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Capital Markets

Value-Based Anomalies

Dr. Keith AndersonThe York Management School

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Learning Outcomes

• Appreciate the large apparent hole in efficient markets theory

• Learn some more about a few of the anomalies: the P/E, PSR and PEG ratio

• Take my PhD work into the P/E anomaly as an example of how to advance research

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Value-Based Anomalies: Overview

I. Why is researching anomalies important?

II. Review of the P/E anomaly literature

III. The PSR anomaly

IV. The PEG ratio

V. My PhD research

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Recommended Reading

David Dreman (1998), Contrarian Investment Strategies: The Next Generation

Library G 2.63 DRE From £2.93 on Amazon

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Part I: Why is Anomaly Research Important?

• CAPM: the dominant paradigm• Proposes a straight-line relationship between a

stock’s volatility with respect to the market and the returns expected from it

• Taught to thousands of business students every year

• What they don’t tell you...

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The Academic Argument

• Many so-called ‘anomalies’ documented• ‘Anomalies’ only for the CAPM: each seems to

show a statistic that can forecast returns• CAPM says that beta is the only variable that

should be able to predict returns

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The Academic Argument

• P/E anomaly was the earliest (Nicholson (1960))• Predated the CAPM itself (Sharpe (1964))• Eclipsed by price-to-book-value in recent years• Problem: No replacement model with sound

underlying theory as the CAPM has• May move in future towards other models based

on F&F 3-factor model or behavioural finance

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The Practical Argument

• This is all just a dry philosophical debate for market operators

• Want to spot shares that are going to go up • Extra level of risk also important to them• Several value-based quantitative funds in the US• Only one ‘fund’ in the UK: Barclays iShare UK

Dividend Plus. See

http://uk.ishares.com/en/rc/stream/pdf/-/publish/repository/documents/en/downloads/factsheet_ftse_uk_dividend_plus.pdf

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Question Sheet

• Now read the UK Dividend Plus factsheet and try to answer the questions

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Part II: The Price-Earnings Anomaly

• The most popular statistic for looking at a company’s value at its current price

• Historical P/E:

• Prospective P/E:

• E/P often used in academic literature – why?

yearcompany last in Earnings

price Share

yearnext for forecast Consensus

price Share

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What is a Price-Earnings Ratio?

• Original theory (Gordon and Shapiro (1956)):

P: current price of the stockE: last announced company earningsb: payout ratior: discount rateg: dividend or earnings growth rate

• So higher growth rate g → smaller denominator → higher P/E, ceteris paribus

E

P

g -r

b - 11P b

E r g

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• Standard P/E 8 to 12, or 15+ for larger growth stocks

• Compare to tech stock boom: AOL P/E of 275, Yahoo P/E of 1900, Amazon P/E of ∞

• Varying expectations of future earnings growth, both cross-sectionally & through time

• Going the other way, expectations of bad news can give extraordinarily low P/Es

What is a Price-Earnings Ratio?

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Early Work on the P/E Effect

• Nicholson (1960): 3-page paper with 100 stocks• 14.7 times original investment after 20 years for

lowest P/E quintile versus 4.7 times for highest• Glamour stocks may merit high P/Es but often

prices have grown faster than earnings• Rarely, price action continues spectacularly• Seen as representative of growth stocks generally• Reality eventually makes itself felt

“High price-earnings multiples typically reflect investor satisfaction with companies of high quality, or with those which have experienced several years of expansion and rising earnings. In such cases, prices have often risen faster than earnings. A resultant increase in price-earnings ratios may be justified in individual instances, but under the impact of public approval or even glamour, it often runs to extremes.

...

Some growth stocks appear to be exceptions, at least for temporary periods, and in individual instances price advances have continued spectacularly.”

Nicholson (1960) p.4514

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Early Work on the P/E Effect

• Nicholson (1968) looked at P/E, PSR, and PBV over holding periods up to 7 years

P/E7-year growth

Sales/ price

7-year growth

Book value / price

7-year growth

< 10 131% > 5 138% > 1.5 149%

10-12 87% 2-5 108% 1-1.5 112%

12-15 88% 1-2 107% 0.6-1 91%

15-20 75% 0.6-1 89% 0.3-0.6 90%

> 20 71% < 0.6 69% < 0.3 86%

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• First paper by an academic Basu (1975 & 1977): looked at NYSE industrials 1957-71

  E/P Quintile

Avg.Rtn p.a. %

beta

A (highest) 9.3 1.11

A* 9.6 1.06

B 9.3 1.04

C 11.7 0.97

D 13.6 0.94

E (lowest) 16.3 0.99

Early Work on the P/E Effect

“The average annual rates of return decline...as one moves from low P/E to high P/E portfolios. However, contrary to capital market theory, the higher returns on the low P/E portfolios were not associated with higher levels of systematic risk” (p666)

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• Ball (1978) re Phlogiston: see Dreman pp.151-2• Jaffe, Keim & Westerfield (1989): January, size

& P/E effects all significant• Fuller, Huberts & Levinson (1993): Ball’s

(1978) ‘omitted risk factors’ couldn’t account for better returns from low P/E stocks

• Fama and French (1992 and 1993): model with market return, size and PBV could ‘explain’ value stock returns after the fact

• P/E effect subsumed by PBV and size effects

More Recent Findings

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• Lakonishok, Schleifer & Vishny (1994): value vs. glamour stocks 1963-1990 on the basis of past sales growth

• Differences in expected future growth rates consistently overestimated

• Outperformance of value stocks 10-11% per year• Value strategies aren’t fundamentally riskier –

value stocks did particularly well in ‘bad’ states of the world

More Recent Findings

LSV(1994)

• P/E did not produce as large an effect as price to book value or price to cash flow, possibly because

“stocks with temporarily depressed earnings are lumped together with well-performing glamour stocks in the high expected growth/low E/P category. These stocks with depressed earnings do not experience the same degree of poor future stock performance as the glamour stocks, perhaps because they are less overpriced by the market.”

(page 1550)19

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• A recognised value indicator, in use since 1920s• Efficient markets believers say it must be a proxy

for some sort of risk• Has lost its importance in recent years due to price

to book value being preferred in the Fama and French 3-factor model

• But still has its proponents such as Dreman (and me)

The P/E: Summary

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• A value/glamour indicator that is less easy to manipulate than the P/E

• Particularly useful for loss-makers• Out-of-favour firms barely making a profit could

move from the highest P/E group to a more appropriate low PSR group

• But PSR has two important weaknesses:– no good for financial services companies– best to stratify by industry

Part III: The PSR Anomaly

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The PSR AnomalyLiterature on the PSR

• Nicholson (1968) first to assess PSRs• Senchack & Martin (1987): US stocks 1975-

1984 excluding financial services firms

PSR* Quintile

Quarterly return beta

Low PSR* 7.27% 1.1132 5.92% 1.0133 5.28% 0.9074 4.47% 0.814High PSR* 3.78% 0.892

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• Nathan, Sivakumar & Vijayakumar (2001): important to stratify PSR by industry. Long PSR1PE1 and short PSR5PE5 gave +37.78% p.a

• Sole UK work: Leledakis and Davison (2001)• Found that PSR and gearing together had

significantly more predictive power than F&F’s size and PBV together

The PSR Anomaly

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• Now try the questions on the PSR

Question Sheet

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Part IV: The PEG Ratio

• Popular in recent years for valuing growth stocks• Formula is

• Implicit assumption: earnings growth rates tend to be sustained over several years

• BUT Little (1962) and Rayner and Little (1966) showed that earnings growth is indistinguishable from a random walk

P/E ratio

earnings growth rate

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The PEG Ratio

• Sort companies into past growth rate deciles: immediately revert to average of the market

• Subsequent differences no more than would be expected from chance alone

• Replicated using US data by Lintner and Glauber (1967)

• More recently by Chan, Karceski and Lakonishok (2003) looking at all US companies 1951-1997

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The PEG Ratio

• ‘Earnings as a random walk’ idea hasn’t dented the popularity of Jim Slater’s Zulu Principle books (1992 and 1996)

• Market participants still seem generally to believe that growth rates are sustained over several years and can be predicted. Seehttp://www.companynews.co.uk/star/stepbystep2.htm

• PEG ratio is also prominent in popular company information database Company REFS which Slater helped to design

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The PEG Ratio

“It ain't so much the things we don’t know that get us into trouble. It's the things we know that just ain't so.”

- Variously attributed to Josh Billings,

Artemus Ward and Mark Twain

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Part V: My PhD Work

Two areas of results covered here:

1. Long-term P/Es

2. Deconstructing the P/E ratio

•Academic: widens the gap in returns between high and low P/E stocks that needs to be explained by any valuation theory

•Practitioners: obvious practical applications for portfolio managers

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• All UK shares 1975-2003 including AIM• LSPD for company names, then Datastream

thereafter• Excluded financial sector companies, including

investment trusts• For companies that went bust, set RI manually to 0

Data Sources

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•All papers up to now use the one-year historical P/E for assigning companies to deciles or quintiles

•Why should only one year of earnings be relevant for predicting future returns?

“Average earnings...should cover a period of not less than five years, and preferably seven to ten years” (Graham and Dodd (1934, p.452))

•Remember LSV (1994) p.1550 quote•Assign companies to deciles using EP1, the

traditional E/P, up to EP8:i

n

jij

i nP

EPS

EPn

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Part VA: The Long-Term P/E

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EP1 EP2 EP3 EP4 EP5 EP6 EP7 EP8

Highest P/E 18.28% 18.20% 18.62% 16.65% 17.84% 17.83% 18.15% 16.26%

Decile 2 19.25% 19.36% 16.41% 17.98% 16.94% 17.42% 16.16% 16.71%

Decile 3 18.38% 17.32% 18.92% 18.68% 17.78% 17.51% 17.05% 16.43%

Decile 4 16.44% 18.96% 19.45% 18.42% 19.49% 17.81% 18.61% 18.42%

Decile 5 17.96% 18.06% 17.73% 18.58% 17.62% 19.11% 18.34% 19.54%

Decile 6 18.53% 18.73% 19.32% 18.98% 19.97% 19.69% 19.81% 19.81%

Decile 7 21.59% 19.53% 19.86% 20.77% 19.61% 20.18% 19.86% 19.39%

Decile 8 20.86% 20.55% 21.33% 22.11% 21.81% 20.42% 20.58% 21.11%

Decile 9 22.47% 21.75% 22.00% 22.08% 22.48% 22.88% 22.48% 23.05%

Lowest P/E 24.26% 22.82% 21.89% 22.18% 24.27% 25.51% 27.57% 27.87%

D10 – D1 5.98% 4.62% 3.28% 5.52% 6.44% 7.67% 9.42% 11.62%

Long-Term P/E Decile Returns

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High P

/E

Decile

2

Decile

3

Decile

4

Decile

5

Decile

6

Decile

7

Decile

8

Decile

9

Low P

/E

EP1EP8

10%

12%

14%

16%

18%

20%

22%

24%

26%

28%

Long-Term P/E Decile Returns

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Increasing into the

future

Increasing into the past

Equal

weights Linear

Inverse square

Linear Inverse square

Linear Regression

Highest P/E 16.26% 16.89% 17.84% 15.81% 15.19% 16.68%

Decile 2 16.71% 16.30% 16.44% 16.05% 16.79% 14.83%

Decile 3 16.43% 18.10% 18.03% 16.95% 16.52% 17.40%

Decile 4 18.42% 17.24% 17.48% 18.35% 19.05% 17.60%

Decile 5 19.54% 18.93% 17.96% 19.14% 19.00% 19.77%

Decile 6 19.81% 19.66% 20.03% 20.69% 19.42% 18.28%

Decile 7 19.39% 20.11% 20.76% 19.92% 20.80% 20.36%

Decile 8 21.11% 20.79% 21.50% 20.27% 21.00% 22.33%

Decile 9 23.05% 23.83% 20.77% 23.48% 23.84% 22.89%

Lowest P/E 27.87% 26.68% 27.75% 27.98% 27.01% 28.45%

D10 – D1 11.62% 9.79% 9.91% 12.17% 11.82% 11.77%

Weighting Past Years of Earnings

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The Long-Term P/E Ratio - Summary

• EP8 resolution 12% versus 6% for traditional EP1• Any fund manager who takes a longer-term view

of earnings will gain a competitive advantage • Individual past years of earnings aren’t equally

valuable for predicting returns: earnings from five to eight years ago are better at predicting returns than the traditional P/E!

• Not much success with clever weighting systems. Remaining work sticks to equally-weighted EP8

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Part VB: Decomposing the P/E Ratio

• Several regular influences on a company’s P/E, including:– The year– The sector– Size– Idiosyncratic effects

• Question: do these different effects have different values in predicting returns?

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Influences on the P/E

P/ELow P/E

High returns

YearLow P/E

High returns

SectorHigh P/E

High returns

SizeLow P/E

High returns

IdiosyncraticLow P/E

High returns

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Market Average P/Es by Year

0

5

10

15

20

25

30

AverageP/E

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Sector P/Es

• Average P/E calculated for each sector with ten or more company/year returns

• Averaged over all 29 years• 132 LSPD G17 categories• P/E varies from 28.7 (Oil and gas exploration and

production) to 6.4 (Steel)• Conclusion: Slightly better returns for high P/E

sectors!

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Size P/Es

• Group companies into 20 categories based on market capitalisation on portfolio formation date

• E/P averaged for each category over all years• Category limits vary from year to year• Average P/Es vary consistently according to

market capitalisation• Large fund managers naturally tend to buy large

companies to avoid liquidity problems

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Average P/Es by Size Category

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Market Value Category

AverageP/E

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Calculating the Idiosyncratic E/P

• Define the idiosyncratic E/P as that part of a company’s E/P that is not explained by its year, sector or size:

• Note this is not a regression and there is no error term! Rearranging,

AverageEP

IdioEP

AverageEP

EPG

AverageEP

MVEP

AverageEP

YearEP

AverageEP

ActualEP iiiii 17

3

17i

ii i i

ActualEP AverageEPIdioEP

YearEP MVEP G EP

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E/P Decomposition Linear Regression Model

• Linear regression model is

• Coefficients are

Rtn01 = 0.736 + 0.479 YearEP + 0.274 MVEP -0.093 G17EP + 0.091 IdioEP

• All significant at 1% level

iiiiii uIdioEPEPGMVEPYearEPRtn 43210 1701

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E/P DecompositionLinear Regr Model

• Year E/P is much better at predicting returns, but we can’t choose which year to invest in!

• MVEP three times as useful as G17EP or IdioEP• Effect of G17 E/P is the opposite way round to the

others: a higher sector P/E means better returns

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Decile Returns using the Decomposed E/P

EP1 EP8 Decomposed

E/P Highest P/E 18.28% 16.26% 11.93% Decile 2 19.25% 16.71% 14.66%

Decile 3 18.38% 16.43% 15.84% Decile 4 16.44% 18.42% 16.94%

Decile 5 17.96% 19.54% 20.49% Decile 6 18.53% 19.81% 19.64%

Decile 7 21.59% 19.39% 21.27% Decile 8 20.86% 21.11% 23.84%

Decile 9 22.47% 23.05% 23.72% Lowest P/E 24.26% 27.87% 30.23%

D10 – D1 5.98% 11.62% 18.30%

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Decomposed E/P Portfolio Example

£1,000

£10,000

£100,000

£1,000,000

£10,000,000

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

LinRegr Value LinRegr Glamour EP8 Value EP8 Glamour

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E/P Decomposition Summary

• Four influences (year, sector, size and idiosyncratic components) identified

• Sector works in the opposite direction to the rest• Decomposed the influences and put them back

together again in a weighted P/E• Sector influence reversed• D10-D1 difference in returns: 6% for traditional

P/E → 12% for EP8 → 18% for decomposed E/P• Value decile now returns 30% per annum

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Summary

I hope you now• Understand more about some of the anomalies

facing efficient markets theory and how to test them

• Particularly about the P/E ratio and why it has dropped out of favour recently

• Appreciate the sort of work that could advance this research

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References

• Ball, R. 1978. Anomalies in Relationships between Securities' Yields and Yield-Surrogates. Journal of Financial Economics, 6(2/3): 103-26.

• Basu, S. 1975. The Information Content of Price-Earnings Ratios. Financial Management, 4(2): 53-64.

• Basu, S. 1977. The Investment Performance of Common Stocks in relation to their Price-Earnings Ratios. The Journal of Finance, 32(3): 663-82.

• Chan, L.C.K., Karceski, J. & Lakonishok, J. 2003. The Level and Persistence of Growth Rates. The Journal of Finance, 58(2): 643-84.

• Dreman, D.N. 1998. Contrarian Investment Strategies: The Next Generation. New York: Simon & Schuster.

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References

• Fama, E.F. & French, K.R. 1992. The Cross-Section of Expected Stock Returns. The Journal of Finance, 47(2): 427-65.

• Fama, E.F. & French, K.R. 1993. Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics, 33(1): 3-56.

• Fuller, R.J., Huberts, L.C. & Levinson, M.J. 1993. Returns to E/P Strategies, Higgeldy Piggeldy Growth, Analysts' Forecast Errors, and Omitted Risk Factors. Journal of Portfolio Management, 1993(Winter): 13-24.

• Gordon, M. & Shapiro, E. 1956. Capital Equipment Analysis: The Required Rate of Profit. Management Science, 3: 102-10.

• Graham, B. & Dodd, D. 1934. Security Analysis. New York: McGraw-Hill.

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References

• Jaffe, J., Keim, D.B., & Westerfield, R. 1989. Earnings Yields, Market Values, and Stock Returns. The Journal of Finance, 44(1): 135-48.

• Lakonishok, J., Schleifer, A. & Vishny, R. 1994. Contrarian Investment, Extrapolation, and Risk. The Journal of Finance, 49(5): 1541-78.

• Leledakis, G. & Davidson, I. 2001. Are Two Factors Enough? The U.K. Evidence. Financial Analysts Journal, 57(6): 96-105.

• Linter, J. & Glauber, R. 1967. Higgledy Piggledy Growth in America. In Lorie, J. and Brealey, R., editor, Modern Developments in Investment Management. Hinsdale, IL: Dryden Press.

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References

• Little, I.M.D. 1962. Higgledy Piggledy Growth. Journal of the Oxford University Institute of Statistics, 24(4): 387-412.

• Miller, W. and McGarry, P.C. 1966. 452 ways to beat the market. Financial Analysts Journal, 23(4): 96-105.

• Nathan, S., Sivakumar, K., & Vijayakumar, J. 2001. Returns to Trading Strategies Based on Price-to-Earnings and Price-to-Sales Ratios. Journal of Investing, 10(2): 17-28.

• Nicholson, S.F. 1960. Price-Earnings Ratios. Financial Analysts Journal, 16(4): 43-45.

• Nicholson, S.F. 1968. Price-Earnings Ratios in relation to Investment Results. Financial Analysts Journal, 24(1): 105-09.

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References

• Rayner, A.C. & Little, I.M.D. 1966. Higgledy Piggledy Growth Again. Oxford: Basil Blackwell.

• Senchack, A.J. & Martin, J.D. 1987. The Relative Performance of the PSR and PER Investment Strategies. Financial Analysts Journal, 43(2): 46-56.

• Slater, J. 1992. The Zulu Principle. London: Texere Publishing.

• Slater, J. 1996. Beyond the Zulu Principle. London: Texere Publishing.