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
t Mark
et
Efficien
t Mark
et
LineLine
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
t Mark
et
Efficien
t Mark
et
LineLine
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
t Mark
et
Efficien
t Mark
et
LineLine
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
t Mark
et
Efficien
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et
LineLine
TrueTrue Abnormal Profit Abnormal Profit
Priced Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
True Abnormal Profit
Priced Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
True Abnormal Profit
Priced Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
True Abnormal Profit
Priced Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
True Abnormal Profit
Priced Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
True Abnormal Profit
Priced Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
True Abnormal Profit
Priced Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
True Abnormal Profit
Priced Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
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
t Mark
et
Efficien
t Mark
et
LineLine
Priced Abnormal Profit
True Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
Priced Abnormal Profit
True Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
Priced Abnormal Profit
True Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
Priced Abnormal Profit
True Abnormal Profit
The Position of Portfolios in Abnormal Profit SpaceThe Position of Portfolios in Abnormal Profit Space
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
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
Efficien
t Mark
et
Efficien
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et
LineLine
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
t Mark
et
Efficien
t Mark
et
LineLine
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
t Mark
et
Efficien
t Mark
et
LineLine
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
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
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
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
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
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
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
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
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
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
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
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
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 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
Efficien
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et
Efficien
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et
LineLine
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
t Mark
et
Efficien
t Mark
et
LineLine
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
t Mark
et
Efficien
t Mark
et
LineLine
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
t Mark
et
Efficien
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et
LineLine
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
t Mark
et
Efficien
t Mark
et
LineLine
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
t Mark
et
Efficien
t Mark
et
LineLine
TrueTrue Abnormal Profit Abnormal Profit
PricedPriced Abnormal Profit Abnormal Profit
Efficien
t Mark
et
Efficien
t Mark
et
LineLine
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
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
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
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