The Theory of Active Portfolio Management

1
Chapter 28

• The Theory ofActive PortfolioManagement

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
Rate of Return of a Perfect Market Timer
5
Returns from 1987 - 1996
Year Lg. Stock Return T-Bill Return 87
5.34 5.50 88 16.86 6.44 89
31.34 8.32 90 -3.20 7.86 91
30.66 5.65 92 7.71 3.54 93
9.87 2.97 94 1.29 3.91 95
37.71 5.58 96 23.00 5.20 Average
16.06 Standard Dev. 14.05
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With Perfect Forecasting Ability

• Switch to T-Bills in 87, 90 and 94
• No negative returns or losses
• Average Ret. 17.44
• S.D. Ret. 12.38
• Results with perfect timing
• Increase in mean return
• Lower S.D.

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
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Reward to Variability Measures
Appraisal Ratio
?
A
?
(eA)
?
Alpha for the active portfolio
A
?
Unsystematic standard deviation for active
(eA)
13
Reward to Variability Measures
Combined Portfolio
E
)

-
2
2
m
f
2
S









A

p
?eA
14
Treynor-Black Allocation
CAL
E(r)
CML
P
A
M
Rf
?
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Summary Points Treynor-Black Model

• Sharpe Measure will increase with added ability
  to pick stocks
• Slope of CALgtCML
• (rp-rf)/?p gt (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