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active.ppt
1. Equity Portfolio Management:
Active or Passive?
• Passive:
– LT buy and hold
– Indexation
• Replication of an index (broad or specialized
• Sampling and Tracking Error
• = 0
– Rebalancing
3. Rebalancing an Equity Portfolio
• Why?
– to manage tracking error (if indexing or not)
– to maintain a desired set of weights or risk level
– client needs change
– Market risk level changes
– bankruptcies, mergers, IPOs
• Why not?
– it’s costly!
4. Rebalancing: Example 1
Jan. 1 Price per
Share
Number
of Shares
$ Value % of
Total
Value
Beta
X 20 167 $3340 0.333 1.2
Y 15 222 $3330 0.333 1.6
Z 35 95 $3325 0.333 0.8
Total $9995 1.20
5. Rebalancing: Example 1
June 1 Price per
Share
Number
of Shares
$ Value % of
Total
Value
Beta
down
20%
X 16 167 $2672 0.256 1.3
up
33%
Y 20 222 $4440 0.425 1.7
unch. Z 35 95 $3325 0.319 0.8
Total 10445 1.31
6. Rebalancing: Example 1
• Portfolio is no longer equally weighted
• To rebalance:
– Sell Y, buy X and Z
– Positions must be reset to $10445/3 = $3482
– Sell 4440 - 3482 = $958 of Y (48 shares)
– Buy 3482 - 2672 = $810 of X (51 shares)
– Buy 3482 - 3325 = $157 of Z (4 shares)
7. Rebalancing: Example 1
June 1
Rebal-
anced
Price per
Share
Number
of Shares
$ Value % of
Total
Value
Beta
X 16 167 $3488 0.334 1.3
Y 20 222 $3480 0.334 1.7
Z 35 95 $3465 0.332 0.8
Total 10433 1.27
8. Rebalancing: Example 1
• LT effects of this strategy?
• Alternatives?
• Example 2: Rebalancing to reestablish a
specific level of systematic risk (Target Beta
= 1.2)
9. Rebalancing: Example 2
• Reestablishing a beta of 1.2:
– No unique solution for more than 2 securities
– Need to sell high stocks and buy low stocks
– For example, sell Y, buy Z, hold X constant
– p = (.256)(1.3)+(WY)(1.7)+(1-.256-WY)(.8)
– Find Y such that p = 1.2
• WY = .302 => WZ = 1-.256-.302 = .442
• $3488 in X, $3151 in Y, $4611 in Z
10. Active Equity Strategies
• Beat the market on a risk adjusted basis!
• Need a benchmark
• More expensive: turnover, research
• Must outperform on a fee-adjusted basis
11. Active Equity Strategies
• Styles:
– Sector Rotation: move in/out of sectors as
economy improves/declines
– Earnings Momentum: overweight stocks
displaying above average earnings growth
– Enhanced Index Fund - majority of funds track
index, some funds are actively managed
– Quantitative Investment Management
12. Quantitative Investment
Management
• How do we forecast performance ?
– Screening (Fundamental or Technical factors)
– Rank based on some set of factors that
correlates with future performance (such as
regression analysis)
• How do we improve forecasting model?
– Add more data (more observations)
– Uncover new causal relationships (variables)
13. Quantitative Investment
Management
• Regardless of forecast, there are three basic results
common to QIM:
– 1. Information comes from unexpected events
• events with low probability have high info content!
14. QIM
– 2. Profitable QIM techniques won’t be commercialized
• Starting with a multifactor model:
• Ri = b1F1 + b2F2 + . . . + bkFk + ei
• It isn’t easy to get information from these residuals:
– 1. patterns are complex
– 2. quality of data is limited
– 3. outliers may draw undue attention (although irrelevant)
– 4. human judgement is superior
– 5. analysis must be flexible (more data, constraints)
– 6. danger of data mining
– 7. even if significant, outliers are too few in number!
15. QIM
– 3. Non-linear models are important
• Neural Networks
• Genetic Algorithms
• Fuzzy Logic
• Non-Linear Dynamics
• Classification Trees (Recursive Partitioning)
