Second Investment Course

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Second Investment Course November 2005

• Topic Six
• Measuring Superior Investment Performance

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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)

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Developing the Capital Asset Pricing Model
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Developing the Capital Asset Pricing Model (cont.)
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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?

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Using the SML in Performance Measurement (cont.)
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Using CAPM to Estimate Expected Return Empresa
Nacional de Telecom
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Estimating Mutual Fund Betas FMAGX vs. GABAX
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Estimating Mutual Fund Betas FMAGX vs. GABAX
(cont.)
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Estimating Mutual Fund Betas FMAGX vs. GABAX
(cont.)
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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

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Estimating the Fama-French Three-Factor Return
Model FMAGX vs. GABAX
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Fama-French Three-Factor Return Model FMAGX vs.
GABAX (cont.)
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Fama-French Three-Factor Return Model FMAGX vs.
GABAX (cont.)
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Style Classification Implied by the Factor Model
Value
Growth
FMAGX
GABAX

Large
Small
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Fund Style Classification by Morningstar

• FMAGX

• GABAX

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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

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The Wrong Question

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

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Fund Performance versus Style Rotation (Rolling
12 Month Returns)
Higher Small-Cap Returns
R2000-R1000
Percent Beating SP 500
Higher Large-Cap Returns
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The Wrong Question (cont.)
Stylized Fact Most active mutual fund managers
compete against the wrong benchmark
SP 500
Diversified Equity Mutual Funds
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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)

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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

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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)

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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?

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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

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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

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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)

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Methodology Fund Mapped by Style Group
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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.

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Performance Analysis
Distributions of Out-of-Sample Future Alphas
(FALPHA) Quarterly Equally Weighted 1979-2003
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Time Series Analysis
Pooled Regressions Fund Characteristics versus
Future Alpha 1979-2003
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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

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Cross-Sectional Performance Results
Fama-MacBeth Regressions Fund Characteristics
versus Future Alpha 1979-2003
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Logit Performance Analysis
Fund Characteristics versus a Positive Future
Alpha 1979-2003
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Probability of Finding a Superior Active Manager

• Probability of Future Positive 3-month Alpha
• Median Manager Controls for Turnover, Assets,
  Diversify, and Volatility

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Probability of Finding a Superior Active Manager
(cont.)

• Probability of Future Positive 3-month Alpha
• Best Manager Controls for Turnover, Assets,
  Diversify, and Volatility

EXPR EXPR EXPR EXPR EXPR EXPR
Std. Dev. Group -2 (Low) -1 0 1 2 (High) (High Low)
PALPHA -2 (Low) 0.5051 0.4968 0.4884 0.4801 0.4718 (0.0333)
PALPHA -1 0.5282 0.5199 0.5116 0.5033 0.4950 (0.0333)
PALPHA 0 0.5512 0.5430 0.5347 0.5264 0.5181 (0.0331)
PALPHA 1 0.5741 0.5659 0.5577 0.5495 0.5412 (0.0328)
PALPHA 2 (High) 0.5965 0.5885 0.5804 0.5723 0.5641 (0.0324)
PALPHA (High Low) 0.0915 0.0918 0.0920 0.0922 0.0923
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Portfolio Strategies Based on Active Manager
Search
Asset Weighted Alpha Deciles - Quarterly
Rebalance 1979-2003
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Portfolio Strategies (cont.)
Asset Weighted - Quarterly Rebalance Formation
Variables Separated by Upper and Lower Quartile
Values 1979-2003
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The Benefit of Selecting Good Managers and
Avoiding Bad Managers
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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.

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

• Portfolio Characteristics

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Cumulative Returns versus SP 500
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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