MEASURING PORTFOLIO PERFORMANCE: ReturnBased Attribution Robert A. Korajczyk Asset Management Practi

1
MEASURING PORTFOLIOPERFORMANCEReturn-Based
AttributionRobert A. KorajczykAsset
Management PracticumFINC 934C
October 15, 2007
2
Why?

• We always have the option of passive management.
• Has the manager added value relative to their
  investment style?
• What has the manager's investment style been?
• Has the managers style changed?

3
Properties of good performance benchmarks.

• Minimizes the noise induced by the luck component
• Should not penalize managers for events beyond
  their control
• Ex post performance is much more variable (noisy)
  than true ability.

4
Measurement of returns

• Internal Method
• Sensitive to Timing of Inflows/Outflows
• Time Weighted Method
• Not Sensitive to Timing of Inflows/Outflows
• GIPS requires time weighted.

5
Measurement of returns

• Assume that the manager earns - 10 in the first
  half of the year and 20 in the second half.
• CASE 1 50Mil invested at the beginning of the
  year and 45Mil at the half year point.
• CASE 2 50Mil invested at the beginning of the
  year and 20Mil withdrawn at the half year point.

6
Measurement of returns
7
Measurement of Returns

• Case 1
• -50 45/(1y/2) 108/(1y/2)2 ? y 17.4
• Case 2
• -50 20/(1y/2) 30/(1y/2)2 ? y 0
• Time weighted return
• (1 - 0.10)(1 0.20) 1 0.08, or 8

8
Evaluating Stable Style Mangers

• Benchmark Choice
• Other Managers in same style category
• Passive benchmark adjusted returns
• Beta-adjusted benchmark returns
• Multi-index benchmarks
• Asset lists

9
Evaluating Stable Style Mangers

• Passive benchmark adjusted returns

• Does not adjust for differences in beta
• Implicit assumption Beta 1

10
Single-Index Benchmarks
11
Single-Index Benchmarks
12
Single-Index Benchmarks
13
Index Sensitivity - Beta
Beta measures the sensitivity of the portfolio to
movements in the index ßpI corr(Rp,
RI)std(Rp)/std(RI) Rp return on the
portfolio RI return on the index RF return
on short term bills corr(.,.)
correlation std(.) standard deviation
14
Estimation Linear Regression
15
Mutual Funds

• Vanguard Total Market (TickerVTSMX)
• Windsor Fund (TickerVWNDX)
• Wellesley Fund (TickerVWINX)
• Fidelity Low Priced (Ticker FLPSX)
• Vanguard Index 500 (Ticker VFINX)
• Fidelity Magellan (TickerFMAGX)
• Strong Corporate Bond (Ticker STCBX)
• Federated US Government Bond (Ticker FEDBX)

16
Estimation Linear Regression
17
Mutual Funds
18
Mutual Funds
19
Mutual Funds
20
Mutual Funds
21
ETFs SDS ProShares UltraShort SP500
22
Benchmark Adjusted Return vs. a

• Passive benchmark adjusted returns
• Risk adjusted return (a)
• Market timing return

23
Multi-Index Benchmarks

• Measure sensitivity to multiple asset classes or
  sub-sectors
• Implicitly assumes the asset class portfolios can
  be used to form and efficient portfolio
• No consensus about which asset classes to use

24
Estimation Linear Regression
Rpt - RFt apI ßp1(R1t - RFt) ßp2(R2t -
RFt) ... ßpk(Rkt - RFt) ?pt
25
Mutual Funds Sector Exposures (ßs)
26
Mutual Funds Sector Exposures (ßs)
27
Mutual Funds Sector Exposures (ßs)
28
Mutual Funds Sector Exposures (ßs)
29
Evaluating Market Timing Managers (Tactical Asset
Allocators)
30
Market Timing
31
Market Timing

• Define an "up" market RIt - RFt 0
• Define yt Max0, -(RIt - RFt)
• Estimate
• Rpt - RFt a bp(RIt - RFt) dpyt ept

32
Market Timing

• In "up" market yt 0 and bp is the up market
  beta
• In down markets, the regression is
• Rpt - RFt as (bp dp)(RIt - RFt) ept
• so (bp dp) is the down market beta and dp is
  the difference between up and down betas

33
Measured Performance and Future Performance

• Forecasting negative vs. positive a
• Which past horizon?
• Selection/survival bias.
• Style drift