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Asset Management
Lecture 15
Outline for today
Performance Attribution
Decomposing overall performance into components
Components are related to specific elements of performance
Example componentsBroad Allocation IndustrySecurity Choice
Performance Attribution
For the managed portfolio P, set up a ‘Benchmark’ or ‘Bogey’ portfolio B:
Suppose there are n asset classes Select a benchmark index for each asset
class B has fixed weights in asset classes
Target weights
Performance Attribution
Calculate the return on the ‘Bogey’ and on the managed portfolio
Explain the difference in return based on component weights or selection
Summarize the performance differences into appropriate categories
Performance Attribution
n
ipipip
n
iBiBiB rwrrwr
11
B: Bogey portfolio P: the managed portfolio
Formula for Attribution
)(1
11
BiBi
n
ipipi
n
iBiBi
n
ipipiBp
rwrw
rwrwrr
Formula for Attribution
)(
)(
Bipipi
BiBipi
BiBipipi
rrw
rww
rwrw
Contribution from asset allocation
Contribution from security selection
Total contribution from asset class i
)(1
BiBi
n
ipipiBp rwrwrr
Performance Attribution
Portfolio return from ith asset class = rPiWPi
)(
)(
Bipipi
BiBipi
BiBipipi
rrw
rww
rwrw
Example
A portfolio invests in three asset classesEquityBondsCash (money market securities)
The portfolio return over the month is 5.34%
Managed Portfolio Portfolio Actual Portfolio
Component Weight Return Return
Equity 0.7 7.2800% 5.0960%
Bonds 0.07 1.8900% 0.1323%
Cash 0.23 0.4800% 0.1104%
Return on Managed 5.3387%
Example
The choice of Bogey portfolio: a passive benchmarkPassive (index) benchmark in each asset
classPassive (“neutral”, “usual”) asset allocation
Depends on investor risk tolerance
Example
Bogey Portfolio Weight Return on Portfolio
Component Index Benchmark Index Return
Equity S&P500 0.6 5.8100% 3.4860%
Bonds Lehman Index 0.3 1.4500% 0.4350%
Cash Money Market 0.1 0.4800% 0.0480%
Return on Bogey 3.9690%
Excess return of managed portfolio= 5.34%-3.97%=1.37%
Performance Attribution Summary
Asset Allocation 0.3099%
Selection
Equity Returns Weights
Sector Allocation 1.2898% 0.7 0.9029%
Security Selection 0.1802% 0.7 0.1261%
1.4700% 0.7 1.0290%
Fixed Income 0.4400% 0.07 0.0308%
Total Excess Return on the Portfolio 1.3697%
Example
Actual Weight Benchmark Excess Market Performance
in Portfolio Weight Weight Return Contribution
Equity 0.7 0.6 0.1 5.8100% 0.5810%
Fixed Income 0.07 0.3 -0.23 1.4500% -0.3335%
Cash 0.23 0.1 0.13 0.4800% 0.0624%
Contribution of
Asset Allocation 0.3099%
Contribution of Asset Allocation BiBipi rww )(
Performance Attribution Summary
Asset Allocation 0.3099%
Selection
Equity Returns Weights
Sector Allocation 1.2898% 0.7 0.9029%
Security Selection 0.1802% 0.7 0.1261%
1.4700% 0.7 1.0290%
Fixed Income 0.4400% 0.07 0.0308%
Total Excess Return on the Portfolio 1.3697%
Example
Contribution of Security Selection )( Bipipi rrw
Portfolio Index Excess Portfolio Performance
Performance Performance Performance Weight Contribution
Equity 7.2800% 5.8100% 1.4700% 0.7 1.0290%
Fixed Income 1.8900% 1.4500% 0.4400% 0.07 0.0308%
Contribution of
Selection 1.0598%
Performance Attribution Summary
Asset Allocation 0.3099%
Selection
Equity Returns Weights
Sector Allocation 1.2898% 0.7 0.9029%
Security Selection 0.1802% 0.7 0.1261%
1.4700% 0.7 1.0290%
Fixed Income 0.4400% 0.07 0.0308%
Total Excess Return on the Portfolio 1.3697%
Example
Contribution to sector selection BiBipi rww )(
)( Bipipi rrw
Performance Attribution Summary
Asset Allocation 0.3099%
Selection
Equity Returns Weights
Sector Allocation 1.2898%
Security Selection 0.1802%
1.4700% 0.7 1.0290%
Fixed Income 0.4400% 0.07 0.0308%
Total Excess Return on the Portfolio 1.3697%
=1.47%-1.2898%
Performance Attribution Summary
Asset Allocation 0.3099%
Selection
Equity Returns Weights
Sector Allocation 1.2898% 0.7 0.9029%
Security Selection 0.1802% 0.7 0.1261%
1.4700% 0.7 1.0290%
Fixed Income 0.4400% 0.07 0.0308%
Total Excess Return on the Portfolio 1.3697%