1. Portfolio Performance Evaluation
Chapter 24
Portfolio Performance Evaluation
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-1

2. Introduction Complicated subject
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
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-2

3. Dollar- and Time-Weighted Returns
Dollar-weighted returns:
Internal rate of return considering the cash flow from or to investment
Returns are weighted by the amount invested in each stock
Time-weighted returns:
Not weighted by investment amount
Equal weighting
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-3

4. Text Example of Multiperiod Returns
Period Action
0 Purchase 1 share at $50
1 Purchase 1 share at $53
Stock pays a dividend of $2 per share
2 Stock pays a dividend of $2 per share
Stock is sold at $108 per share
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-4

5. Dollar-Weighted Return
Period Cash Flow
share purchase
1 +2 dividend share purchase
2 +4 dividend shares sold
Internal Rate of Return:
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-5

6. Time-Weighted Return Simple Average Return: (10% + 5.66%) / 2 = 7.83%
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-6

7. Averaging Returns Arithmetic Mean: Text Example Average:
( ) / 2 = 7.81%
Geometric Mean:
Text Example Average:
[ (1.1) (1.0566) ]1/2 - 1
= 7.83%
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-7

8. Geometric and Arithmetic Means Compared
Past Performance
Generally the geometric mean is preferable to arithmetic
Predicting Future Returns from historical returns
Use a weighted average of arithmetic and geometric averages of historical returns if the forecast period is less than the estimation period
Use geometric is the forecast and estimation period are equal
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-8

9. Abnormal Performance What is abnormal?
Abnormal performance is measured:
Benchmark portfolio
Market adjusted
Market model / index model adjusted
Reward to risk measures such as the Sharpe Measure:
E (rp-rf) / p
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-9

10. Factors Leading to Abnormal Performance
Market timing
Superior selection
Sectors or industries
Individual companies
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-10

11. Risk Adjusted Performance: Sharpe
1) Sharpe Index
rp - rf  p
rp = Average return on the portfolio
rf = Average risk free rate 
= Standard deviation of portfolio
return p
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-11

12. M2 Measure Developed by Modigliani and Modigliani
Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio
If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-12

13. M2 Measure: Example
Managed Portfolio: return = 35% standard deviation = 42%
Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6%
Hypothetical Portfolio:
30/42 = .714 in P (1-.714) or .286 in T-bills
(.714) (.35) + (.286) (.06) = 26.7%
Since this return is less than the market, the managed portfolio underperformed
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-13

14. Risk Adjusted Performance: Treynor
2) Treynor Measure
rp - rf ßp
rp = Average return on the portfolio
rf = Average risk free rate
ßp = Weighted average for portfolio
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-14

15. Risk Adjusted Performance: Jensen
3) Jensen’s Measure
= rp - [ rf + ßp ( rm - rf) ]  p 
= Alpha for the portfolio p
rp = Average return on the portfolio
ßp = Weighted average Beta
rf = Average risk free rate
rm = Average return on market index port
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-15

16. Appraisal Ratio Appraisal Ratio = ap / s(ep)
Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk
Nonsystematic risk could, in theory, be eliminated by diversification
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-16

17. 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
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-17

18. 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
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-18

19. Market Timing
Adjusting portfolio for up and down movements in the market:
Low Market Return
low ßeta
High Market Return
high ßeta
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-19

20. Example of Market Timing
rp - rf * * * * * * * * * * * * * * * * * * * * *
rm - rf * *
Steadily Increasing the Beta
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-20

21. 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
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-21

22. Attributing Performance to Components
Set up a ‘Benchmark’ or ‘Bogey’ portfolio:
Use indexes for each component
Use target weight structure
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
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23. 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
Summarise the performance differences into appropriate categories
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-23

24. Formula for Attribution
Where B is the bogey portfolio and p is the managed portfolio
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-24

25. Contributions for Performance
Contribution for asset allocation (wpi - wBi) rBi
+ Contribution for security selection wpi (rpi - rBi)
= Total Contribution from asset class wpirpi -wBirBi
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-25

26. Complications to Measuring Performance
Two major problems:
Need many observations even when portfolio mean and variance are constant
Active management leads to shifts in parameters making measurement more difficult
To measure well:
You need a lot of short intervals
For each period you need to specify the makeup of the portfolio
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-26

27. Evaluation in Practice
Traditionally based on quarterly data
Sample used to range 5-10 years
Currently, managers need to disclose exact composition quarterly
Some window dressing do take place
Portfolio values are published on daily basis
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-27

28. Style Analysis Based on regression analysis
Examines asset allocation for broad groups of stocks
More precise than comparing to the broad market
Sharpe’s analysis: 97.3% of returns attributed to style
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-28

29. Summary Appropriate performance measures: Noisy portfolio returns
Sharpe
Information ratio
Treynor or Jenson
Noisy portfolio returns
Timing the market
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-29

30. Summary Measuring selection success Use of appropriate benchmark
Style analysis
Rating of funds
Morningstar ratings
Risk-adjusted ratings
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus
Slides prepared by Harminder Singh
24-30