1. Stern School of Business
New York University
Stern School of Business
Portfolio Management
Prof. Ian Giddy
New York University

2. Agenda
How to evaluate portfolio performance What portfolio theory tells us
How to put stocks or funds that outperform the market into your “active” portfolio

3. Why Measure Performance?
Performance evaluation: “the science of attribution”
Example: Why did this taxi take so long?
The traffic; the driver; my lousy instructions?
How much should I tip this taxi driver?
Would I use this taxi company again?

4. Portfolio Performance Evaluation
How well did the portfolio do?
How do we adjust for risk, to compare different managers?
Why?
Risk
Timing
Asset allocation
Security selection

5. Abnormal Performance What is abnormal?
Performance can be measured against:
Benchmark portfolio
Market adjusted
Market model / index model adjusted
Reward to risk measures such as the Sharpe measure:
E (rp-rf) / p

6. Performance Evaluation Issues
Theoretically correct measures are difficult to construct
Different statistics or measures are appropriate for different types of investment decisions or portfolios
Many industry and academic measures are different
The nature of active management leads to measurement problems

7. Measuring Portfolio Returns
Dollar-weighted return (IRR) vs
Time-weighted return
Arithmetic average
Geometric average

8. Performance Evaluation Measures
Sharpe’s measure
The portfolio’s average excess return per unit of total risk
Treynor’s measure
The portfolio’s average excess return per unit of systematic risk
Jensen’s measure
The excess of the portfolio’s return over that predicted by the CAPM
Appraisal ratio
Portfolio’s abnormal return per unit of risk that could be diversified by holding a market index portfolio

9. Performance Evaluation Measures
Sharpe’s measure
Treynor’s measure
Jensen’s measure

Appraisal ratio

10. Risk Adjusted Performance: Sharpe
1) Sharpe Index
rp = Average return on the portfolio
rf = Average risk free rate p
= Standard deviation of portfolio
return 

11. Risk Adjusted Performance: Treynor
2) Treynor Measure
rp = Average return on the portfolio
rf = Average risk free rate
ßp = Weighted average for portfolio

12. Risk Adjusted Performance: Jensen
3) Jensen’s Measure  
= Alpha for the portfolio p
rp = Average return on the portfolio
ßp = Weighted average Beta
rf = Average risk free rate
rm = Avg. return on market index port.

13. Which Measure is Appropriate?
It depends on investment assumptions
1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market.
2) If many alternatives are possible, use the Jensen or the Treynor measure
The Treynor measure is more complete because it adjusts for risk

14. Limitations
Assumptions underlying measures limit their usefulness
When the portfolio is being actively managed, basic stability requirements are not met
Practitioners often use benchmark portfolio comparisons to measure performance

15. Factors That Lead to Abnormal Performance
Market timing
Superior selection
Sectors or industries
Individual companies

16. Performance Attribution
Decomposing overall performance into components
Components are related to specific elements of performance
Example components
Broad Allocation
Industry
Security Choice
Up and Down Markets

17. Performance Attribution
Asset allocation choices
Broad market allocations: equity, bonds, etc.
Industry choices
Security selection
Evaluation: compare the portfolio returns at each level with returns on the appropriate index (benchmark portfolio or passive strategy)

18. Process of Attributing Performance to Components
Set up a ‘Benchmark’ or ‘Bogey’ portfolio
Use indexes for each component
Use target weight structure

19. Process of Attributing Performance to Components
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

20. Performance Attribution: 1. Excess Return

21. Performance Attribution: 2. Asset Allocation

22. Performance Attribution: 3. Security Selection

23. Performance Attribution: 4. Summary
Source:

24. Active Portfolio Management
Stock-picking and active portfolio management must pay, else the market would not be efficient!
The optimal risky portfolio maximizes the reward-to-variability ratio; the slope of the CAL:
ACTIVE
CAPITAL ALLOCATON LINE
E(rp)
PASSIVE
CAPITAL ALLOCATON LINE

25. Lure of Active Management
Are markets totally efficient?
Some managers outperform the market for extended periods
While the abnormal performance may not be too large, it is too large to be attributed solely to noise
Evidence of anomalies such as the turn of the year exist
The evidence suggests that there is some role for active management 2

26. Market Timing
Adjusting portfolio for up and down movements in the market
Low Market Return - low ßeta
High Market Return - high ßeta

27. Adjust the portfolio for movements in the market
Market Timing
Adjust the portfolio for movements in the market
Shift between stocks and money market instruments or bonds
Results: higher returns, lower risk (downside is eliminated)
With perfect ability to forecast behaves like an option 3

28. Example of Market Timing
rp - rf * * * * * * * * * * * * * * * * * * * * *
rm - rf * *
Steadily Increasing the Beta

29. Market Timing: An Option on the S&P
Value of perfect timing is a call option worth C
Timing ability measured by PBull+ PBear-1
Value of timing ability is (PBull+ PBear -1)C
P = the proportion of correct forecasts rf rM rf

30. Rate of Return of a Perfect Market TimerrM rf 4

31. Returns on Stocks and Bills
Year 71 72 73 74 75 76 77 78 79 80
Stock Ret.
.1431
.1898
-.1466
-.2647
.3720
.2384
-.0718
.0656
.1844
.3242
T-Bill Ret
.0439
.0384
.0693
.0800
.0580
.0508
.0512
.0718
.1038
.1124
Avg. Ret.
S.D. Ret.
.1034
.2068
.0680
.0248 5

32. With Perfect Forecasting Ability
Switch to T-Bills in ‘73, ‘74, ‘77, ‘78
No negative returns or losses
Average Ret. = .1724
S.D. Ret. = .1118
Results with perfect timing
70% increase in mean return
46% lower S.D. 6

33. With Imperfect Ability to Forecast
Long horizon to judge the ability
Judge proportions of correct calls
Bull markets and bear market calls 7

34. Conclusion: Hold Three Things
Risk-free asset
Passive portfolio
Active portfolio

35. Superior Selection Ability
Concentrate funds in undervalued stocks or undervalued sectors or industries
Balance funds in an active portfolio and in a passive portfolio
Active selection will mean some unsystematic risk 8

36. Used to guage performance of professional portfolios
Sharpe’s Ratio
Used to guage performance of professional portfolios
ACTIVE CAL
E(rp)
PASSIVE CAL

37. Treynor-Black Model
Model used to combine actively managed stocks with a passively managed portfolio
Using a reward-to-risk measure that is similar to the the Sharpe Measure, the optimal combination of active and passive portfolios can be determined 9

38. Security Selection
Alpha is the expected return on a security above that explained by its beta and the security market line:
Treynor-Black model says weight of each security should be based on ratio of its mispricing to its nonsystematic risk:

39. Treynor-Black Model: Assumptions
Analysts will have a limited ability to find a select number of undervalued securities
Portfolio managers can estimate the expected return and risk, and the abnormal performance for the actively-managed portfolio
Portfolio managers can estimate the expected risk and return parameters for a broad market (passively managed) portfolio 10

40. Reward to Variability Measures
Passive Portfolio : [ E ( r m ) - f m ] 2 S 2 m = 11

41. Reward to Variability Measures
Appraisal Ratio  A 
(ep) 
= Alpha for the active portfolio A 
= Unsystematic standard
deviation for active
(Ap) 12

42. Reward to Variability Measures
Combined Portfolio :  [ A [ E ( r m ) - f m 2 2 S 2 = ] + ] p
eA 13

43. Treynor-Black Allocation
CAL
Optimal Portfolio
E(r)
CML
Active Portfolio
Market Portfolio Rf  14

44. Implementing the Treynor-Black Approach
Use passive portfolio (index fund) as baseline; find its E(rM) and E(VarM)
Analyze a few securities; find mispriced ones
For each security, use estimates of Alpha, Beta and residual risk to determine optimum weights
Determine optimal weights for active and passive portfolios

45. Summary Points: Treynor-Black Model
Sharpe Measure will increase with added ability to pick stocks
Slope of CAL>CML
(rp-rf)/p > (rm-rf)/p
P is the portfolio that combines the passively managed portfolio with the actively managed portfolio
The combined efficient frontier has a higher return for the same level of risk 15

46. Summary
How to evaluate portfolio performance
How to put stocks or funds that outperform the market into your “active” portfolio
Portfolio theory helps construct the right active/passive/riskfree mix.

50. Ian Giddy Ian H. Giddy NYU Stern School of Business
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