The Inefficient Stock MarketWhat Pays Off and Why

(Prentice Hall, 1999)Visit our web-site at HaugenSystems.com

What

Probability Distribution For Returns to a Portfolio

Possible Rates of Returns

Probability

Expected Return

Variance of Return

Risk Factor ModelsRisk Factor Models

The variance of stock returns can be split into two The variance of stock returns can be split into two components:components:Variance = systematic risk + diversifiable riskVariance = systematic risk + diversifiable riskSystematic risk is computed using the following spreadsheet.Systematic risk is computed using the following spreadsheet.

Risk Factor ModelsRisk Factor Models

Factor betas are estimated by relating stock returns Factor betas are estimated by relating stock returns to (unexpected) percentage changes in the factor to (unexpected) percentage changes in the factor over a period where the stock’s character is similar over a period where the stock’s character is similar to the present.to the present.

Relationship Between Return to General Relationship Between Return to General Electric and Changes in Interest Rates Electric and Changes in Interest Rates

-25%-25%

-20%-20%

-15%-15%

-10%-10%

-5%-5%

0%0%

5%5%

10%10%

15%15%

20%20%

25%25%

Return to G.E.Return to G.E.

-10%-10% -5%-5% 0%0% 5%5% 10%10%

Percentage Change in Yield on Long-term Govt. Bond Percentage Change in Yield on Long-term Govt. Bond

Line of Best FitLine of Best Fit

April, 1987April, 1987

Spreadsheet for Computing Systematic RiskSpreadsheet for Computing Systematic Risk

Portfolio BetaPortfolio Beta Portfolio BetaPortfolio Beta(Inflation)(Inflation) (Oil Price)(Oil Price)

1.001.00 Correlation BetweenCorrelation BetweenInflation and Oil PriceInflation and Oil Price

Portfolio BetaPortfolio Beta

(Inflation)(Inflation)

Portfolio BetaPortfolio Beta(Oil Price)(Oil Price)

Correlation BetweenCorrelation Between

Inflation and Oil PriceInflation and Oil Price 1.001.00

Risk Factor ModelsRisk Factor Models

Factor correlations can be estimated over a Factor correlations can be estimated over a longer period because they are, presumably, longer period because they are, presumably, more stable over time. This may increase the more stable over time. This may increase the predictive accuracy of factor models relative to predictive accuracy of factor models relative to more naïve historical estimates. more naïve historical estimates.

Relationship Between Rate of Inflation and Percentage Change in Price of Oil

-1 -0.5 0 0.5 1 1.5 2Monthly Rate of Inflation

-40

-20

0

20

40

60

80

100

120

140

Monthly Percentage Change in Price of Oil

Line of Best Fit

Computing Portfolio Systematic RiskComputing Portfolio Systematic Risk

Portfolio Beta * Portfolio Beta * 1.001.00

(Inflation) (Inflation)

+Portfolio Beta * Portfolio Beta * Correlation Between(Inflation) (Oil Price) Inflation and Oil Price

+Portfolio Beta * Portfolio Beta * 1.001.00 (Oil Price) (Oil Price)

+Portfolio Beta * Portfolio Beta * Correlation Between (Inflation) (Oil Price) Inflation and Oil Price

=Portfolio Systematic RiskPortfolio Systematic Risk

Risk Factor ModelsRisk Factor Models

If your factors have truly captured the structure behind the If your factors have truly captured the structure behind the correlations between stock returns, then portfolio diversifiable correlations between stock returns, then portfolio diversifiable risk can be estimated by summing the products of (a) the risk can be estimated by summing the products of (a) the diversifiable risk of each stock and (b) the square of its portfolio diversifiable risk of each stock and (b) the square of its portfolio weight.weight.

DiversifiableDiversifiable Risk Decreases with the Number of Stocks in a PortfolioRisk Decreases with the Number of Stocks in a Portfolio

40

1 47 10

13 1619

2225

2831

3437

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

.10

Div

ersi

fiab

le R

isk

D

iver

sifi

able

Ris

k

Number of Stocks in PortfolioNumber of Stocks in Portfolio

Study by Fedenia Study by Fedenia (University of Wisconsin)(University of Wisconsin)

Study covers all NYSE stocks (1963-94)Study covers all NYSE stocks (1963-94) Goal is to find lowest volatility portfolio for next 12 months for 100 randomly selected stks.Goal is to find lowest volatility portfolio for next 12 months for 100 randomly selected stks. The naïve estimate finds the low volatility portfolio over the previous 60 months.The naïve estimate finds the low volatility portfolio over the previous 60 months. Creates a risk model using, as factors, 5 portfolios that account for the correlations between Creates a risk model using, as factors, 5 portfolios that account for the correlations between

the 100 stocks.the 100 stocks. Finds the lowest volatility portfolio with risk model.Finds the lowest volatility portfolio with risk model. Repeats process 270 times for each year.Repeats process 270 times for each year.

Study by Fedenia Study by Fedenia (University of Wisconsin)(University of Wisconsin)

Average annualized volatility in the next year Average annualized volatility in the next year using the naïve estimate: 12.32%using the naïve estimate: 12.32%

Average annualized volatility in the next year Average annualized volatility in the next year using the risk factor model: 11.93%using the risk factor model: 11.93%

Expected Return Factor ModelsExpected Return Factor Models The factors in an expected return model represent the character of the The factors in an expected return model represent the character of the

companies. They might include the history of their stock prices, its size, companies. They might include the history of their stock prices, its size, financial condition, cheapness or dearness of prices in the market, etc.financial condition, cheapness or dearness of prices in the market, etc.

Factor payoffs are estimated by relating individual stock returns to Factor payoffs are estimated by relating individual stock returns to individual stock characteristics over the cross-section of a stock individual stock characteristics over the cross-section of a stock population (here the largest 3000 U.S. stocks).population (here the largest 3000 U.S. stocks).

Five Factor FamiliesFive Factor Families

Risk Risk LiquidityLiquidityPrice level Price level Growth potentialGrowth potentialPrice historyPrice history

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Book to Price

-100%

-50%

0%

50%

100%

-1.5

Tota

l R

etu

rnRelationship Between Total Return and Book to Price Ratio

January, 1981

Line of Best Fit

The Most Important FactorsThe Most Important Factors

The monthly slopes (payoffs) are averages over the The monthly slopes (payoffs) are averages over the period 1979 through mid 1986. “T” statistics on the period 1979 through mid 1986. “T” statistics on the averages are computed, and the stocks are ranked by averages are computed, and the stocks are ranked by the absolute values of the “Ts”.the absolute values of the “Ts”.

Most Important Factors

1979/01 through1986/06

1986/07 through 1993/12

Factor Mean Confidence Mean Confidence

One-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%

Projecting Expected ReturnProjecting Expected Return

The components of expected return are obtained by multiplying the projected The components of expected return are obtained by multiplying the projected payoffpayoff to each factor (here the average of the past 12) by the stock’s current to each factor (here the average of the past 12) by the stock’s current exposureexposure to the to the factor. Exposures are measured in standard deviations from the cross-sectional mean.factor. Exposures are measured in standard deviations from the cross-sectional mean.

The individual components are then summed to obtain the aggregate expected return The individual components are then summed to obtain the aggregate expected return for the next period (here a month)for the next period (here a month)

Factor Exposure Payoff ComponentBook\Price 1.5 S.D. x 20 B.P. = 30 B.P.

Short-Term Reversal 1.0 S.D. x -10 B.P. = -10 B.P.. . . .. . . .. . . .. . . .. . . .. . . .

Estimating Expected Stock ReturnsEstimating Expected Stock Returns

Trading Volume -2 S.D. x -20 B.P. = 40 B.P.Total Excess ReturnTotal Excess Return 80 B.P.80 B.P.

The Model’s Out-of-sample Predictive The Model’s Out-of-sample Predictive PowerPower

The 3000 stocks are ranked by expected return and formed into deciles The 3000 stocks are ranked by expected return and formed into deciles (decile 10 highest).(decile 10 highest).

The performance of the deciles is observed in the next month. Then The performance of the deciles is observed in the next month. Then expected returns are re-estimated, and the deciles are re-ranked.expected returns are re-estimated, and the deciles are re-ranked.

The process continues through 1993.The process continues through 1993.

Logarithm of Cumulative Decile Performance

1

2

3

45

678

9

10

-1

-0.5

0

0.5

1

1.5

2

2.5

80Q1 81Q1 82Q1 83Q1 84Q1 85Q1 86Q1 87Q1 88Q1 89Q1 90Q1 91Q1 92Q1 93Q1 94Q1 95Q1 96Q1 97Q1 98Q1

Date

3 4 5 6 7 8 9 10Decile

-40%

-30%

-20%

-10%

0%

10%

20%

30%

0 1 2

Realized Return

Realized Return for 1984 by Decile

(Y/X = 5.5%)

Y

X

Extension of Study to Other Periods

(Nardin Baker)

• The same family of factors is used on a similar stock population.

• Years before and after initial study period are examined to determine slopes and spreads between decile 1 and 10.

19971997

0%0%

10%10%

20%20%

30%30%

40%40%

50%50%

60%60%

70%70%

80%80%

90%90%

100%100%

19751975 19771977 19791979 19811981 19831983 19851985 19871987 19891989 19911991 19931993 19951995

YearsYears

19981998

difference

slope

Slope and SpreadSlope and Spread

Decile Risk Characteristics

The characteristics reflect the character of the deciles over the period 1979-1993.

Fama-French Three- Factor Model

Monthly decile returns are regressed on monthly differences in the returns to the following:

S&P 500 and T bills.

The 30% of stocks that are smallest and largest.

The 30% of stocks with highest book-to-price and the lowest.

Sensitivities (Betas) to Market Returns

10

Decile

1 2 3 4 5 6 7 8 9

0.95

1

1.05

1.1

1.15

1.2

1.25

Market Beta

Sensitivities (Betas) to Relative Performance of Small and Large Stocks

2 3 4 5 6 7 8 9 10Decile0

0.1

0.2

0.3

0.4

0.5

1

Size Beta

Sensitivities (Betas) to Relative Performance of Value and Growth Stocks

Decile8 9 10

1 2 3 4 5 6 7

-0.2

-0.1

0

0.1

0.2

0.3

Value/Growth Beta

Fundamental Characteristics

Averaged over all stocks in each decile and over all months (1979-83)

Risk

Decile Risk Characteristics

Debt to EquityDebt to Equity

1.031.030.850.85

StockVolatility

1 2 3 4 5 6 7 8 9 10

Decile

0%0

1

2

3

4

5

6

7

8

Interest CoverageMarket Beta

Debt to Equity

VolatilityVolatility

41.42%41.42%

33.22%33.22%

10%

20%

30%

40%

50%

Coverage Coverage

1.761.76

6.636.63

BetaBeta 1.001.001.211.21

Liquidity

Size and Liquidity Characteristics

$0

$10

$20

$30

$40

$50

$60

$70

1 2 3 4 5 6 7 8 9 10

Decile

Stock Price

Trading Volume

$400

$500

$600

$700

$800

$900

$1,000

$1,100

Size

$14.93$14.93

$30.21$30.21

PricePrice

$470$470

$1011$1011

SizeSize

$42.42$42.42

$60.89$60.89

Trading VolumeTrading Volume

Price History

Technical History

1 2 3 4 5 6 7 8 9 10

Decile

-20%

-10%

0%

10%

20%

30%

Excess Return

2 months2 months

-1.80%-1.80%

1.21%1.21%

12 months12 months

-15.74%-15.74%

30.01%30.01%

3 months

-6.89%

8.83%

6 months6 months

-12.14%-12.14%

16.60%16.60%

1 1 monmonthth

0.09%0.09%

-0.14%-0.14%

Profitability

Current Profitability

Asset TurnoverAsset Turnover115%115%

Return on EquityReturn on Equity15.39%15.39%

Profit MarginProfit Margin 7.86%7.86%

Return on AssetsReturn on Assets 6.50%6.50%

90%

100%

110%

120%

Asset Turnover

2 3 4 5 6 7 8 9 10

Decile

80%-10%

0%

10%

20%

1

Profit Margin Return on Assets Return on Equity Earnings Growth

Earnings GrowthEarnings Growth 0.95%0.95%

Trends in Profitability

1 2 3 4 5 6 7 8 9 10

Decile

5 Year Trailing Growth

-1.5%

-1.0%

-0.5%

0.0%

Profitability Trends(Growth In)

Asset TurnoverAsset Turnover

-0.13%-0.13%Profit MarginProfit Margin

-0.95%-0.95% Return on AssetsReturn on Assets

-1.11%-1.11% Return on EquityReturn on Equity

-1.18%-1.18%

Cheapness in Stock Price

Price Level

Sales-to-PriceSales-to-Price214%214%

207%207%

Cash Flow-to-PriceCash Flow-to-Price

6%6%

17%17%

Earnings-to-PriceEarnings-to-Price

-1.55%-1.55%

10%10%

Dividend-to-PriceDividend-to-Price2.19%2.19%

3.69%3.69%

50%

100%

150%

200%

Sales-to-Price Book-to-Price

3 4 5 6 7 8 9 10

Decile

0%-10%

0%

10%

20%

1 2

Cash Flow-to-Price

Earnings-to-Price

Dividend-to-Price

Book-to-PriceBook-to-Price81%81%

80%80%

Simulation of Investment Performance

• Efficient portfolios are constructed quarterly, assuming 2% round-trip transactions costs within the Russell 1000 population.– Turnover controlled to 20% to 40% per annum.– Maximum stock weight: 5%.– No more that 3X S&P 500 cap. weight in any stock.– Industry weight to within 3% of S&P 500.– Turnover controlled to within 20% to 40%.

10%11%

12%13%

14%15%

18%

17%

16%

20%

19%

12%

Ann

ualiz

ed to

tal r

etur

n

17% 18%13% 14% 15% 16%

Annualized volatility of return

1000 Index

GI

H

L

Optimized Portfolios in the Russell 1000 Population: 1979-1993Optimized Portfolios in the Russell 1000 Population: 1979-1993

Possible Sources of Bias• Survival bias: excluding firms that go inactive

during test period.• Look-ahead bias: using data that was unavailable

when you trade.• Bid-asked bounce: if this month’s close is a bid,

there is 1 chance in 4 that next and last month’s close will be at an asked, showing reversals.

• Data snooping: using the results of prior studies as a guide and then testing with their data.

• Data mining: spinning the computer.

Using the Ad Hoc Expected Return Factor Model

Internationally• The most important factors across the 5

largest stock markets (1985-93).

Using the Ad Hoc Expected Return Factor Model

Internationally• The most important factors across the 5

largest stock markets (1985-93).

• Simulating investment performance.– Within countries, constraints are those stated

previously.

– Positions in countries are in accord with relative total market capitalization.

Mean Payoffs and Confidence Probabilities for theTwelve Most Important Factors of the World (1985-93)

One-month stock return

Book to price

Twelve-month stock return

Cash flow to price

Earnings to price

Sales to price

Three-month stock return

Debt to equity

Variance of total return

Residual variance

Five-year stock return

Return on equity

United StatesUnited States

Mean Confidence Level(DifferentFrom Zero)

-0.32% 99%

0.14% 99%

0.23% 99%

0.18% 99%

0.16% 99%

0.08% 99%

-0.01% 38%

-0.06% 96%

-0.06% 94%

-0.08% 99%

-0.01% 31%

0.11% 99%

GermanyGermany

Mean Confidence Level(DifferentFrom Zero)

-0.26% 99%

0.16% 99%

0.08% 99%

0.08% 99%

0.04% 83%

0.10% 99%

-0.14% 99%

-0.06% 96%

-0.04% 83%

-0.04% 80%

-0.02% 51%

0.01% 31%

FranceFrance

Mean Confidence Level(DifferentFrom Zero)

-0.33% 99%

0.18% 99%

0.12% 99%

0.15% 99%

0.13% 99%

0.05% 99%

-0.08% 99%

-0.09% 99%

-0.12% 99%

-0.09% 99%

-0.06% 94%

0.10% 99%

United United KingdomKingdom

Mean Confidence Level(DifferentFrom Zero)

-0.22% 99%

0.12% 99%

0.21% 99%

0.09% 99%

0.08% 99%

0.05% 91%

-0.08% 99%

-0.10% 99%

-0.01% 38%

-0.03% 77%

-0.06% 96%

0.04% 80%

JapanJapan

Mean Confidence Level(Different

From Zero)-0.39% 99%

0.12% 99%

0.04% 86%

0.05% 91%

0.05% 94%

0.13% 99%

-0.26% 99%

-0.01% 31%

-0.11% 99%

0.00% 8%

-0.07% 98%

0.05% 92%

Optimization in France, Germany, U. K., Japan and across the Optimization in France, Germany, U. K., Japan and across the five largest countries. 1985-1994five largest countries. 1985-1994

19.0%19.0%

17.0%17.0%

15.0%15.0%

13.0%13.0%

11.0%11.0%

9.0%9.0%

7.0%7.0%

5.0%5.0%

10% 12% 14% 16% 18% 20% 22% 24%

G

I

HFranceFrance

FranceFranceindexindex

U. K.U. K. H

I

G U. K.U. K.indexindex

GermanyGermany

GermanyGermanyindexindex

H

I

G

JapanJapan

H

I

GG

JapanJapanindexindex

five largest five largest countries countries

(including U.S.)(including U.S.)

H

I

G

index ofindex offive largestfive largestcountriescountries

Annualized Annualized total total

returnreturn

Annualized volatility of returnAnnualized volatility of return

Expansion of the 1996 Study

(Nardin Baker)

Performance In Different Countries: 1985 - 1998 (Sept.)

0%

5%

10%

15%

20%

25%

30%

12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32%

Volatility

Return

AUS BEL CAN CHE DEU ESP FRA

GBR HKG ITA JPN NLD SWE USA

Actual Performance

Performance before fees, after transactions costs and includes reinvested dividends

Industrif inans Contact: Ole Jakob Wold +47.22.473300 Measured in Norw egian Krone (NOK), Managed to stay neutral in country and sector w eightsPast performance is not a guarantee of future results Managed using modif ied (Haugen-Baker) JFE Expected Return Model by Baker at Grantham Mayo Van Otterloo, Inc.

Industrifinans ForvaltningGlobal Fund

170.65%

144.04%

-20.00%

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

140.00%

160.00%

180.00%

start jan.95 apr jul oct jan.96 apr jul oct jan.97 apr jul oct jan.98 apr jul oct jan.99 apr

Cumulative return since inception (31 October 1994)

Industrifinans WorldMorgan Stanley World NOK

Performance measured before fees, after transactions costs and includes reinvested dividends

Industrif inans Contact: Ole Jakob Wold +47.22.473300 Measured in Norw egian Krone (NOK), Managed to stay neutral in country and sector w eightsPast performance is not a guarantee of future results Managed using modif ied (Haugen-Baker) JFE Expected Return Model by Baker at Grantham Mayo Van Otterloo, Inc.

Industrifinans ForvaltningProbability that the expected return to the Global Fund has been higher than the Morgan Stanley World Index

92.2%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

dec.94 mar jun sep dec.95 mar jun sep dec.96 mar jun sep dec.97 mar jun sep dec.98 mar

Probability of out-performing the Morgan Stanley World Index since inception (31 October 1994)

AI Contact: Dennis Bein 213.688.3015 Performance before fees, after transactions costs and includes reinvested dividendsPast performance is not a guarantee of future results Managed using Haugen expected return model & Barra optimizer & risk model

Analytic InvestorsEnhanced Equity Institutional Composite

130.31%

102.73%

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

140.00%

start nov.96 jan.97 mar may jul sep nov jan.98 mar may jul sep nov jan.99 mar

Cumulative return since inception (30 Sep 1996)

Institutional CompositeS&P 500

AI Contact: Dennis Bein 213.688.3015 Performance before fees, after transactions costs and includes reinvested dividendsPast performance is not a guarantee of future results Managed using Haugen expected return model & Barra optimizer & risk model

Analytic InvestorsProbability that the expected return to the Enhanced Equity Institutional Composite has been higher than the S&P 500 Index

93.3%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

nov.96 feb.97 may aug nov feb.98 may aug nov feb.99

Probability of out-performing the S&P 500 Index since inception (30 Sep 1996)

Performance of 413 Mutual Funds 10/96 -

9/98

• “T” stat. on mean monthly out-performance to S&P 500

• Large funds with highest correlation with S&P with a 36 month history

Three YearThree Year OutOut--(Under)(Under)-Performance T-Distribution-Performance T-Distribution

0%0%

5%5%

10%10%

15%15%

20%20%

25%25%

to -5.0 -5.0 to

-4.5

-4.5 to

-4.0

-4.0 to

-3.5

-3.5 to

-3.0

-3.0 to

-2.5

-2.5 to

-2.0

-2.0 to

-1.5

-1.5 to

-1.0

-1.0 to

-0.5

-0.5 to

0.0

0.0 to

0.5

0.5 to

1.0

1.0 to

1.5

1.5 to

2.0

2.0 to

T-statistics for mean T-statistics for mean outout--(under)(under) performance performance

Per

cen

t o

f sa

mp

leP

erce

nt

of

sam

ple