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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. Equity Portfolio Management: Active or Passive?. Equity Portfolio Management: Active or Passive?.

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active or passive issues and strategies
Active or Passive? Issues and Strategies
  • Market Efficiency
  • Anomalies
  • Market Timing
  • A theoretical model of active portfolio management (Treynor-Black)
  • Quantitative Investment Management
equity portfolio management active or passive1
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
indexation
Indexation
  • Identify a Benchmark Index
    • replicate benchmark index performance
    • a true passive strategy will not attempt to outperform index
    • Tracking Error = measure of accuracy
tracking error measure 1
Tracking Error: Measure 1
  • TE1 =where Rpt and Rbt are portfolio and benchmark returns respectively
tracking error measure 11
Tracking Error: Measure 1
  • TE2 = σeThis 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 σe later
rebalancing an equity portfolio
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!
rebalancing example 12
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)
rebalancing example 14
Rebalancing: Example 1
  • LT effects of this strategy?
  • Alternatives?
  • Example 2: Rebalancing to reestablish a specific level of systematic risk (Target Beta = 1.2)
rebalancing example 2
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
active equity strategies
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
active management is forecasting
Active Management is Forecasting!
  • The Fundamental Law of Active Management: (Grinold and Kahn) IR = IC x (BR)0.5
  • IR = information ratio
    • “reward-to-risk” or a/σe
  • IC = information coefficient
    • correlation between forecast and actual (CORR(E(a), a)
  • BR = breadth
    • # of stocks evaluated per period
ir ic x br 0 5
IR = IC x (BR)0.5
  • Example:
    • a stockpicker has an IC of .035 and makes 200 “bets” per quarter (800 per year)
    • IR = (.035)(800)0.5 = .99 (is this good??)
    • BARRA research indicates that an IR of +1.0 is in the 90th percentile (-1.0 is in 10th, 0 is in 50th)
    • What if I’m an industry picker?
using the fundamental law to forecast alpha
Using the Fundamental law to forecast alpha
  • Suppose that there is some indicator or signal that we use to forecast performance. Call it S. S can be a single factor (price-to-book) or the result of a multifactor analysis. Standardize S. (e.g., S=+1.0 is 1 s.d. above the mean of 0)
  • Adapting the fundamental law:a = IC x σe x Sa = Skill x Volatility x Signal
using the fundamental law to forecast alpha1
Using the Fundamental law to forecast alpha
  • Example:
    • Your analysis produces a binary “buy” or “sell” recommendation. Your IC = .05 (really good!)
treynor black model
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?
treynor black model assumptions
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
treynor black construction step 1
Treynor-Black: Construction (Step 1)
  • Assume: ri = rf + bi(rM - rf) + ei
  • For analyzed security k: rk = rf + bk(rM - rf) + ek + ak => estimate ak, bk, s2(ek)
  • To construct A: wk = (ak/s2(ek))/(S[ai/s2(ei)]) => determine aA, bA, s2(eA)
treynor black construction step 2
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‘)
active equity strategies1
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