposition that is used for the benchmark relative attribution analysis. See the following figure.
Creating Fixed Income Options & Field Map Field – Optional Fields Tab
The following table describes each option.
Option | Description |
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Portfolio |
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Par Value | The nominal or face value of the portfolio's bond. |
Coupon | The interest rate paid by the bond in percent. |
Convexity | The effective convexity of the bond. For a bond: - Without embedded options, this input is the standard convexity.
- With embedded options, this is an option adjusted convexity that is calculated consistently for all bonds being analyzed. This input is the result of an analytical process that evaluates the effective convexity of the bond after the effects of bond optionality have been removed. All option adjusted yields, durations, and convexities should be calculated with a consistent analytical process.
This input is only used to calculate the price return convexity decomposition.
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Local Market Value | The local market price of the portfolio's bond. |
Benchmark |
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Par Value | The nominal or face value of the benchmark's bond. |
Coupon | The interest rate paid by the bond in percent. |
Convexity | The effective convexity of the bond. For a bond: - Without embedded options, this input is the standard convexity.
- With embedded options, this is an option adjusted convexity that is calculated consistently for all bonds being analyzed. This input is the result of an analytical process that evaluates the effective convexity of the bond after the effects of bond optionality have been removed. All option adjusted yields, durations, and convexities should be calculated with a consistent analytical process.
This input is only used to calculate the price return convexity decomposition.
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Local Market Value | The local market price of the benchmark's bond. |
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Additional Return DecompositionsYou can calculate additional bond return components using the Optional Fields tabs on the Creating Fixed Income Options & Field Map Field dialog box. These additional components are return decomposition outputs. They are not currently available as relative return attribution effects.
Total Return Decomposition |
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Currency Return | ((1+ RBase) / (1 + RLocal)) - 1 |
Currency Cross Product | RLocal * RCurrency |
Local Yield Return | ( 1 + OAYield Begin / 2) ^ (2 * Days in Period / Days In Year) - 1 |
Local Price Return | ( - (OAD Begin * OAYield Change)) |
Yield Return Decomposition |
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Coupon | = (Coupon Begin * (Days in Period/Days In Year)) / (Market Value Local Begin / Par Value Begin) |
Accretion or Amortization | = RYield Local – Coupon |
Price Return Convexity Decomposition |
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Return due to Convexity | (OAC Begin * (OAYield Change) ^ 2) / 2 |
Return excluding Convexity | RPrice Local + Return due to Convexity |
Convexity can be added as a second term to duration that more precisely evaluates a bond's sensitivity to changes in yield. Convexity is the measure of how much a bond's price/yield curve deviates from a straight line (measure of the degree of curvature of the price/yield relationship at the price/yield point). Convexity used with duration provides a more accurate approximation of the percentage price change.
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