1. Performance Evaluation and Active Portfolio Management
CHAPTER 18
Performance Evaluation and Active Portfolio Management

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 managements leads to measurement problems

3. Abnormal Performance What is abnormal?
Abnormal performance is measured:
Comparison groups
Market adjusted
Market model / index model adjusted
Reward to risk measures such as the Sharpe Measure:
E (rp-rf) / sp

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

5. Comparison Groups Simplest method Most popular
Compare returns to other funds with similar investment objectives

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

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

8. Risk Adjusted Performance: Jensen
3) Jensen’s Measure
= rp - [ rf + ßp ( rm - rf) ] a p
= Alpha for the portfolio a p
rp = Average return on the portfolio
ßp = Weighted average Beta
rf = Average risk free rate
rm = Avg. return on market index port.

9. 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

10. M2 Measure: Example Managed Portfolio Market T-bill Return 35% 28% 6%
Stan. Dev 42% % %
Hypothetical Portfolio: Same Risk as Market
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

11. Figure 17-2 The M2 of Portfolio P

12. T2 (Treynor Square) Measure
Used to convert the Treynor Measure into percentage return basis
Makes it easier to interpret and compare
Equates the beta of the managed portfolio with the market’s beta of 1 by creating a hypothetical portfolio made up of T-bills and the managed portfolio
If the beta is lower than one, leverage is used and the hypothetical portfolio is compared to the market

13. T2 Example Port. P. Market Risk Prem. (r-rf) 13% 10% Beta 0.80 1.0
Alpha % 0%
Treynor Measure
Weight to match Market w = bM/bP = 1.0 / 0.8
Adjusted Return RP* = w (RP) = 16.25%
T2P = RP* - RM = 16.25% - 10% = 6.25%

14. Figure 17-3 Treynor Square Measure

15. 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 a or the Treynor measure
The Treynor measure is more complete because it adjusts for risk

16. Exercise2
1. A managed portfolio has a standard deviation equal to 22% and a beta of 0.9 when the market portfolio's standard deviation is 26%. The adjusted portfolio P* needed to calculate the M2 measure will have _____ invested in the managed portfolio and the rest in T-bills.  a. 84.6% b. 118% c. 18% d. 15.4%

17. Exercise 2
 Use the following to answer questions 2-4: The average returns, standard deviations and betas for three funds are given in previous slide along with data for the S&P 500 index. The risk free return during the sample period is 6%.    
2. You wish to evaluate the three mutual funds using the Sharpe measure for performance evaluation. The fund with the highest Sharpe measure of performance is __________.  a. Fund A b. Fund B c. Fund C d. Indeterminable   
3. You wish to evaluate the three mutual funds using the Treynor measure for performance evaluation. The fund with the highest Treynor measure of performance is __________.  a. Fund A b. Fund B c. Fund C d. Indeterminable
4. You wish to evaluate the three mutual funds using the Jensen measure for performance evaluation. The fund with the highest Jensen measure of performance is __________.  a. Fund A b. Fund B c. Fund C d. S&P500

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

19. 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

20. 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

21. Rate of Return of a Perfect Market Timer What if the forecast is not precise?rM rf 4

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

23. Figure 17-6 Characteristic Lines

24. Style Analysis Introduced by Bill Sharpe
Explaining percentage returns by allocation to style
Style Analysis has become popular with the industry

25. 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