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Second Investment Course November 2005

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... Investment Performance. We can use the concept of 'alpha' to measure superior investment performance: ... Two investment advisors are comparing performance. ... – PowerPoint PPT presentation

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Title: Second Investment Course November 2005


1
Second Investment Course November 2005
  • Topic Six
  • Measuring Superior Investment Performance

2
Estimating the Expected Returns and Measuring
Superior Investment Performance
  • We can use the concept of alpha to measure
    superior investment performance
  • a (Actual Return) (Expected Return) Alpha
  • In an efficient market, alpha should be zero for
    all investments. That is, securities should, on
    average, be priced so that the actual returns
    they produce equal what you expect them to given
    their risk levels.
  • Superior managers are defined as those investors
    who can deliver consistently positive alphas
    after accounting for investment costs
  • The challenge in measuring alpha is that we have
    to have a model describing the expected return to
    an investment.
  • Researchers typically use one of two models for
    estimating expected returns
  • - Capital Asset Pricing Model
  • - Multi-Factor Models (e.g., Fama-French
    Three-Factor Model)

3
Developing the Capital Asset Pricing Model
4
Developing the Capital Asset Pricing Model (cont.)
5
Using the SML in Performance Measurement An
Example
  • Two investment advisors are comparing
    performance. Over the last year, one averaged a
    19 percent rate of return and the other a 16
    percent rate of return. However, the beta of the
    first investor was 1.5, whereas that of the
    second was 1.0.
  • a. Can you tell which investor was a better
    predictor of individual stocks (aside from the
    issue of general movements in the market)?
  • b. If the T-bill rate were 6 percent and the
    market return during the period were 14 percent,
    which investor should be viewed as the superior
    stock selector?
  • c. If the T-bill rate had been 3 percent and the
    market return were 15 percent, would this change
    your conclusion about the investors?

6
Using the SML in Performance Measurement (cont.)
7
Using CAPM to Estimate Expected Return Empresa
Nacional de Telecom
8
Estimating Mutual Fund Betas FMAGX vs. GABAX
9
Estimating Mutual Fund Betas FMAGX vs. GABAX
(cont.)
10
Estimating Mutual Fund Betas FMAGX vs. GABAX
(cont.)
11
The Fama-French Three-Factor Model
  • The most popular multi-factor model currently
    used in practice was suggested by economists
    Eugene Fama and Ken French. Their model starts
    with the single market portfolio-based risk
    factor of the CAPM and supplements it with two
    additional risk influences known to affect
    security prices
  • - A firm size factor
  • - A book-to-market factor
  • Specifically, the Fama-French three-factor model
    for estimating expected excess returns takes the
    following form

12
Estimating the Fama-French Three-Factor Return
Model FMAGX vs. GABAX
13
Fama-French Three-Factor Return Model FMAGX vs.
GABAX (cont.)
14
Fama-French Three-Factor Return Model FMAGX vs.
GABAX (cont.)
15
Style Classification Implied by the Factor Model
Value
Growth
Large
Small
16
Fund Style Classification by Morningstar
  • FMAGX
  • GABAX

17
Active vs. Passive Equity Portfolio Management
  • The conventional wisdom held by many investment
    analysts is that there is no benefit to active
    portfolio management because
  • - The average active manager does not produce
    returns that exceed those of the benchmark
  • - Active managers have trouble outperforming
    their peers on a consistent basis
  • However, others feel that this is the wrong way
    to look at the Active vs. Passive management
    debate. Instead, investors should focus on ways
    to
  • - Identifying those active managers who are most
    likely to produce superior risk-adjusted return
    performance over time
  • This discussion is based on research authored
    jointly with Van Harlow of Fidelity Investments
    titled
  • The Right Answer to the Wrong Question
  • Identifying Superior Active Portfolio Management

18
The Wrong Question
  • Stylized Fact
  • Most active mutual fund managers cannot
    outperform the SP 500 index on a consistent
    basis

19
Fund Performance versus Style Rotation (Rolling
12 Month Returns)
Higher Small-Cap Returns
R2000-R1000
Percent Beating SP 500
Higher Large-Cap Returns
20
The Wrong Question (cont.)
Stylized Fact Most active mutual fund managers
compete against the wrong benchmark
SP 500
Diversified Equity Mutual Funds
21
Defining Superior Investment Performance
  • Over time, the value added by a portfolio
    manager can be measured by the difference between
    the portfolios actual return and the return that
    the portfolio was expected to produce.
  • This difference is usually referred to as the
    portfolios alpha.
  • Alpha (Actual Return) (Expected Return)

22
Measuring Expected Portfolio Performance
  • In practice, there are three ways commonly used
    to measure the return that was expected from a
    portfolio investment
  • - Benchmark Portfolio Return
  • Example SP 500 or Russell 1000 indexes for a
    U.S. Large-Cap Blend fund manager, IPSA index for
    Chilean equity manager
  • Pros Easy to identify Easy to observe
  • Cons Hypothetical return ignoring taxes,
    transaction costs, etc. May not be
    representative of actual investment universe No
    explicit risk adjustment
  • - Peer Group Comparison Return
  • Example Median Return to all U.S. Small-Cap
    Growth funds for a U.S. Small-Cap Growth fund
    manager, Sistema fondo averages for Chilean AFP
    managers
  • Pros Measures performance relative to managers
    actual competition
  • Cons Difficult to identify precise peer group
    Median manager may ignore large dispersion in
    peer group universe Universe size disparities
    across time and fund categories
  • - Return-Generating Model
  • Example Single Risk-Factor Model (CAPM)
    Multiple Risk-Factor Model (Fama-French
    Three-Factor, Carhart Four-Factor)
  • Pros Calculates expected fund returns based on
    an explicit estimate of fund risk Avoids
    arbitrary investment style classifications
  • Cons No direct investment typically Subject to
    model misspecification and factor measurement
    problems Model estimation error

23
The Wrong Question (Revisited)
  • Stylized Fact
  • Across all investment styles, the median
    manager cannot produce positive risk-adjusted
    returns (i.e., PALPHA using return model)

24
The Right Answer
  • When judging the quality of active fund managers,
    the important question is not whether
  • The average fund manager beats the benchmark
  • The median manager in a given peer group
    produces a positive alpha
  • The proper question to ask is whether you can
    select in advance those managers who can
    consistently add value on a risk-adjusted basis
  • Does superior investment performance persist from
    one period to the next and, if so, how can we
    identify superior managers?

25
Lessons from Prior Research
  • Fund performance appears to persist over time
  • Original View
  • Managers with superior performance in one period
    are equally likely to produce superior or
    inferior performance in the next period
  • Current View
  • Some evidence does support the notion that
    investment performance persists from one period
    to the next
  • The evidence is particularly strong that it is
    poor performance that tends to persist (i.e.,
    icy hands vs. hot hands)
  • Security characteristics, return momentum, and
    fund style appear to influence fund performance
  • Security Characteristics
  • After controlling for risk, portfolios containing
    stocks with different market capitalizations,
    price-earnings ratios, and price-book ratios
    produce different returns
  • Funds with lower portfolio turnover and expense
    ratios produce superior returns

26
Lessons from Prior Research (cont.)
  • Security characteristics, return momentum, and
    fund style appear to influence fund performance
    (cont.)
  • Fund Style Definitions
  • After controlling for risk, funds with different
    objectives and style mandates produce different
    returns
  • Value funds generally outperform growth funds on
    a risk-adjusted basis
  • Style Investing
  • Fund managers make decisions as if they
    participate in style-oriented return performance
    tournaments
  • The consistency with which a fund manager
    executes the portfolios investment style mandate
    affects fund performance, in both up and down
    markets
  • Active fund managers appear to possess genuine
    investment skills
  • Stock-Picking Skills
  • Some fund managers have security selection
    abilities that add value to investors, even after
    accounting for fund expenses
  • A sizeable minority of managers pick stocks well
    enough to generate superior alphas that persist
    over time

27
Data and Methodology for Performance Analysis
  • CRSP (Center for Research in Security Prices) US
    Mutual Fund Database
  • Survivor-Bias Free database of monthly returns
    for mutual funds for the period 1962-2003
  • Screens
  • Diversified domestic equity funds only
  • Eliminate index funds
  • Require 30 prior months of returns to be included
    in the analysis on any given date
  • Assets greater than 1 million
  • Period 1979 2003 in order to analyze
    performance versus an index fund and have
    sufficient number of mutual funds
  • Return-generating model
  • Fama-French
  • E(Rp) RF bmE(Rm) RF bsmlSML
    bhmlHML
  • Style classification
  • Map funds to Morningstar-type style categories
    based on Fama-French SML and HML factor exposures
    (LV, LB, LG, MV, MB, MG, SV, SB, SG)

28
Methodology Fund Mapped by Style Group
29
Methodology (cont.)
Evaluate Performance
Estimate Model
Time
3 Months (1 Month)
36 Months
  • Use past 36 months of data to estimate model
    parameters
  • Standardized data within each peer group on a
    given date to allow for time-series and
    cross-sectional pooling Brown, Harlow, and
    Starks (JF, 1996)
  • Evaluate performance
  • Use estimated model parameters to calculate
    out-of-sample alphas based on factor returns from
    the evaluation period
  • Roll the process forward one quarter (one month)
    and estimate all parameters again, etc.

30
Performance Analysis
Distributions of Out-of-Sample Future Alphas
(FALPHA) Quarterly Equally Weighted 1979-2003
31
Time Series Analysis
Pooled Regressions Fund Characteristics versus
Future Alpha 1979-2003
32
Cross-Sectional Analysis
  • Use past 36 months of data to estimate model
    parameters
  • Run a sequence of Fama-MacBeth cross-sectional
    regressions of future performance against fund
    characteristics and model parameters (alpha and
    R2 )
  • Average the coefficient estimates from
    regressions across the entire sample period
  • T-statistics based on the time-series means of
    the coefficients

33
Cross-Sectional Performance Results
Fama-MacBeth Regressions Fund Characteristics
versus Future Alpha 1979-2003
34
Logit Performance Analysis
Fund Characteristics versus a Positive Future
Alpha 1979-2003
35
Probability of Finding a Superior Active Manager
  • Probability of Future Positive 3-month Alpha
  • Median Manager Controls for Turnover, Assets,
    Diversify, and Volatility

36
Probability of Finding a Superior Active Manager
(cont.)
  • Probability of Future Positive 3-month Alpha
  • Best Manager Controls for Turnover, Assets,
    Diversify, and Volatility

37
Portfolio Strategies Based on Active Manager
Search
Asset Weighted Alpha Deciles - Quarterly
Rebalance 1979-2003
38
Portfolio Strategies (cont.)
Asset Weighted - Quarterly Rebalance Formation
Variables Separated by Upper and Lower Quartile
Values 1979-2003
39
The Benefit of Selecting Good Managers and
Avoiding Bad Managers
40
Implementing a Fund of Funds Strategy An
Example
Methodology
  • Use past 9 months of daily data to estimate model
    and in-sample alpha
  • Optimize portfolio based on an assumption of risk
    aversion, i.e., risk-return tradeoff preference
  • Compute the performance of the portfolio over the
    next three (one) months
  • Roll the process forward each quarter and
    estimate all parameters again, etc.

41
Fund of Funds Strategy
Fidelity Advisor Diversified Equity Fund Styles
(6/04)
42
Fund of Funds Portfolio Strategy
Portfolio Weights Over Time
  • Portfolio Characteristics

43
Cumulative Returns versus SP 500
44
Active vs. Passive Management Conclusions
  • Both passive and active management can play a
    role in an investors portfolio
  • Strong evidence for both positive and negative
    performance persistence (i.e., alpha persistence)
  • Prior alpha is the most significant variable for
    forecasting future alpha
  • Expense ratio, risk measures, turnover and assets
    are also useful in forecasting future alpha
  • The existence of performance persistence provides
    a reasonable opportunity to construct portfolios
    that add value on a risk-adjusted basis
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