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The Size Effect. Brett Bates Greg Chedwick Chris Ferre Matt Karam. The Size Effect. 2 Articles by Marc Reinganum: “Abnormal Returns in Small Firm Portfolios” (1981) “ Portfolio Strategies Based on Market Capitalization’ (1983)

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the size effect
The Size Effect

Brett Bates

Greg Chedwick

Chris Ferre

Matt Karam

the size effect1
The Size Effect
  • 2 Articles by Marc Reinganum:
    • “Abnormal Returns in Small Firm Portfolios” (1981)
    • “Portfolio Strategies Based on Market Capitalization’ (1983)
  • The Capital Asset Pricing Model (CAPM) asserts that two assets with the same beta will have the same expected return
  • The model implies that small firms will only command higher risk premiums if they have higher betas
  • Do abnormal returns exist, that are not explained by Beta?
capital asset pricing model
Capital Asset Pricing Model

Security Market Line

E(Ri) = Rf+ βi(E(Rm) − Rf)

E(Ri) =the expected return on the capital asset

Rf= the risk-free rate of interest

βi =(beta coefficient) = the sensitivity of the asset returns to market returns

E(Rm) = the expected return of the market

E(Rm) - Rf=the market premium or risk premium

the test
The Test
  • CAPM implies that any two assets with the same Beta will possess identical expected returns
  • Since the Beta of the Market Portfolio by definition = 1.0, the difference between the return of another portfolio with a Beta near 1.0 and that of the market portfolio measures Abnormal Return
  • If CAPM is correct, over long time periods the difference in returns should be zero.
  • Simple test of the CAPM is to form portfolios with Betas near 1.0 and determine whether the mean abnormal returns are statistically different from zero.
the data
The Data
  • Collected NYSE & AMEX stock prices from 1962 - 1975
  • Ranked all stocks by December 31 stock market values, and divided into 10 equally equally-weighted portfolios.
  • Combined daily returns of securities to obtain portfolio returns.
  • Equal weights were applied to all securities and portfolios were adjusted for beta risk
  • Re-balanced portfolio by repeating step 2 at the end of each year.
  • Calculated abnormal returns (Daily returns of portfolios minus daily return of the equally-weighted NYSE/AMEX index)
  • Analyzed portfolios in 2 ways:
    • Computed Average Rates of Return for year subsequent to formation
    • Computed Average Rates of Return for second year after formation
  • Persistence of small firm abnormal returns reduces the chance that the results are due to market inefficiencies.
  • Portfolio with smallest firms on average experienced returns >20% a year higher than portfolio with largest firms.
  • Investors can form portfolios that systematically earn abnormal returns based on firm size.
  • CAPM does not adequately describe stock return behavior.
  • The persistence of positive abnormal returns for small firm portfolios seriously violates the null hypothesis that the mean abnormal returns associated with the simple one-period CAPM are zero.
portfolio strategies based on market capitalization background
Portfolio Strategies Based on Market Capitalization – Background
  • Inspired by size effect theory posed by R. W. Banz, Mark Reinganum corroborated size effect in 1981.
    • Banz divided the stocks on the NYSE into quintiles based on market capitalization. The returns from 1926 to 1980 for the smallest quintile outperformed the other quintiles
  • Reinganum (1983) takes it a step further
    • CAPM is deficient in accounting for the differences in rates of returns with equivalent beta risk
portfolio strategies based on market capitalization issue
Portfolio Strategies Based on Market Capitalization – Issue
  • Does market capitalization have an effect on the rate of return of a portfolio over time?
  • Do actively managed portfolios outperform passively managed portfolios?
portfolio strategies based on market capitalization sourced data
Portfolio Strategies Based on Market Capitalization - Sourced Data
  • Market capitalizations and stock returns came from the University of Chicago’s CRSP daily tape file
    • Data from 1963 to 1980 comprised from stocks listed on the New York and American Stock Exchanges
  • Data cleansing due to delisting
    • Acquisitions
    • Bankruptcy
    • Failure to satisfy listing requirements of the exchange
portfolio strategies based on market capitalization test design
Portfolio Strategies Based on Market Capitalization - Test Design
  • Multipurpose Design
    • Firm Size
      • Ten equally weighted portfolios grouped by market capitalization
    • Active vs. Passive
      • Actively managed portfolio were rebalanced every based on year end market capitalization
      • Passively managed portfolio compositions were not altered for the duration of the 18 year test
      • In both cases, proceeds from delisted securities were reinvested into S&P 500 Index fund
active strategy results
Active Strategy Results
  • Market Capitalization size returns evident across the portfolio spectrum
    • MV1 returned cumulative returns of 4528%
    • MV2 returned cumulative returns of 1850%
    • MV3 returned cumulative returns of 2016%
    • MV5 returned cumulative returns of 1179%
    • MV10 returned cumulative returns of 312 %
passive strategy results
Passive Strategy Results
  • Small Firms did better even without rebalancing
    • MV1 returned cumulative returns of 1026%
    • MV5 returned cumulative returns of 562%
    • MV10 returned cumulative returns of 328%
  • Mean returns for small firms is substantially greater than the mean holding period return for large firms (as much as 22.2% per year)
  • The odds for small versus large firm doubling in value were 10:1
  • The downside: a small firm was almost twice as likely to experience a one-year return of 25% or less
  • Over time, the returns of big winners more than offset the losses within the small portfolio

Average Returns were systematically related to market capitalization.

  • Smaller firms outperformed larger ones on average even after adjusting for risk as measured by beta
  • Returns Astounding
    • $1 invested in 1962 in small capitalization became $46 by 1980
    • Firms earn approximately twice as much as firms with twice the market capitalization
  • Firms investing using size strategies should be actively managed rather than passive
  • In short market capitalization was an excellent indicator for long run rates of return
modern applications
Modern Applications
  • Hedge Funds
  • Index Funds – Mid 1970s
  • Exchange Traded Funds – Early 1990s
    • Spiders (SPDR)
    • Active management ETFs - 2008
index and sector funds
Index and Sector Funds
  • Offer target-specific index tracking
  • Cannot outperform the constituents of their index
  • Standardized survival biases
etfs and active spdrs
ETFs and Active SPDRs
  • Exchange trading allows intra-day volatility
  • Actively managed and rebalanced
  • Less-Standardized biases (includes alpha)
hedge funds
Hedge Funds
  • No Standardization (high alpha dependence)
  • No trading, no intra-day volatility
  • Unique investment goals
  • High survival bias
  • Strategy is AUM dependent