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Brett Bates Greg Chedwick Chris Ferre Matt Karam

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2 Articles by Marc Reinganum: o “Abnormal Returns in Small Firm Portfolios” (1981) o “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?

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Security Market LineE(R i ) = R f + β i (E(R m ) − R f ) E(R i ) = the expected return on the capital asset R f = the risk-free rate of interest β i =(beta coefficient) = the sensitivity of the asset returns to market returns E(R m ) = the expected return of the market E(R m ) - R f = the market premium or risk premium

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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.

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1. Collected NYSE & AMEX stock prices from 1962 - 1975 2. Ranked all stocks by December 31 stock market values, and divided into 10 equally equally-weighted portfolios. 3. Combined daily returns of securities to obtain portfolio returns. 4. Equal weights were applied to all securities and portfolios were adjusted for beta risk 5. Re-balanced portfolio by repeating step 2 at the end of each year. 6. Calculated abnormal returns (Daily returns of portfolios minus daily return of the equally-weighted NYSE/AMEX index) 7. Analyzed portfolios in 2 ways: 1. Computed Average Rates of Return for year subsequent to formation 2. Computed Average Rates of Return for second year after formation

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During First Year During Second Year Portfolio Mean Abnormal Return %'sBeta Avg Median Market Value ($M) Mean Abnormal Return %'sBeta Avg Median Market Value ($M) 1 6.421.00 8.306.381.02 8.30 2 3.471.02 20.002.661.01 20.00 3 (0.71)1.00 34.10-0.330.99 34.10 4 (1.11)1.00 54.50-0.970.99 54.50 5 (2.60)0.94 86.10-1.950.93 86.10 6 (4.18)0.88 138.30-4.880.87 138.30 7 (3.99)0.90 233.50-4.860.91 233.50 8 (4.00)0.83 413.00-4.790.82 413.00 9 (5.24)0.83 705.30-5.830.83 705.30 10 (4.79)0.82 1,759.90-5.630.83 1,759.90

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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.

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Inspired by size effect theory posed by R. W. Banz, Mark Reinganum corroborated size effect in 1981. o 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 o CAPM is deficient in accounting for the differences in rates of returns with equivalent beta risk

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Does market capitalization have an effect on the rate of return of a portfolio over time? Do actively managed portfolios outperform passively managed portfolios?

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Market capitalizations and stock returns came from the University of Chicago’s CRSP daily tape file o Data from 1963 to 1980 comprised from stocks listed on the New York and American Stock Exchanges Data cleansing due to delisting o Acquisitions o Bankruptcy o Failure to satisfy listing requirements of the exchange

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Multipurpose Design o Firm Size Ten equally weighted portfolios grouped by market capitalization o 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

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Market Capitalization size returns evident across the portfolio spectrum o MV1 returned cumulative returns of 4528% o MV2 returned cumulative returns of 1850% o MV3 returned cumulative returns of 2016% o MV5 returned cumulative returns of 1179% o MV10 returned cumulative returns of 312 %

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Portfolio1963-19681969-19741975-1980 MV11166-56739 MV2599-63661 MV3472-51663 MV4355-59712 MV5303-51559 MV6268-48567 MV7200-47454 MV8166-39365 MV9152-34308 MV1089-19169

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Small Firms did better even without rebalancing o MV1 returned cumulative returns of 1026% o MV5 returned cumulative returns of 562% o MV10 returned cumulative returns of 328%

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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

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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

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Hedge Funds Index Funds – Mid 1970s Exchange Traded Funds – Early 1990s o Spiders (SPDR) o Active management ETFs - 2008

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Offer target-specific index tracking Cannot outperform the constituents of their index Standardized survival biases

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Exchange trading allows intra-day volatility Actively managed and rebalanced Less-Standardized biases (includes alpha)

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

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McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 9 The Capital Asset Pricing Model.

McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 9 The Capital Asset Pricing Model.

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