| Inputs |
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| Fund Returns | Base Return Fund Local Return Fund Trade Return Fund Price Return Fund See Detecting Inconsistent |
Returns for details on using the Base Return Fund to identify inconsistencies in performance data. | |
Index Returns | Base Return Index Local Return Index Trade Return Index Price Return Index See Detecting Inconsistent Returns |
for details on using the Base Return Index to identify inconsistencies in performance data. | |
| Weights | Base Weight Fund Base Weight Index |
| 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 for details on using the Base Return Fund to identify inconsistencies in performance data. | |
| Fund Contributions | Base Contribution Fund |
| Index Returns | Accret Amort Return Index |
Index See Detecting Inconsistent Returns |
for details on using the Base Return Index to identify inconsistencies in performance data. | |
| 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 |
| 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 |
| for details on using the Base Return Fund In-Out Difference and Base Return Index In-Out Difference to identify inconsistencies in performance data. | |
| Attribution Effects | Allocation Note: These options display the effects before the multiple-period smoothing algorithm is applied. |
| Smoothed Attribution Effects | Smoothed Allocation Interaction Note: These options display the effects after the smoothing algorithm is applied. |
| Weights | Average Base Weight Difference Average Base Weight Fund Average Base Weight Index Base Weight Difference |
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Duration 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 |
|---|---|---|
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.
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You 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:
- From any Eagle window, click the Eagle Navigator button to access the Eagle Navigator.
- Enter System in the Start Search text box and click the System Parameter (Performance Center) link.
You see the Performance Center and the Performance System Parameters workspace.
...
- Select Sys Item 11, Maximum number of Key Rate Duration points for Fixed Income Attribution, right click and select Edit.
You see the Edit Performance System Parameter 11 dialog box.
...
- Edit the value in the Item Value text box and click Save.
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You 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 |
|---|---|
Portfolio |
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:
|
Local Market Value | The local market price of the portfolio's bond. |
Benchmark |
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:
|
Local Market Value | The local market price of the benchmark's bond. |
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You 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 |
|---|
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 |
|---|
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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