6 - 0 Second Investment Course – November 2005 Topic Six: Measuring Superior Investment Performance

6 - 1 Estimating the Expected Returns and Measuring Superior Investment Performance We can use the concept of “alpha” to measure superior investment performance:  = (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)

6 - 2 Developing the Capital Asset Pricing Model

6 - 3 Developing the Capital Asset Pricing Model (cont.)

6 - 4 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 - 5 Using the SML in Performance Measurement (cont.)

6 - 6 Using CAPM to Estimate Expected Return: Empresa Nacional de Telecom

6 - 7 Estimating Mutual Fund Betas: FMAGX vs. GABAX

6 - 8 Estimating Mutual Fund Betas: FMAGX vs. GABAX (cont.)

6 - 9 Estimating Mutual Fund Betas: FMAGX vs. GABAX (cont.)

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:

Estimating the Fama-French Three-Factor Return Model: FMAGX vs. GABAX

Fama-French Three-Factor Return Model: FMAGX vs. GABAX (cont.)

Fama-French Three-Factor Return Model: FMAGX vs. GABAX (cont.)

Style Classification Implied by the Factor Model FMAGX * * GABAX Small Large Value Growth

Fund Style Classification by Morningstar FMAGX GABAX

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”

The Wrong Question Stylized Fact: Most active mutual fund managers cannot outperform the S&P 500 index on a consistent basis

Higher Small-Cap Returns Higher Large-Cap Returns R2000-R1000 Percent Beating S&P 500 Fund Performance versus Style Rotation (Rolling 12 Month Returns)

S&P 500 Diversified Equity Mutual Funds Stylized Fact: Most active mutual fund managers compete against the “wrong” benchmark The Wrong Question (cont.)

Defining Superior Investment Performance Over time, the “value added” by a portfolio manager can be measured by the difference between the portfolio’s actual return and the return that the portfolio was expected to produce. This difference is usually referred to as the portfolio’s alpha. Alpha = (Actual Return) – (Expected Return)

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: S&P 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 manager’s 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

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)

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?

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  Return Momentum: Funds following return momentum strategies generate short-term performance persistence When used as a separate risk factor, return momentum “explains” fund performance persistence

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 portfolio’s 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  Investment Discipline: Fund managers who control tracking error generate superior performance relative to traditional active managers and passive portfolios  Manager Characteristics: The educational backgrounds of managers systematically influence the risk-adjusted returns of the funds they manage

CRSP (Center for Research in Security Prices) US Mutual Fund Database  Survivor-Bias Free database of monthly returns for mutual funds for the period 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(R p ) = RF + {  m [E(R m ) – RF] +  sml [SML] +  hml [HML]} 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) Data and Methodology for Performance Analysis

Methodology: Fund Mapped by Style Group

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. Estimate Model Evaluate Performance 36 Months 3 Months (1 Month) Time Methodology (cont.)

Distributions of Out-of-Sample Future Alphas (FALPHA) Quarterly – Equally Weighted Performance Analysis

Pooled Regressions – Fund Characteristics versus Future Alpha Time Series Analysis Parameter Variable Parameter Estimate Prob Estimate Prob Diversify (R-Sq) Expense Ratio Turnover Assets Intercept Past Alpha 1 Month Alpha 3 Month Alpha (0.036) (0.012) (0.055) (0.023) Volatility(0.012) (0.006)

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 R 2 ) Average the coefficient estimates from regressions across the entire sample period T-statistics based on the time-series means of the coefficients Cross-Sectional Analysis

Cross-Sectional Performance Results Parameter Variable Parameter Estimate Prob Estimate Prob Diversify (R-Sq) Expense Ratio Turnover Assets Past Alpha 1 Month Alpha 3 Month Alpha (0.021) (0.012) (0.023) (0.019) Volatility(0.011) (0.022) Fama-MacBeth Regressions – Fund Characteristics versus Future Alpha

Logit Performance Analysis Fund Characteristics versus a Positive Future Alpha Parameter Variable Parameter Estimate Prob Estimate Prob Diversify (R-Sq) Expense Ratio Turnover Assets Intercept Past Alpha 1 Month Alpha 3 Month Alpha (0.085) (0.021) (0.159) (0.117) (0.033) (0.228) Volatility(0.003) (0.022)

Probability of Finding a Superior Active Manager Probability of Future Positive 3-month Alpha Median Manager Controls for Turnover, Assets, Diversify, and Volatility

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: Std. Dev. Group -2 (Low)0+1+2 (High)(High – Low) PALPHA:-2 (Low) (0.0333) (0.0333) (0.0331) (0.0328) +2 (High) (0.0324) (High – Low)

Portfolio Strategies Based on Active Manager Search Asset Weighted Alpha Deciles - Quarterly Rebalance

Asset Weighted - Quarterly Rebalance Formation Variables Separated by Upper and Lower Quartile Values Portfolio Strategies (cont.)

The Benefit of Selecting Good Managers and Avoiding Bad Managers

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. Implementing a “Fund of Funds” Strategy: An Example Estimate Model Evaluate Performance 9 Months 3 Months (1 Month) Time Methodology

“Fund of Funds” Strategy Fidelity Advisor Diversified Equity Fund Styles (6/04)

“Fund of Funds” Portfolio Strategy Portfolio Weights Over Time Portfolio Characteristics

Cumulative Returns versus S&P 500

Active vs. Passive Management: Conclusions Both passive and active management can play a role in an investor’s 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