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The Size Effect

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

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  1. The Size Effect Brett Bates Greg Chedwick Chris Ferre Matt Karam

  2. 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?

  3. 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

  4. 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.

  5. 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

  6. Mean Abnormal Daily Returns of 10 Market Value Portfolios

  7. Results: • 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.

  8. 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

  9. 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?

  10. 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

  11. 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

  12. Portfolio Strategies Based on Market Capitalization – The Market Portfolios

  13. 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 %

  14. Active Strategy Results

  15. Cumulative Returns

  16. 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%

  17. Passive Strategy Results

  18. Considerations • 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

  19. Conclusion 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

  20. Modern Applications • Hedge Funds • Index Funds – Mid 1970s • Exchange Traded Funds – Early 1990s • Spiders (SPDR) • Active management ETFs - 2008

  21. Index and Sector Funds • Offer target-specific index tracking • Cannot outperform the constituents of their index • Standardized survival biases

  22. Index and Sector Funds

  23. ETFs and Active SPDRs • Exchange trading allows intra-day volatility • Actively managed and rebalanced • Less-Standardized biases (includes alpha)

  24. ETFs and Active SPDRs

  25. ETFs and Active SPDRs

  26. ETFs and Active SPDRs

  27. ETFs and Active SPDRs

  28. Hedge Funds • No Standardization (high alpha dependence) • No trading, no intra-day volatility • Unique investment goals • High survival bias • Strategy is AUM dependent

  29. Hedge Funds

  30. Hedge Funds

  31. Hedge Funds

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