1. Performance Evaluation and Active Portfolio Management
Bm410: Investments
Performance Evaluation
and Active Portfolio
Management
Or figuring out if you or your manager is good or just lucky!

2. Objectives
A. Understand active portfolio management and performance evaluation
B. Understand how to calculate risk adjusted rates of return
C. Decompose returns into components attributable to asset allocation and securities selection

3. A. Active Portfolio Management and Performance Evaluation
Why are these two topics so important?
Active Portfolio Management and Performance Evaluation are very difficult tasks and are critical to investing
Very few have done it well
They are very complicated subjects
Theoretically correct measures are difficult to construct
Different statistics or measures are appropriate for different types of investment decisions and portfolios

4. Active Portfolio Management and Performance Evaluation (continued)
How are these topics viewed?
Academics and industry view them from different areas
Industry and academic measures are different-- sometimes extremely different, with different results
The key area is measuring performance
Most performance measurement is for a buy and hold strategy, or at best, a steady state
Active management complicates this process, for it is by definition changing

5. Active Portfolio Management and Performance Evaluation (continued)
The nature of active management leads to very challenging measurement problems
Remember, managers may be buying and selling at any point in time
What are asset classes?
What about risk?
Risk is more complex than just variance or standard deviation
Is it upside or downside?

6. Active Portfolio Management (continued)
What is Active Portfolio Management?
The process of using current, historical, and publicly available data to actively manage a portfolio in an effort to:
Earn investment returns in excess of the manager’s specified benchmark (or benchmark, bogey, target) after all costs, including transactions costs, taxes, management, and other fees
Earn consistent excess returns period after period--and not just from luck

7. Active Portfolio Management (continued)
Are markets totally efficient?
This is a critical question
Some managers outperform the market for extended periods, but not others. Why?
While the abnormal performance in some instances may not be large, it is too large to be attributed solely to noise
Evidence remains that anomalies, such as the turn of the year, exist
The evidence suggests that there is a role for active portfolio management in inefficient markets
It even suggests there is a role in efficient markets 2

8. Active Portfolio Management (continued)
What are abnormal returns?
Abnormal returns are investment returns which, after fees and transactions costs, are in excess of:
A specified benchmark portfolio
Can be a specified index (S&P 500, sector, or another real or proxy portfolio)
A market proxy adjusted for risk
A market model / adjusted index model
A reward to risk measure, such as the Sharpe Measure: E (rp-rf) / sp

9. Active Portfolio Management (continued)
What major factors lead to abnormal returns?
1. Superior Market timing (or asset allocation)
Shifting assets between a poor-performing asset class and a better performing asset class to outperform a specified benchmark which includes both asset classes
2. Superior selection (or stock or asset selection_
Picking sectors, industries, or companies within a specified benchmark which outperform that specified benchmark

10. 1. Superior Market Timing Ability
What is superior market timing ability?
A process where the manager gains abnormal returns from adjusting the portfolio for movements in the market
The manager shifts among stocks, money market instruments and bonds based on their expectations for returns from each asset class
What are the results of superior market timing?
Higher returns with lower risk
With perfect forecasting abilities, the portfolio behaves like an option
However, no one has perfect forecasting abilities

11. Superior Market Timing (continued)
With perfect market timing ability (PMTA)
What would your actions have been since ?
Switch to T-Bills in 73, 74, 77, 78, 81, 90, 00, 01, 02
No negative returns or losses
Average S&P500 Return: % PFA 16.7%
Standard Deviation % %
Results with perfect timing?
You would have had a 54% increase in mean return
You would have a 37% lower standard deviation of returns 6

12. Superior Market Timing (continued)
With imperfect forecasting ability
How would you judge performance?
Long horizon necessary to judge the ability
Judge proportions of correct calls
Judge both bull markets and bear market calls
What is the evidence from the real world: “Market Timing Also Stumps Most Pros”
By the time there is enough information to judge to value added, most portfolio managers have retired, written books, or gone back to being teachers 7

13. 2. Superior Selection Ability
What is superior selection ability?
The ability of a manager to build an investment portfolio which generates abnormal returns through buying undervalued stocks, sectors or industries and selling overvalued stocks, sectors or industries
Does this require total active management?
A portfolio manager might balance funds in both an active portfolio and in a passive portfolio
The goal is to overweight/buy actively managed funds when they outperform the benchmark, and run passively when actively managed funds under-perform 8

14. Questions
Any questions on active management?

15. B. Calculate Risk-adjusted Performance
How do you determine whether a portfolio manager is generating abnormal returns?
Is it just returns?
Should you also be concerned about risk?
It is not just returns that matters—they must be adjusted for risk.
There are a number of recognized performance measures available:
Sharp Index
Treynor Measure
Jensen’s Measure

16. Risk Adjusted Performance: Sharpe
Sharpe Index
A ratio of your “excess return” divided by your portfolio standard deviation
rp – rf sp
rp = Average return on the portfolio
sp = Standard deviation of portfolio return
The Sharpe Index is the portfolio risk premium divided by portfolio risk as measured by standard deviation

17. Risk Adjusted Performance: Treynor
Treynor Measure
This is similar to Sharpe but it uses the portfolio beta instead of the portfolio standard deviation
rp – rf ßp
rp = Average return on the portfolio
rf = Average risk free rate
ßp = Weighted average b for portfolio
It is the portfolio risk premium divided by portfolio risk as measured by beta

18. Risk Adjusted Performance: Jensen
Jensen’s Measure
This is the ratio of your portfolio return less CAPM determined portfolio return
ap = rp - [ rf + ßp (rm – rf) ]
ap = Alpha for the portfolio
rp = Average return on the portfolio
ßp = Weighted average Beta
rf = Average risk free rate
rm = Avg. return on market index port.
It is portfolio performance less expected portfolio performance from CAPM

19. Risk Adjusted Performance (continued)
Which Measure is Appropriate? Are there some general guidelines?
Generally, if the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market is best
If many alternatives are possible, or this is only part of the portfolio, use the Jensen a or the Treynor measure.
Of these two, the Treynor measure is more complete because it adjusts for risk

20. Risk Adjusted Performance (continued)
Are their limitations of risk adjustment measures?
Yes, very much so. The assumptions underlying measures limit their usefulness
Know the key assumptions and be careful!
When the portfolio is being actively managed, basic stability requirements are not met
Be careful
Practitioners often use benchmark portfolio comparisons and comparisons to other managers to measure performance
This is largely because they are easier

21. Risk Adjusted Performance Problem
Consider the following data for a particular sample period: Portfolio P Market
Average return % %
Beta
Standard Deviation % %
Calculate the following performance measures for P and the market: Sharpe, Jensen (alpha), and Treynor. The T-bill rate during the period was 6%. By which measures did P outperform the market.

22. Answer Sharpe = (rp – rf )/ sd Jensen = rp – [rf + ßp (rm – rf)]
Portfolio P Market
Average return % %
Beta
Standard Deviation % %
Sharpe = (rp – rf )/ sd
Portfolio (35-6)/42 = .69
Market (28-6)/30 = .73
Jensen = rp – [rf + ßp (rm – rf)]
Portfolio alpha = 35 – [ (28-6) = 2.6%
Market alpha = 0

23. Answer Treynor = (rp – rf )/ ßp Portfolio P Market
Average return % %
Beta
Standard Deviation % %
Treynor = (rp – rf )/ ßp
Portfolio (35-6)/1.2 = 24.2
Market (28-6)/1.0 = 22.0
The portfolio outperformed the market in terms of the Jensen’s alpha and the Treynor measure, but not the Sharpe ratio.

24. Questions
Any questions on risk-adjusted performance measures?

25. C. Portfolio Attribution and Decomposing Portfolio Returns
What is Portfolio Attribution?
Portfolio attribution is the process of decomposing portfolio returns into components, generally attributable to asset allocation and securities selection (although other components can be added as well)
What is the importance of these components?
These components are related to specific elements of portfolio performance
What are examples of some of these components?
Broad Allocation, security choice, industry, trading, etc.

26. Portfolio Attribution (continued)
How do you determine portfolio attribution?
1. Set up a ‘Benchmark’ or ‘Bogey’ portfolio which includes all relevant asset classes
Use indexes for each component
Use target weight structure
2. Compare your portfolio returns in each asset class to the benchmark returns of each index
3. Calculate your attribution

27. Portfolio Attribution (continued)
Why is it important to attribute performance to the portfolio’s components?
It can explain the difference in return based on component weights or selection
It can summarize the performance differences into appropriate categories
What happens if you don’t perform portfolio attribution?
You will not know why you are performing as you are?
You will not know how to improve

28. Portfolio Attribution Problem
Consider the following information regarding the performance of a money manager during a recent month. The equity index is the S&P500, Bonds the Salomon Brothers Index, and cash is the Lehman Cash.
Asset Class Actual Actual Benchmark Benchmark
Return Weight Weight Return
Equity Fund 2.0% %
Bond Fund % %
Cash Fund % %
a. What was the managers return in the month? What was the over/underperformance?

29. Answer Asset Class Actual Actual Benchmark Benchmark
Return Weight Weight Return
Equity % %
Bonds % %
Cash % %
a. What was the managers return in the month? What was the over or underperformance?
The managers return was (2.0%*.7) + (1.0%*.2) + (.5%*.1) or 1.65%.
The index return was (2.5%*.6) + (1.2%*.3) + (.5%*.1) or 1.91%. the total underperformance was .26% for the portfolio or 1.65%-1.91%.

30. Portfolio Attribution Problem
Asset Class Actual Actual Benchmark Benchmark
Return Weight Weight Return
Equity % %
Bonds % %
Cash % %
b. What was the contribution of security selection to relative performance?
c. What was the contribution of asset allocation to relative performance? Confirm that the sum of selection and allocation contributions equals her total excess return relative to the bogey.

31. Answer Part B
b) What was the contribution of security selection to relative performance?
(1) (2) (1*2)
Market Diff. Ret. Man. Port. Wgt. Contribution
Equity % %
Bonds % %
Cash % %
Contribution of Security Selection %
(1) Fund return less index return (2.0%-2.5%)
(2) Actual weight of the managed portfolio
(1*2) Contribution of asset class security selection to the portfolio

32. Problem Part C
c. What was the contribution of asset allocation to relative performance? Confirm that the sum of selection and allocation contributions equals her total excess return relative to the bogey.
(3) (4) (3*4)
Market Excess Weight Index-BM Contribution
Equity % % %
Bonds % % %
Cash % % %
Contribution of Asset Allocation %
(3) Weight of actively managed fund less benchmark weight (- is underweight)
(4) Asset class return less total portfolio return (equity is or .59%, bond is =-.71)
(3*4) Contribution of the asset class to the total portfolio

33. Overall Attribution Results
The actively managed portfolio under performed the benchmarks by .26% or 26 basis points (1.65%-1.91%). This underperformance was a combination of a -.39% contribution to security selection and a .13% contribution from asset allocation.
While the manager picked the asset classes that performed the best, she didn’t do as well picking the stocks. She needs to work on stock selection or just index that part of the portfolio construction process.

34. Portfolio Attribution Summary
Performance Evaluation and Active Portfolio Management are very difficult tasks
Very few have done it well
Active management is a difficult topic
While some active managers have proven their ability to deliver consistent excess returns, the numbers are few
Finding adequate statistics to evaluate performance is critical
Understand the assumptions on which the statistics are based

35. Questions
Any questions on portfolio attribution?

36. Review of Objectives
A. Do you understand the importance of performance evaluation and active portfolio management?
B. Do you understand how to calculate risk adjusted rates of return?
C. Do you understand how to decompose returns into components attributable to asset allocation and securities selection?