1. The Theory of Active Portfolio Management
Chapter 27

2. 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.

3. 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.

4. Return of a Perfect Market TimerrM rf

5. Returns from 1990 - 1999 Year Lg Stocks T-Bills 1990 -3.20 7.86 1991
30.66
5.65
1992
7.71
3.54
1993
9.87
2.97
1994
1.29
3.91
1995
37.71
5.58
1996
23.07
1998
28.58
5.11
1999
21.04
4.80

6. With Perfect Forecasting Ability
Switch to bills in 1990 and 1994
Mean =18.94% Standard Deviation = 12.04%
Invested in large stocks for the entire period
Mean =17.41% Standard Deviation =14.11%
The results are clearly related to the period

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

8. 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.

9. 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.

10. 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.

11. Reward to Variability Measures
Passive Portfolio :

12. Reward to Variability Measures
Appraisal Ratio:

13. Reward to Variability Measures
Combined Portfolio :

14. Treynor-Black Allocation
CAL
E(r)
CML P A M Rf 

15. 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.