Active 3927

  • View
    212

  • Download
    0

Embed Size (px)

Text of Active 3927

  • 7/29/2019 Active 3927

    1/23

    Active or Passive? Issues and

    Strategies Market Efficiency

    Anomalies

    Market Timing

    A theoretical model of active portfolio

    management (Treynor-Black)

    Quantitative Investment Management

  • 7/29/2019 Active 3927

    2/23

    Equity Portfolio Management:

    Active or Passive?

  • 7/29/2019 Active 3927

    3/23

    Equity Portfolio Management:

    Active or Passive? Passive:

    LT buy and hold

    Indexation

    Replication of an index (broad or specialized

    Sampling and Tracking Error

    = 0Rebalancing

  • 7/29/2019 Active 3927

    4/23

    Indexation

    Identify a Benchmark Index

    replicate benchmark index performance

    a true passive strategy will not attempt tooutperform index

    Tracking Error = measure of accuracy

  • 7/29/2019 Active 3927

    5/23

    Tracking Error: Measure 1

    TE1 =

    where Rpt and Rbt are portfolio and benchmark returns

    respectively

    n

    RRn

    t

    btpt

    1

    2)(

  • 7/29/2019 Active 3927

    6/23

    Tracking Error: Measure 1

    TE2 = e

    This 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 e later

  • 7/29/2019 Active 3927

    7/23

    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!

  • 7/29/2019 Active 3927

    8/23

    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

    Z35 95 $3325 0.333 0.8

    Total $9995 1.20

  • 7/29/2019 Active 3927

    9/23

    Rebalancing: Example 1

    June 1 Price perShare

    Numberof Shares

    $ Value % ofTotalValue

    Beta

    down20% X 16 167 $2672 0.256 1.3

    up33%

    Y 20 222 $4440 0.425 1.7

    unch. Z 35 95 $3325 0.319 0.8

    Total 10445 1.31

  • 7/29/2019 Active 3927

    10/23

    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)

  • 7/29/2019 Active 3927

    11/23

    Rebalancing: Example 1

    June 1

    Rebal-

    anced

    Price perShare

    Numberof Shares

    $ Value % ofTotalValue

    Beta

    X 16 167 $3488 0.334 1.3

    Y 20 222 $3480 0.334 1.7

    Z 35 95 $3465 0.332 0.8Total 10433 1.27

  • 7/29/2019 Active 3927

    12/23

    Rebalancing: Example 1

    LT effects of this strategy?

    Alternatives?

    Example 2: Rebalancing to reestablish a

    specific level of systematic risk (TargetBeta = 1.2)

  • 7/29/2019 Active 3927

    13/23

    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

  • 7/29/2019 Active 3927

    14/23

    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

  • 7/29/2019 Active 3927

    15/23

    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 /e

    IC = information coefficient

    correlation between forecast and actual (CORR(E(), )

    BR = breadth

    # of stocks evaluated per period

  • 7/29/2019 Active 3927

    16/23

    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 in50th)

    What if Im an industry picker?

  • 7/29/2019 Active 3927

    17/23

    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 amultifactor analysis. Standardize S. (e.g., S=+1.0

    is 1 s.d. above the mean of 0)

    Adapting the fundamental law:

    = IC x e x S = Skill x Volatility x Signal

  • 7/29/2019 Active 3927

    18/23

    Using the Fundamental law to forecast alpha

    Example:

    Your analysis produces a binary buy or sell

    recommendation. Your IC = .05 (really good!)

    Stock Sigma Buy or Sell Score Alpha

    A .15 Buy +1.0 .0075

    B .20 Buy +1.0 .01

    C .15 Sell -1.0 -.0075D .30 Sell -1.0 -.015

    E .25 Sell -1.0 -.0125

  • 7/29/2019 Active 3927

    19/23

    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?

  • 7/29/2019 Active 3927

    20/23

    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 () for analyzed securities

    Find optimal weights of analyzed securities to create active

    component (A) Combine A, M and risk-free asset to achieve efficiency

  • 7/29/2019 Active 3927

    21/23

    Treynor-Black: Construction

    (Step 1) Assume: ri = rf+ i(rM - rf) + ei

    For analyzed security k:

    rk= rf+ k(rM - rf) + ek+ k=> estimate k, k, s

    2(ek)

    To construct A:

    wk= (k/s2(ek))/(S[i/s2(ei)])=> determine A, A, s

    2(eA)

  • 7/29/2019 Active 3927

    22/23

    Treynor-Black: Construction

    (Step 2) w0 = (A/s

    2(eA))/[(E(rM)-rf)/s2

    M]

    w* = w0/(1+(1-A)w0)

    w0

    * is the proportion of A in the new,

    enhanced market portfolio (M)

  • 7/29/2019 Active 3927

    23/23

    Active Equity Strategies

    Styles:

    Sector Rotation: move in/out of sectors as

    economy improves/declinesEarnings Momentum: overweight stocks

    displaying above average earnings growth

    Enhanced Index Fund - majority of funds trackindex, some funds are actively managed

    Quantitative Investment Management

Search related