Active or Passive? Issues and Strategies

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Active or Passive? Issues and Strategies

• Market Efficiency
• Anomalies
• Market Timing
• A theoretical model of active portfolio
  management (Treynor-Black)
• Quantitative Investment Management

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Equity Portfolio Management Active or Passive?
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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

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Indexation

• Identify a Benchmark Index
• replicate benchmark index performance
• a true passive strategy will not attempt to
  outperform index
• Tracking Error measure of accuracy

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Tracking Error Measure 1

• TE1 where Rpt and Rbt are portfolio and
  benchmark returns respectively

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Tracking Error Measure 1

• TE2 seThis represents the standard
  deviation of the error terms of a regression
  equation explaining returns from the portfolio
  with returns from the benchmark.
• We will revisit se later

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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?
• its costly!

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Rebalancing Example 1
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Rebalancing Example 1
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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)

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Rebalancing Example 1
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Rebalancing Example 1

• LT effects of this strategy?
• Alternatives?
• Example 2 Rebalancing to reestablish a specific
  level of systematic risk (Target Beta 1.2)

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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 gt WZ 1-.256-.302 .442
• 3488 in X, 3151 in Y, 4611 in Z

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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

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Treynor-Black Model

• Suppose you can identify securities that you
  expect to outperform (or underperform) on a
  risk-adjusted basis
• How do you exploit this model?

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Treynor-Black Model Assumptions

• Analysts can only produce quality analysis on a
  small number of securities
• There is a passive market portfolio (M)
• Forecasts of return (E(rM) and risk (s) exist
• Determine abnormal return (a) for analyzed
  securities
• Find optimal weights of analyzed securities to
  create active component (A)
• Combine A, M and risk-free asset to achieve
  efficiency

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Treynor-Black Construction (Step 1)

• Assume ri rf bi(rM - rf) ei
• For analyzed security k rk rf bk(rM - rf)
  ek ak gt estimate ak, bk, s2(ek)
• To construct A wk (ak/s2(ek))/(Sai/s2(ei))
  gt determine aA, bA, s2(eA)

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Treynor-Black Construction (Step 2)

• w0 (aA/s2(eA))/(E(rM)-rf)/s2M
• w w0/(1(1-?A)w0)
• w0 is the proportion of A in the new, enhanced
  market portfolio (M)

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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