The Inefficient MarketWhat Pays Off and Why

Part 2: Why

Prentice Hall 1999

Visit our web-site at HaugenSystems.com

Why.Why.

The Topography ofThe Topography of the Stock Marketthe Stock Market

True Abnormal ProfitTrue Abnormal Profit

Best estimate (using all relevant Best estimate (using all relevant information and state-of-the-art analysis) information and state-of-the-art analysis) of the risk adjusted, present value of a of the risk adjusted, present value of a firms future abnormal profits.firms future abnormal profits.

TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal Profit Abnormal Profit

Growth StocksGrowth Stocks

Value StocksValue Stocks

Efficien

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under-under-priced priced stockstock

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

will will produceproduceexcessexcessreturnreturn

TrueTrue Abnormal Profit Abnormal Profit

Priced Abnormal Profit

Efficien

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over-over-priced priced stockstock

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Growth StocksGrowth Stocks

Value StocksValue Stocks

will will produceproduceexcessexcessreturnreturn

TrueTrue Abnormal Profit Abnormal Profit

Priced Abnormal Profit

Efficien

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will will produceproducedeficient deficient returnreturn

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Growth StocksGrowth Stocks

Value StocksValue Stocks

ImprecisionImprecision

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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Efficien

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True Abnormal Profit

Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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et

Efficien

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True Abnormal Profit

Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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True Abnormal Profit

Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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Efficien

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True Abnormal Profit

Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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Efficien

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True Abnormal Profit

Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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Efficien

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True Abnormal Profit

Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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True Abnormal Profit

Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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True Abnormal Profit

Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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Priced Abnormal Profit

True Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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Priced Abnormal Profit

True Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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Efficien

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Priced Abnormal Profit

True Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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et

Efficien

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LineLine

Priced Abnormal Profit

True Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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Priced Abnormal Profit

TrueTrue Abnormal Profit Abnormal Profit

Available assets

IMPRECISION:IMPRECISION:Different prices for Different prices for stocks with the samestocks with the sameTRUE Abnormal ProfitTRUE Abnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

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TrueTrue Abnormal Profit Abnormal Profit

Priced Abnormal Profit

Available assets

IMPRECISION:IMPRECISION:Stocks with the Stocks with the same price have same price have different TRUE different TRUE abnormal profitabnormal profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

Priced Abnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

Priced Abnormal Profit

Bias

The Market Over-The Market Over-reacts to Success reacts to Success

and Failureand Failure

Mean-reversion in Mean-reversion in Relative ProfitabilityRelative Profitability

How Fast?How Fast?

Fuller, Huberts, and Levinson1973 - 1990

Relative Subsequent Growth in Highest, High,Relative Subsequent Growth in Highest, High, Low and Lowest Quintiles of E/P Ratio Low and Lowest Quintiles of E/P Ratio

-10%-10% -8%-8% -6%-6% -4%-4% -2%-2% 0%0% 2%2% 4%4% 6%6% 8%8% 10%10%

Growth in Earnings per Share Relative to Middle Quintile

Lowest E/P(Growth)Lowest E/P(Growth)Low E/PLow E/PHigh E/PHigh E/PHighest E/P (Value)Highest E/P (Value)

1 Year ahead1 Year ahead

2 Years ahead2 Years ahead

3 Years ahead3 Years ahead

4 Years ahead4 Years ahead

5 Years ahead5 Years ahead

6 Years ahead6 Years ahead

7 Years ahead7 Years ahead

8 Years ahead8 Years ahead

Number of Years Number of Years After RankingAfter Ranking

Is the Market Surprised Is the Market Surprised by the Speed of Mean-by the Speed of Mean-

reversion?reversion?

La Porta, Lakonishok,Shleifer, & Vishny

1971-1992

-1.0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0%

Three day rate of returnThree day rate of return

-2.0% -1.5%

ValueValueGrowthGrowth

First year following ranking

Second yearfollowing ranking

Third yearfollowing ranking

Fourth yearfollowing ranking

Fifth yearfollowing ranking

Returns of Growth and Value StocksReturns of Growth and Value Stocks Around Earnings Announcement DatesAround Earnings Announcement Dates

Implications for Market’s

Topography

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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et

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

t Mark

et

LineLine

TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

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LineLine

TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

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LineLine

TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

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LineLine

TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

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LineLine

TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

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Efficien

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TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

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LineLine

TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decile

high high BB//PP decile decileoror

low low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

t Mark

et

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

Available assets

low low BB//P P deciledecileoror

high high EE//BB decile decilehigh high BB//PP decile decile

ororlow low EE//BB decile decile

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

BIAS:BIAS:Overreaction to Overreaction to Abnormal ProfitAbnormal Profit

TrueTruePricedPriced

over-over-pricedpriced

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under-under-pricedpriced

TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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et

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True Abnormal Profit

Available assets

Value investors head WestValue investors head West

GrowthGrowth investorsinvestors

headhead NorthNorth

PricedPriced Abnormal ProfitAbnormal Profit

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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True Abnormal Profit

Available assets

Pure Pure GrowthGrowth

willwillunderunder

performperformGARPGARPwillwill

outperformoutperformmarketmarket

PricedPriced Abnormal ProfitAbnormal Profit

The Relative The Relative Positions of Positions of The DecilesThe Deciles

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

Super StocksSuper Stocks

Stupid StocksStupid Stocks

PricedPriced Abnormal ProfitAbnormal Profit

What’s Behind What’s Behind the Payoff the Payoff

to Profitability?to Profitability?

Imprecision - you can buy more Imprecision - you can buy more profitable companies without having profitable companies without having

to pay more expensive prices.to pay more expensive prices.

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

Priced Abnormal Profit Priced Abnormal Profit

What’s Behind What’s Behind the Payoff the Payoff

to Cheapness?to Cheapness?Imprecision & bias - you can buy Imprecision & bias - you can buy cheaper stocks without sacrificing cheaper stocks without sacrificing

profitability & market exaggerates the profitability & market exaggerates the length of the short-run.length of the short-run.

The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal Profit Abnormal Profit

Efficien

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TrueTrue Abnormal Profit Abnormal Profit

PricedPriced Abnormal ProfitAbnormal Profit

What’s Behind What’s Behind the Negative the Negative Payoff to Risk?Payoff to Risk?

How long has the payoff to How long has the payoff to risk been negative? Let’s risk been negative? Let’s look at the history of the look at the history of the

cumulative cumulative relativerelative performance of the low performance of the low

volatility portfolio and the volatility portfolio and the S&P 500 stock index.S&P 500 stock index.

Cumulative Difference in Return Between Cumulative Difference in Return Between Low Volatility Portfolio and S&P 500Low Volatility Portfolio and S&P 500

-35%-35%

-25%-25%

-15%-15%

-5%-5%

5%5%

15%15%

25%25%

Cumulative Cumulative DifferenceDifference

19281928 19381938 19481948 19581958 19681968 19781978 19881988

Cumulative Difference in Return Between Cumulative Difference in Return Between Low Volatility Portfolio and S&P 500 Low Volatility Portfolio and S&P 500

-35%-35%

-25%-25%

-15%-15%

-5%-5%

5%5%

15%15%

25%25%

19281928 19381938 19481948 19581958 19681968 19781978 19881988

Cumulative Cumulative DifferenceDifference

Cumulative Difference in Return Between Cumulative Difference in Return Between Low Volatility Portfolio and S&P 500 Low Volatility Portfolio and S&P 500

-35%-35%

-25%-25%

-15%-15%

-5%-5%

5%5%

15%15%

25%25%

19281928 19381938 19481948 19581958 19681968 19781978 19881988

Cumulative Cumulative DifferenceDifference

Two Theories Two Theories Explaining the Explaining the

Negative Payoff to Negative Payoff to RiskRisk

I. Over-valued and I. Over-valued and Risky Growth StocksRisky Growth Stocks

Expensive growth stocks tendExpensive growth stocks tend– To produce low future returnsTo produce low future returns– To be more riskyTo be more risky

Fama/French 1992 Table IIFama/French 1992 Table II

Book to Market Equity of Portfolios Ranked by BetaBook to Market Equity of Portfolios Ranked by Beta

0.50.5

0.60.6

0.70.7

0.80.8

0.90.9

11

0.60.6 0.80.8 11 1.21.2 1.41.4 1.61.6 1.81.8

BetaBeta

Book to Book to Market EquityMarket Equity

II. Agency Problems II. Agency Problems of Financial Analysts*of Financial Analysts*

*Sias, *Sias, Financial Analysts’ JournalFinancial Analysts’ Journal, 1996, 1996

Studies NYSE stocks -1977-91Studies NYSE stocks -1977-91 Forms size deciles in each yearForms size deciles in each year Within each size decile, he forms 3 equal-numbered groupings based on percentage institutionally heldWithin each size decile, he forms 3 equal-numbered groupings based on percentage institutionally held Computes volatility using weekly dataComputes volatility using weekly data

Median Institutional Holdings, Capitalization, and Volatility by Capitalization Institutional Holdings Sorted Portfolios, NYSE Firms, 1977-91

Portfolio

Smallest

Decile 2

Decile 3

Decile 4

Decile 5

Decile 6

Decile 7

Decile 8

Decile 9

Largest

Institutional Holdings (%)

High Low ConfidenceLevel(High

minus Low)

.2275 .2144 99%

.3335 .3082 99%

.3978 .3623 99%

.4760 .4227 99%

.5268 .4510 99%

.5564 .4558 99%

.5916 .4390 99%

.6361 .4408 99%

.6566 .3887 99%

.6428 .3455 99%

Capitalization ($millions)

High Low ConfidenceLevel(High

minus Low)

28.56 18.56 99%

60.46 52.15 99%

91.87 84.05 99%

151.10 135.25 99%

222.35 207.45 99%

364.45 326.80 99%

562.80 514.90 99%

926.75 838.20 99%

1,629.00 1,491.50 99%

3,777.00 4,338.50 99%

Annualized StandardDeviation Of

Weekly Returns (%)High Low Confidence

Level(High

minus Low)

43.27 49.47 99%

36.70 32.81 99%

36.49 30.86 99%

35.05 29.85 99%

33.39 28.70 99%

32.02 25.56 99%

30.65 27.19 99%

29.21 25.38 99%

28.34 24.52 99%

26.03 23.80 99%

There May be Two There May be Two Causes for the Inversion in the Causes for the Inversion in the

Relationship Between RiskRelationship Between Risk and Expected Return and Expected Return

The market’s tendency to over-price the more volatile, growth stocksThe market’s tendency to over-price the more volatile, growth stocks The attraction of institutional investors to the more newsworthy, The attraction of institutional investors to the more newsworthy,

volatile stocksvolatile stocks

What’s Behind the What’s Behind the Technical Payoffs Technical Payoffs to Price History?to Price History?

Short-term reversalsShort-term reversalsIntermediate momentumIntermediate momentum

Long-term reversalsLong-term reversals

Short-term ReversalsShort-term Reversals

Price pressure.Price pressure. Reversals of over-reactions to new Reversals of over-reactions to new

information.information.

Intermediate Momentum Intermediate Momentum and Long-term Reversalsand Long-term Reversals

Repetition of earnings surprises of the same sign (Bernard & Thomas).

Over-estimating the length of the short-run.

Jegadeesh and Titman*Jegadeesh and Titman* Observe stock returns around earnings

announcement dates. Compute difference in returns to decile

winners and losers over previous six months.

Study spans the period 1965 -1989.

**Journal of Finance, 1993Journal of Finance, 1993

Cumulative Difference Between Winner and Loser Cumulative Difference Between Winner and Loser Portfolio Rates of Return at Announcement DatesPortfolio Rates of Return at Announcement Dates

-5.00%-5.00%

-4.00%-4.00%

-3.00%-3.00%

-2.00%-2.00%

-1.00%-1.00%

0.00%0.00%

1.00%1.00%

2.00%2.00%

3.00%3.00%

4.00%4.00%

5.00%5.00%

Cum

ulat

ive

Diff

eren

ce

Cum

ulat

ive

Diff

eren

ce

Betw

een

Win

ner

and

Lose

r Be

twee

n W

inne

r an

d Lo

ser

Port

folio

Rat

es o

f Ret

urn

Port

folio

Rat

es o

f Ret

urn

11 33 55 77 171799 1111 1313 1515 1919 2121 2323 2525 2727 2929 3131 3333 3535

Months Following 6-Month Performance PeriodMonths Following 6-Month Performance Period

Cumulative Difference Between Winner and Loser Cumulative Difference Between Winner and Loser Portfolio Rates of Return at Announcement DatesPortfolio Rates of Return at Announcement Dates

-5.00%-5.00%

-4.00%-4.00%

-3.00%-3.00%

-2.00%-2.00%

-1.00%-1.00%

0.00%0.00%

1.00%1.00%

2.00%2.00%

3.00%3.00%

4.00%4.00%

5.00%5.00%

Cum

ulat

ive

Diff

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ce

Cum

ulat

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Diff

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ce

Betw

een

Win

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and

Lose

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Port

folio

Rat

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f Ret

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Port

folio

Rat

es o

f Ret

urn

11 33 55 77 171799 1111 1313 1515 1919 2121 2323 2525 2727 2929 3131 3333 3535

Months Following 6-Month Performance PeriodMonths Following 6-Month Performance Period

Cumulative Difference Between Winner and Loser Cumulative Difference Between Winner and Loser Portfolio Rates of Return at Announcement DatesPortfolio Rates of Return at Announcement Dates

-5.00%-5.00%

-4.00%-4.00%

-3.00%-3.00%

-2.00%-2.00%

-1.00%-1.00%

0.00%0.00%

1.00%1.00%

2.00%2.00%

3.00%3.00%

4.00%4.00%

5.00%5.00%

Cum

ulat

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Diff

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Cum

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Diff

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Betw

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and

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Port

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Rat

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Port

folio

Rat

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Months Following 6-Month Performance PeriodMonths Following 6-Month Performance Period

11 33 55 77 171799 1111 1313 1515 1919 2121 2323 2525 2727 2929 3131 3333 3535

Building Weak Building Weak Expected Return Expected Return

Factor ModelsFactor Models

BrennanChordia

&Subrahmanyam

MethodologyMethodology Study 970 NYSE stocks over the period 1977-89. Rank stocks first by size and form quintiles. Within each quintile, rank by

book-to-price and form quintiles again to obtain a total of 25 groupings. Construct 5 stock portfolios, the returns to which account, as closely as

possible, for the correlations among the returns to the 980 stocks. Use the portfolios as factors to explain the time-series of individual stock returns. Do the same with the size and B/P portfolio returns.

In any given month, regress the cross-section of returns to the 25 portfolios on a profile of 13 portfolio characteristics. Do the same with the unexplained returns to the 25 portfolios.

Compute means for the 13 regression coefficients (1977-89).

Most Important FactorsMost Important FactorsStudy by Haugen & BakerStudy by Haugen & Baker

1979/01 through1986/06

1986/07 through 1993/12

Factor Mean Confidence Mean ConfidenceOne-month excess return -0.97% 99% -0.72% 99%

returnTwelve-month excess 0.52% 99% 0.52% 99%

Trading volume/marketcap

-0.35% 99% -0.20% 98%

Two-month excess return -0.20% 99% -0.11% 99%Earnings to price 0.27% 99% 0.26% 99%Return on equity 0.24% 99% 0.13% 97%Book to price 0.35% 99% 0.39% 99%Trading volume trend -0.10% 99% -0.09% 99%Six-month excess return 0.24% 99% 0.19% 99%Cash flow to price 0.13% 99% 0.26% 99%

Average Payoffs to the BCS Factor Model Average Payoffs to the BCS Factor Model

Factor

Covering

SizeBook-to-Market

Volume of Trading

Number of Analysts

Dispersion of EarningsEstimates

Percentage Bid-AskedSpread

Percentage InstitutionalOwnership1.00 if in S&P 0OtherwiseReciprocal of SharePrice

Dividend – to – Price

Two-Month Past Return

Five-Month Past Return

Eleven-Month PastReturn

Portfolio ReturnsPortfolio Returns

MeanPayoff

Confidence%

.205 93%

.730 98%

-.033 60%

-.023 20%

-.050 70%

1.020 99%

-.211 80%

-.107 10%

-.006 5%

-.938 93%

-.300 80%

.150 75%

.430 99%

Residual PortfolioResidual PortfolioReturnsReturns

MeanPayoff

Confidence%

-.092 80%

.559 80%

-.231 80%

-.166 65%

-.694 92%

.259 6%

.448 98%

.734 93%

.301 65%

-3.70 65%

-2.18 80%

-.268 20%

1.56 93%

Residual StockResidual StockReturnsReturns

MeanPayoff

Confidence%

-.442 99%

-.256 99%

-.108 90%

.214 99%

-.287 99%

-.534 99%

.179 99%

.184 95%

.069 60%

2.33 85%

-.280 20%

-.929 80%

.778 97%

Response In the case of the 25 portfolios, it’s,

proportionately, like trying to estimate the payoffs to 2 factors with 4 plot points.

In the case of the 25 portfolios, the exposures to all factors except size and B/P are likely to be quite homogeneous.

The unexplained (by their factor model) returns to the individual stocks are likely to be small and for the 40 stock portfolios extremely small.

Diversifiable Risk Decreases with the Number of Stocks in a Portfolio

40

1 4 7 10 13 16 19 22 25 28 31 34 37

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

.10

Div

ersi

fiabl

e R

isk

D

iver

sifia

ble

Ris

k

Number of Stocks in PortfolioNumber of Stocks in Portfolio