Size Effect - The College of Business · Size Effect Outline CAPM EMH ... Efficient Market Hypothesis Weak-Form EMH – – Prices on traded assets (stocks, bonds, or property) already

Size EffectSize Effect

Collaborative Effort by:Collaborative Effort by:

Brian T. Brian T. AllmanAllmanPatrick Patrick HuHuJosh JonesJosh Jones

Yann LingYann Ling--BarnesBarnesJohn NunnJohn Nunn

Size EffectSize EffectOutlineOutlineCAPMCAPMEMHEMHTesting CAPM & EMHTesting CAPM & EMH

Abnormal Returns in Small Firm PortfoliosAbnormal Returns in Small Firm Portfolios

Portfolio Strategies based on Market CapitalizationPortfolio Strategies based on Market Capitalization

ResultsResultsConclusionConclusionRealReal--world Applicationworld Application

CAPMCAPM Capital Asset Pricing ModelCapital Asset Pricing Model

All Expected Stock Returns are a function All Expected Stock Returns are a function of:of:–– Risk free borrowing Rate (Risk free borrowing Rate (RR ff ))–– Riskiness of stock, as measured by Riskiness of stock, as measured by Beta Beta ((BB ii ))–– Excess return on Market Portfolio [Excess return on Market Portfolio [EE((RR mm ))--RR ff ]]

E(RE(Rii ) = ) = RRff ++BBii [[EE((RRmm ))--RRff ]]

CAPMCAPM Capital Asset Pricing ModelCapital Asset Pricing Model

Holding the Market Risk Premium constant, each Holding the Market Risk Premium constant, each % increase of % increase of RiskRisk should provide equivalent % should provide equivalent % increase in increase in ReturnReturn..

[[EE((RRmm ))--RRff ] = ] = ΔΔE(RE(R ii )/)/ΔΔBBii

As Beta increases, Expected Return increases As Beta increases, Expected Return increases equivalentlyequivalently..

EMHEMH Efficient Market HypothesisEfficient Market Hypothesis

WeakWeak--Form EMHForm EMH

–– Prices on traded assets (stocks, bonds, or property) Prices on traded assets (stocks, bonds, or property) already reflect all past publicly available information.already reflect all past publicly available information.

–– Disproves Technical Analysis.Disproves Technical Analysis.

WF EMH

EMH EMH Efficient Market HypothesisEfficient Market Hypothesis

SemiSemi--Strong Form EMHStrong Form EMH

–– Prices reflect all publicly available information and prices Prices reflect all publicly available information and prices instantly change to reflect new public information.instantly change to reflect new public information.

–– Disproves Disproves FundamentalFundamental & Technical Analysis.& Technical Analysis.

WF EMH

S-SF EMH

EMH EMH Efficient Market HypothesisEfficient Market Hypothesis

Strong Form EMHStrong Form EMH

–– Privately available information is instantly reflected Privately available information is instantly reflected within prices.within prices.

–– Disproves Insider Trading & Fundamental Technical Disproves Insider Trading & Fundamental Technical Analysis.Analysis.

S-F EMH

WF EMH

S-SF EMH

Abnormal Returns in Abnormal Returns in Small Firm PortfoliosSmall Firm Portfolios

Purpose:Purpose:

–– To test the performance of small caps vs. large caps.To test the performance of small caps vs. large caps.

–– To test whether abnormal returns that are not explained To test whether abnormal returns that are not explained by beta exist.by beta exist.


The Test:The Test:1.1. Collected NYSE & AMEX stock prices from 1962Collected NYSE & AMEX stock prices from 1962--1975.1975.

Daily returnsDaily returns

Common shares Common shares

2.2. Ranked all stocks by market value and divided into 10 Ranked all stocks by market value and divided into 10 equallyequally--weighted portfolios.weighted portfolios.

3.3. Beta estimates for the portfolios were close to 1.Beta estimates for the portfolios were close to 1.4.4. Combined daily returns to obtain portfolio returns.Combined daily returns to obtain portfolio returns.5.5. ReRe--balanced portfolio by repeating step 2 at the end of balanced portfolio by repeating step 2 at the end of

each year.each year.6.6. Calculated abnormal returns.Calculated abnormal returns.

Daily return of portfolio Daily return of portfolio –– Daily return of NYSEDaily return of NYSE--AMEX index.AMEX index.


Hypothesis:Hypothesis:

–– CAPM implies that any two assets with the same beta CAPM implies that any two assets with the same beta will have the same expected return.will have the same expected return.

–– Mean abnormal returns are zero.Mean abnormal returns are zero.

–– According to CAPM, mean abnormal returns should be According to CAPM, mean abnormal returns should be zero because all the portfolios have betas near one, zero because all the portfolios have betas near one, which should approximate the return of the market as a which should approximate the return of the market as a whole.whole.


Results:Results:

–– Portfolio with smallest firm on average experienced Portfolio with smallest firm on average experienced returns >20% a year returns >20% a year higherhigher than portfolio with largest than portfolio with largest firms.firms.

–– Investors can form portfolios that systematically earn Investors can form portfolios that systematically earn abnormal returns based on firm size.abnormal returns based on firm size.

–– Persistence of small firm abnormal returns reduces the Persistence of small firm abnormal returns reduces the chance that the results are due to market inefficiencies.chance that the results are due to market inefficiencies.

–– CAPM does not adequately describe stock return CAPM does not adequately describe stock return behavior.behavior.

Portfolio strategies based Portfolio strategies based on market capitalizationon market capitalization No matter how you slice it, small caps win out.No matter how you slice it, small caps win out.

Purpose:Purpose:

–– To determine if small firms, on average, earn higher To determine if small firms, on average, earn higher rates of return than large firms.rates of return than large firms.

–– To determine if actively managed portfolios out perform To determine if actively managed portfolios out perform passively managed portfolios.passively managed portfolios.


The Test:The Test:

–– Collected NYSE & AMEX stock prices from 1963Collected NYSE & AMEX stock prices from 1963--1980.1980.

Daily returnsDaily returns

Common shares Common shares

–– Ranked all stocks by market value and divided into 10 Ranked all stocks by market value and divided into 10 equallyequally--weighted portfolios.weighted portfolios.

–– Active vs. Passive portfolio strategy.Active vs. Passive portfolio strategy.

Active Active –– annual portfolio rebalancingannual portfolio rebalancing

Passive Passive –– hold till 1980 without rebalancinghold till 1980 without rebalancing

Placed any proceeds after delisting in an S&P 500 Index fundPlaced any proceeds after delisting in an S&P 500 Index fund


Investment Characteristics of The Market Value Investment Characteristics of The Market Value PortfolioPortfolio

PortfolioAverage Annual

ReturnAverage Percent

on AMEXAverage Median

Value ($M)Average Share

PriceMedian Share

PriceEstimated

Portfolio Beta

MV1 32.77% 92.19% $92.19 $4.60 $5.24 1.58

MV2 23.51% 77.33% $77.33 $10.80 $9.52 1.57

MV3 22.98% 52.09% $52.09 $19.30 $12.89 1.50

MV4 20.24% 34.05% $34.05 $30.70 $16.19 1.46

MV5 19.08% 21.33% $21.33 $47.20 $19.22 1.43

MV6 18.30% 12.73% $12.73 $74.20 $22.59 1.36

MV7 15.64% 8.37% $8.37 $119.10 $26.44 1.28

MV8 14.24% 4.73% $4.73 $209.70 $30.83 1.22

MV9 13.00% 3.39% $3.39 $434.60 $34.43 1.11

MV10 9.47% 2.25% $2.25 $1,102.60 $44.94 0.96


Investment Characteristics of The Market Value Investment Characteristics of The Market Value Portfolio (contPortfolio (cont’’d)d)


Results:Results:

Cumulative Increase, 1963‐1980

Portfolio Size Active Strategy Passive Strategy Difference

Smallest 4528% 1026% 3502%

Largest 312% 328% ‐16%


Results (contResults (cont’’d):d):

Very small firms can generate large gains over long periods of Very small firms can generate large gains over long periods of time, even with passive strategy.time, even with passive strategy.

Small firms with <$20 million in capitalization are in general Small firms with <$20 million in capitalization are in general traded on the American Stock Exchange.traded on the American Stock Exchange.

Smaller firms have larger betas than large firms.Smaller firms have larger betas than large firms.

Size effects exist even after beta adjustments.Size effects exist even after beta adjustments.

Active portfolios out performed passive portfolios.Active portfolios out performed passive portfolios.

Portfolio strategies based Portfolio strategies based on market capitalizationon market capitalization

*Considering Transaction Costs*Considering Transaction Costs

Transaction Cost:Transaction Cost:

–– Estimated average of 950 stocks used per year, Estimated average of 950 stocks used per year, 95 stocks per portfolio95 stocks per portfolio

–– Used Current costs of $10 per tradeUsed Current costs of $10 per trade

Cumulative transaction costs:Cumulative transaction costs:

–– $32,300 for actively managed portfolio$32,300 for actively managed portfolio

–– $1,900 for passively managed portfolio$1,900 for passively managed portfolio

Transaction costs in 1960Transaction costs in 1960’’s & 1970s & 1970’’s >> todays >> today’’ss

CONCLUSIONCONCLUSION

What have we learned from these 2 papers?What have we learned from these 2 papers?

–– Using a CAPM Market Risk Premium of 9% to compare a Using a CAPM Market Risk Premium of 9% to compare a Large Cap Stock with a Small Cap Stock:Large Cap Stock with a Small Cap Stock:

–– ReinganumReinganum disproved CAPM.disproved CAPM.–– Small Cap stocks out perform Large Cap stocks even Small Cap stocks out perform Large Cap stocks even

after additional Risk is considered.after additional Risk is considered.

Portfolio Type: *Beta: E(Ri ) CAPM: *Ri : Observed:Small Cap Portfolio 1.58 16.22% 32.77%

Large Cap Portfolio 0.96 10.64% 9.47%

ReinganumReinganum disproved Semidisproved Semi--Strong Form EMH.Strong Form EMH.

–– Market Capitalization Market Capitalization cancan be used to systematically be used to systematically construct a portfolio that out performs and generates construct a portfolio that out performs and generates consistent abnormal returns.consistent abnormal returns.

CONCLUSIONCONCLUSION

WF EMH

S-SF EMH

RealReal--World ApplicationWorld Application

–– Select security exchangeSelect security exchange

NasdaqNasdaq

NYSENYSE

–– Determine firm size for inclusionDetermine firm size for inclusion

–– Fine tune portfolio criteriaFine tune portfolio criteria

NEXT STEPNEXT STEP

NEXT STEPNEXT STEP

NEXT STEPNEXT STEP

NEXT STEPNEXT STEP

Recent Returns of Small Cap StocksRecent Returns of Small Cap Stocks

–– Total Returns from Morningstar Small Cap, Mid Cap & Total Returns from Morningstar Small Cap, Mid Cap & Large Cap IndexesLarge Cap Indexes

NEXT STEPNEXT STEP

YTD 1 Yr 3 Yr Avg 5 Yr Avg 10 Yr Avg

Small Cap 6.50% 30.33% 10.16% 5.11% 8.23%

Mid Cap 6.82% 28.35% 6.52% 4.67% 7.19%

Large Cap 5.24% 18.83% 1.60% 2.63% 1.94%

Size EffectSize Effect

QUESTIONS?QUESTIONS?

Documents

Size Effect - The College of Business · Size Effect Outline CAPM EMH ... Efficient Market Hypothesis Weak-Form EMH – – Prices on traded assets (stocks, bonds, or property) already