SQA Nov. 15 , 2013 GOALS OF MY TALK

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“The Supraview of U.S. Equity Return Predictive Signals –

The Last 40 Years and Changes in the Last 5 Years”

Prof. John Hand UNC Chapel Hill

SQA Nov. 15th, 2013

GOALS OF MY TALK

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● I will give you my SUPRAVIEW of what academics have discovered since 1970 about the firm-specific characteristics that historically have predicted the cross-section of expected U.S. stock returns.

● My coauthors Jeremiah Green (Penn State) and Frank Zhang (Yale) and I term these firm-specific characteristics as “return predictive signals” or RPS.

● Disclaimer: Certain parts of this talk represent my personal opinions, and are not necessarily shared by my coauthors.

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RPS SUPRAVIEW

● Almost all prior academic RPS research has centered on discovering the identify and returns to one new RPS per paper – the “one new tree” approach.

● What Green, Hand and Zhang (RAST, 2013a) do is take the supraview = looking at the whole forest.

● Taking the supraview and “getting high” is worth the effort and risk because the view from above the trees provides insights that cannot be seen from within the trees on the forest floor.

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POPULATION of RPS (GHZ, RAST 2013a)

● We approximated the population of RPS by:

● Searching top-tier U.S. accounting, finance and practitioner journals for RPS papers published Jan. 1970 – Dec. 2010.

● Following up references in these papers

● Searching SSRN for working papers in these Subject Matter eJournals:

● FEN Capital Markets: Market Efficiency ● FEN Capital Markets: Asset Pricing / Valuation ● ARN Financial Accounting

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DATABASE of RPS (cont’d)

● We categorized each RPS as:

● Accounting-based > In financial statements ● Finance-based > Dependent on stock price ● Other-based > Neither of these

● Minority of ‘mixed’ RPS coded as Finance-based.

● We coded key attributes: Author(s), publication date, first WP date, databases used, RPS name and definition, period of analysis, EW or VW returns, firm characteristics or factors orthogonalized against, and RPS mean return and Sharpe ratio.

5

0

20

40

60

80

100

120

140

160

Cumulative # of ABTS vs. PBTS vs. OBTS, 1970 - 2010

Accounting-based RPS Finance-based RPS Other-based RPS

RESULT # 1 There are 330+ RPS

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4

RESULT # 2a RPS EW_return stats

TABLE 4 Panel A: All types of RPS Panel B: Accounting-based RPS

Mean Std. dev. Sharpe Mean Std. dev. Sharpe Min. 0.8% 4.3% 0.08 3.3% 4.6% 0.37 25th percentile 6.6% 8.6% 0.68 8.5% 9.2% 0.72 Median 10.8% 11.0% 0.87 12.0% 11.5% 0.91 Mean 12.2% 12.1% 1.04 13.2% 12.4% 1.10 75th percentile 16.1% 14.3% 1.29 17.4% 16.7% 1.38 Max. 35.0% 31.2% 2.98 32.4% 31.2% 2.50 Std. dev. 7.1% 5.2% 0.55 6.9% 4.9% 0.97 Skewness 0.9 1.3 1.0 0.9 1.2 0.9 Number of RPS 237 208 208 115 97 97

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RESULT # 2b RPS EW_return stats



Sloan (1996)

10.4% 12.8% 0.81



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TABLE 4 Panel C: Finance-based RPS Panel D: Other-based RPS


Jegadeesh & Titman (1993)

11.4% 18.7% 0.61

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RESULT # 2c RPS VW_return stats


Mean Std. dev. Sharpe Mean Std. dev. Sharpe Min. -2.4% 3.9% -0.21 -1.4% 4.6% -0.11 25th percentile 3.5% 8.6% 0.34 4.2% 8.8% 0.41 Median 7.1% 11.0% 0.61 7.1% 11.0% 0.67 Mean 8.1% 12.2% 0.70 8.0% 12.2% 0.63 75th percentile 10.9% 15.2% 0.84 10.6% 13.8% 0.83 Max. 35.0% 27.9% 3.09 30.1% 27.3% 1.47 Std. dev. 6.3% 5.0% 0.58 5.3% 4.9% 0.31 Skewness 1.4 1.0 2.1 2.0 1.5 0.0 Number of RPS 99 87 87 35 27 27



VW EW

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RESULT # 2d RPS , Sharpe stability

Figure 2, Panel A: Mean RPS returns Figure 2, Panel B: Mean RPS returns All types of RPS combined together Accounting-based RPS only t-stat on [EW RPS] slope = 0.7 t-stat on [EW RPS] slope = 1.6 t-stat on [VW RPS] slope = 0.2 t-stat on [VW RPS] slope = –0.3

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

1970 1980 1990 2000 2010

Hedge returns over time

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

1970 1980 1990 2000 2010

ABTS: HRet over time

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Figure 3, Panel A: Sharpe ratios of RPS returns Figure 3, Panel B: Sharpe ratios of RPS returns All types of RPS combined together Accounting-based RPS only t-stat [EW RPS] slope = 0.7 t-stat [EW RPS] slope = –0.1 t-stat [VW RPS] slope = 0.3 t-stat [VW RPS] slope = 1.1

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

1970 1975 1980 1985 1990 1995 2000 2005 2010

Sharpe ratios over time

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

1970 1980 1990 2000 2010

ABTS: Sharpe ratios over time

RED = VW returns

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RESULT # 2e RPS vs. , vs. Sharpe

Figure 4, Panel A: vs. Figure 4, Panel B: vs. All types of RPS combined together Accounting-based RPS only

[RPS_EW] = 4.7% + 0.61 [RPS_EW] [RPS_EW] = 4.0% + 0.74 [RPS_EW] (4.2) (7.3) (2.4) (6.1)

[RPS_VW] = 2.1% + 0.49 [RPS_VW] [RPS_VW] = 4.2% + 0.24 [RPS_VW] (1.3) (4.1) (2.6) (2.0)

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

0% 5% 10% 15% 20% 25% 30% 35%

ABTS: Ann_HRet vs. Ann_Stdev

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

0% 5% 10% 15% 20% 25% 30% 35%

ABTS: Ann_HRet vs. Ann_Stdev

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Figure 4, Panel C: vs. Sharpe ratio Figure 4, Panel D: vs. Sharpe ratio All types of RPS combined together Accounting-based RPS only

[RPS_EW] = 2.0% + 0.10 SR[RPS_EW] [RPS_EW] = 2.8% + 0.09 SR[RPS_EW] (2.8) (16.1) (2.3) (9.3)

[RPS_VW] = 2.7% + 0.08 SR[RPS_VW] [RPS_VW] = 2.7% + 0.07 SR[RPS_VW] (3.9) (9.8) (2.5) (4.9)

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

-0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

ABTS: Ann_HRet vs. Ann_SR

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

-0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

ABTS: Ann_SR vs. Ann_HRet

RED = VW returns

RED = VW returns

Figure 5, Panel A: RPS discovered and publicly reported by academics, 1970-2010

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

-0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

ABTS: Ann_HRet vs. Ann_SR

Panel B: RPS commonly used by sophisticated investors (as proxied by J.P. Morgan, 1/27/11)

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

-0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

JPM factors -- Russell 3000 -- Sharpes vs. Returns

Largest 1000 Smallest 1000 Smallest 2000 Largest 200


-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

-0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50




-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

-0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50




-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

-0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50



RESULT # 2f vs. Sharpe Academic RPS vs. Practitioner RPS

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What has changed in last 5 years?

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● Some academics are still discovering new RPS …

● But other academics are adopting the supraview:

● Harvey, Liu & Zhu (2013) identify 311 RPS and/or factors to study effects of data snooping.

● McLean & Pontiff (2013) document attenuation of 35% in mean hedge returns to 82 RPS after academic discovery.

● Frank, Jeremiah and I have a working paper in which we take the supraview on the cross-section of expected returns. More on that in a minute …

CONCLUSIONS, part 1

1. Adopting the Supraview on RPS uncovers many new facts about RPS that are informative to both academics and practitioners.

2. The time has come for academics to STOP discovering more RPS. Rather, academics should seek to understand what the population of RPS tells us about risk, return, market efficiency, etc.

3. For example, does the presence of N = 330 RPS indicate that the U.S. stock market is massively inefficient, or that there are far more rationally priced sources of risk to be understood?

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MY TALK, PART 2 – GHZ (2013b, WP)

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● In this new working paper we take the supraview on the cross-section of expected U.S. stock returns. [full text of paper is on SSRN.com]

● How? We update Fama & French (1992) in light of the huge population of documented RPS.

● We report what we think are some remarkable results.

● I will give you my opinion as to some of the implications of our results for academics and investment practitioners.

“The Remarkable Multidimensionality in the

Cross-Section of Expected U.S. Stock Returns”

Jeremiah Green John Hand Frank Zhang

Penn State UNC Yale

Chicago Oct. 24, 2013

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Cumulative number of RPS, 1970-2010

17

0

50

100

150

200

250

300

350


Total RPS

“In the beginning, there was chaos. Then came the CAPM …

Then anomalies erupted, and there was chaos again.”

Cochrane (2011, p. 1058)

18

0

50

100

150

200

250

300

350


Total RPS

FF92 goal: “To evaluate the joint roles of market b, size, E/P, leverage,

and book-to-market in the cross-section of average returns of U.S.

stocks.” (p. 428)

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19

0

50

100

150

200

250

300

350


Total RPS

FF92 find: “If assets are priced rationally, our results suggest that stock risks are

multidimensional … Size and book-to-market provide a simple and powerful characterization

of the cross-section of average stock returns for the 1963-1990 period.” (pp. 428-9)

20

0

50

100

150

200

250

300

350


Total RPS

“Alas, the world is once again descending into chaos … We are going to have to repeat Fama & French’s (1992) anomaly digestion, but with

many more dimensions. We have a lot of questions to answer:

First, which characteristics really provide independent information about average returns? Which are subsumed by others?”

RPS chaos has grown 10X since FF92

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Our main results

● We project 93 RPS onto U.S. returns 1980-2012. We find that a remarkably large 26 RPS are multidimensionally priced as defined by their mean FM coefficients having an abs{t-stat} 3.0 in the cross-section of 1-month ahead returns.

● This is 10X the dimensionality of the current 3-dimensional model of firm size, book-to-market and 12-month momentum that is widely used by academics and investment practitioners.

● We think that 26 is likely an underestimate.

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Our main results (cont’d)

● High dimensionality occurs in part because the average cross-correlation between scaled ranked decile RPS is very small — just 0.03.

● Multidimensional pricing of several famous RPS is quite different to their unidimensional pricing.

● Firm size, book-to-market, and 12-month momentum do not have t-stats large enough to put them in the top 10 largest t-stats in 1-month ahead returns multidimensional regressions.

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Our main results (cont’d)

● Hedge returns on multidimensioned RPS are 2/3rds smaller than those on unidimensioned RPS, while t-stats are between 1/3rd and 2/3rds smaller.

● High dimensionality is present in each decade of our 1980-2012 data period.

● Large firms have far fewer multidimensionally priced RPS than do small firms, but the RPS of large firms explain 3X the amount of cross-sectional return variance.

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Implications that we see

1. Dimensionality of U.S. stock returns is likely higher than we estimate it to be.

2. Controlling for only firm size, book-to-market and 12-month mom is low powered, maybe also biased.

3. NPV of investing in understanding why returns are so multidimensional >> NPV of finding another RPS.

4. How much the estimation of dimensionality has changed over 20+ years means that it is reasonable to take the inferences/conclusions of our study, and future studies, more cautiously than ever.

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Literature on return dimensioning

● Relatively sparse.

● Papers have either proposed a small competing set of priced RPS to replace firm size, book-to-market and 12-month momentum, or have put forward a larger set of RPS beyond firm size, book-to-market and 12-month momentum.

● Hou, Xue & Zhang (2012) exemplify the former approach, while Haugen & Baker (1996), Fama & French (2008) and Lewellen (2013) illustrate the latter method.

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Data & empirical methods: RPS supraview database 100 RPS

● Since FF92, almost all RPS research has centered on discovering and reporting the hedge returns to one new RPS per paper.

● In GHZ (RAST, 2013a) we take the RPS supraview. We find that getting high above the RPS forest yields new insights—and puzzles— that cannot be seen from perspective of a single RPS tree.

● We select 100 RPS primarily from GHZ database.

● RPS based only on CRSP, Compustat or I/B/E/S.

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Data

● Individual RPS listed and defined in Tables 1 and 2.

● Not all RPS can be computed per originating paper for every firm at every point in calendar time.

● But we really want to keep as many RPS as possible, and as many observations per RPS as possible.

● So we:

● Set missing Compustat data to zero (e.g., R&D). ● Set all RPS with post-creation missing values to

mean of the non-missing RPS for that month.

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Table 1 (excerpt)

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# RPS Acronym Author(s) Date, Journal

1 Beta beta Fama & MacBeth 1973, JPE

2 Beta squared betasq Fama & MacBeth 1973, JPE

3 Earnings-to-price ep Basu 1977, JF

4 Firm size (market cap) mve Banz 1981, JFE

5 Dividends-to-price dy Litzenberger & Ramaswamy 1982, JF

6 Unexpected quarterly earnings sue Rendelman, Jones & Latane 1982, JFE

7 Change in forecasted annual EPS chfeps Hawkins, Chamberlin & Daniel 1984, FAJ

8 Book-to-market bm Rosenberg, Reid & Lanstein 1985, JPM

9 36-month momentum mom36m De Bondt & Thaler 1985, JF

10 Forecasted growth in 5-year EPS fgr5yr Bauman & Dowen 1988, FAJ

11 Leverage lev Bhandari 1988, JF

12 Current ratio currat Ou & Penman 1989, JAE

13 % change in current ratio pchcurrat Ou & Penman 1989, JAE

14 Quick ratio quick Ou & Penman 1989, JAE

15 % change in quick ratio pchquick Ou & Penman 1989, JAE

16 Sales-to-cash salecash Ou & Penman 1989, JAE

17 Sales-to-receivables salerec Ou & Penman 1989, JAE

18 Sales-to-inventory saleinv Ou & Penman 1989, JAE

19 % change in sales-to-inventory pchsaleinv Ou & Penman 1989, JAE

20 Cash flow-to-debt cashdebt Ou & Penman 1989, JAE

21 Illiquidity (bid-ask spread) baspread Amihud & Mendelson 1989, JF

22 1-month momentum mom1m Jegadeesh 1990, JF

23 6-month momentum mom6m Jegadeesh & Titman 1990, JF

24 12-month momentum mom12m Jegadeesh 1990, JF

25 Depreciation-to-gross PP&E depr Holthausen & Larcker 1992, JAE

26 % change in depreciation-to-gross PP&E pchdepr Holthausen & Larcker 1992, JAE

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Table 1 (excerpt)

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# RPS Acronym Author(s) Date, Journal

75 Change in # analysts chnanalyst Scherbina 2007, WP

76 Asset growth agr Cooper, Gulen & Schill 2008, JF

77 Change in shares outstanding chcsho Pontiff & Woodgate 2008, JF

78 Industry-adjusted change in profit margin chpmia Soliman 2008, TAR

79 Industry-adjusted change in asset turnover chatoia Soliman 2008, TAR

80 3-day return around earnings

announcement

ear Kishore, Brandt, Santa-Clara & Venkatachalam 2008, WP

81 Revenue surprise rsup Kama 2009, JBFA

82 Cash flow volatility stdcf Huang 2009, JEF

83 Debt capacity-to-firm tangibility tang Hahn & Lee 2009, JF

84 Sin stock sin Hong & Kacperczyk 2009, JFE

85 Employee growth rate hire Bazdresch, Belo & Lin 2009, WP

86 Cash productivity cashpr Chandrashekar & Rao 2009, WP

87 ROA roaq Balakrishnan, Bartov & Faurel 2010, JAE

88 CAPEX and inventory invest Chen & Zhang 2010, JF

89 Real estate holdings realestate Tuzel 2010, RFS

90 Absolute accruals absacc Bandyopadhyay, Huang & Wirjanto 2010, WP

91 Accrual volatility stdacc Bandyopadhyay, Huang & Wirjanto 2010, WP

92 Change in tax expense chtx Thomas & Zhang 2010, WP

93 Maximum daily return in prior month maxret Bali, Cakici & Whitelaw 2011, JFE

94 Percent accruals pctacc Hafzalla, Lundholm & Van Winkle 2011, TAR

95 Cash holdings cash Palazzo 2012, JFE

96 Gross profitability gma Novy-Marx 2012, WP

97 Organizational capital orgcap Eisfeldt & Papanikolaou 2013, JF

98 Secured debt-to-total debt secured Valta 2013, WP

99 Secured debt indicator securedind Valta 2013, WP

100 Convertible debt indicator convind Valta 2013, WP

Table 2 (excerpt)

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# Acronym RPS definition (annual figures are for most recent fiscal year prior to signal date)

1 beta Beta estimated from 3 years of weekly firm and EW market returns ending month t-1 (with at least 52 weeks of returns

available).

2 betasq Beta squared.

3 ep Annual income before extraordinary items (ib) divided by market cap at end of prior fiscal year.

4 mve Natural log of market cap at month-end immediately prior to signal date (prc*shrout).

5 dy Total dividends (dvt) divided by market cap at fiscal year end.

6 sue Unexpected quarterly earnings divided by market cap at end of most recent fiscal quarter. Unexpected earnings is IBES

actual earnings minus median forecasted earnings if available; else unexpected earnings is the seasonally differenced

quarterly earnings before extraordinary items from Compustat quarterly file.

7 chfeps Mean analyst forecast of annual EPS in month prior to fiscal period end date from IBES summary file minus same mean

forecast for prior fiscal period.

8 bm Book value of equity (ceq) divided by end of fiscal year end market cap.

9 mom36m 24-month cumulative return ending month t-13.

10 fgr5yr Most recently available analyst forecasted 5-year growth.

11 lev Total liabilities (lt) divided by fiscal year end market cap.

12 currat Current assets (act) divided by current liabilities (lct).

13 pchcurrat % change in currat.

14 quick Current assets (act) minus inventory (invt), divided by current liabilities (lct).

15 pchquick % change in quick.

16 salecash Annual sales (sale) divided by cash and cash equivalents (che).

17 salerec Annual sales (sale) divided by accounts receivable (rect).

18 saleinv Annual sales (sale) divided by total inventory (invt).

19 pchsaleinv % change in saleinv.

20 cashdebt Earnings before depreciation and extraordinary items (ib+dp) divided by avg total liabilities (lt).

21 baspread Monthly avg of daily bid-ask spread divided by avg of daily bid-ask spread.

22 mom1m Return in month t-1.

23 mom6m 5-month cumulative return ending month t-2.

24 mom12m 11-month cumulative returns ending month t-2.

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Table 4

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Panel A: Distribution of variance inflation factors (VIFs) from pooled time-series

cross-sectional regressions of 1-month ahead stock returns on 100 or 93 RPS

Before

removing

RPS with

VIF > 5

After

removing

RPS with

VIF > 5

# RPS 100 93

Min. 1.0 1.0

Median 1.2 1.1

Mean 3.4 1.3

max. 58.0 4.0

# VIFs > 5 14 0

• betasq • chempia

• currat • stdacc

• pchcurrat • maxret

• mom6m

RPS removed in reducing the

set of 100 RPS to 93 RPS

Panel B: Percentiles of absolute values of cross-correlations

Min.

1st

pctile

25th

pctile Median Mean

75th

pctile

99th

pctile Max.

0.00 0.00 0.00 0.01 0.03 0.03 0.29 0.99

0.00 0.00 0.00 0.01 0.03 0.03 0.27 0.68

N = 100 RPS

N = 93 RPS

Panel B: Percentiles of absolute values of cross-correlations

● Our main design choices are robust, in that in untabulated results, we observe that our general inferences about the multidimensionality of returns are unchanged if we instead use:

● Raw or standardized/normalized RPS ● Winsorized RPS ● Ranking based on all firms combined rather

than separately by size ● WLS vs. OLS ● Not infilling missing observations

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Main design choices (cont’d)

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● Conventional time-series of cross-sectional regns.

● We use three future return horizons that differ in how long they cumulate returns over, and how far ahead of the RPS measurement date they are when they begin to cumulate their returns.

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Fama-MacBeth (1973) regressions

1-month

ahead

returns

13-36 month

ahead returns

Date RPS is

measured

2-12 months

ahead returns

● We use scaled decile ranks approach to defining RPS where each monthly re-measured RPS [0, 1]:

● SDR reduces the effects of outliers.

● SDR coefficients are returns to linear, optimal, pre-transactions costs, dollar-neutral hedge portfolios that are orthogonal to all other independent variables in the regression (Fama, 1976; Abarbanell & Bushee, 1998).

● We term the mean annualized long/short coefficient return estimates as ‘MALSRets’.

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Scaled decile ranked RPS

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● We use 3.0 as cutoff for inferring stat. significance.

● Harvey, Liu & Zhu (2013) criticize 1.96 RPS t-stat cutoff because it fails to take data snooping & data mining biases into account.

● “Whether suggested by theory or empirical work, a t-ratio of 2.0 is too low” (HLZ p. 2).

● “We argue that a newly discovered factor today should have a t-ratio that exceeds 3.0”

● Our use of 3.0 also means we don’t really have to adjust for expected number of significant coefs.

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abs{t-stat} 3.0 cutoff

Table 5. FF92 + mom12m (1980-2012)

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Panel A: 1 month ahead returns (396 non-overlapping monthly regressions)

RPS Pred. sign MALSRet t-stat.

mve - -3.8% -0.9

bm + 13.4% 3.5

mom12m + 6.1% 5.6

All firms

5,018

1.5%

Mean # obs. per regression Mean adjusted R2

RPS Pred. sign MALSRet t-stat. MALSRet t-stat. MALSRet t-stat.

mve - -1.1% -0.7 2.5% 1.5 -13.3% -3.9

bm + 4.2% 1.1 11.9% 2.8 14.1% 3.5

mom12m + 6.3% 4.4 6.8% 5.9 4.5% 3.3

Large-Cap Mid-Cap Small-Cap

996 1,997 2,019

0.7%2.3% 1.5%

Mean # obs. per regression Mean adjusted R2

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Table 6 unidim vs. multidim (partial view)

RPS Pred. sign MALSRet t-stat. MALSRet t-stat. MALSRet t-stat. MALSRet t-stat.

1 beta + -3.9% -0.8 0.1% 0.1 -6.8% -1.7 -1.2% -0.6

2 betasq + -4.1% -0.8 -7.0% -1.8

3 ep + 6.6% 1.2 6.4% 4.3 9.8% 2.8 2.6% 1.2

4 mve - -6.8% -1.8 12.1% 3.8 1.5% 0.5 6.8% 7.3

5 dy + 0.9% 0.2 -2.6% -2.6 5.3% 1.2 -1.5% -1.8

6 sue + 18.4% 12.1 10.2% 13.2 1.1% 0.6 2.4% 3.2

7 chfeps + 10.8% 3.6 2.4% 1.2 0.2% 0.1 2.4% 0.6

8 bm + 15.1% 4.6 10.8% 5.4 11.3% 2.9 9.9% 4.7

9 mom36m - 8.7% 5.2 0.8% 1.9 -2.3% -1.8 -0.6% -1.2

10 fgr5yr - -0.9% -0.2 -4.2% -4.1 -1.0% -0.5 0.2% 0.9

11 lev + 6.6% 1.6 7.1% 3.3 7.1% 1.7 7.3% 4.9

All firms, 13-36 month ahead returns

Unidimensional MultidimensionalUnidimensional Multidimensional

All firms, 1 month ahead returns

# abs{t-stat} 1.96 48 47

37 26# abs{t-stat} 3.0 9 8

27 21

RPS Pred. sign MALSRet t-stat. MALSRet t-stat. MALSRet t-stat. MALSRet t-stat.

90 absacc - -0.6% -0.2 -2.1% -2.5 -4.4% -2.8 -0.8% -0.5

91 stdacc - -8.1% -3.0 -7.8% -4.2

92 chtx + 12.5% 9.7 3.3% 4.0 1.4% 1.0 1.0% 2.1

93 maxret - -8.8% -1.8 -6.4% -2.2

94 pctacc - -5.8% -3.3 -2.2% -1.5 -5.3% -5.5 -1.4% -1.9

95 cash + 5.1% 1.3 3.8% 3.5 -0.8% -0.3 1.8% 1.1

96 gma + 4.3% 2.5 2.4% 1.2 3.4% 2.6 -0.7% -0.4

97 orgcap + 8.7% 3.0 3.4% 2.2 3.2% 1.3 3.0% 1.5

98 secured + 1.6% 0.5 0.1% 0.0 0.9% 0.5 3.2% 1.6

99 securedind + 0.6% 0.3 0.9% 0.8 0.8% 1.1 -0.1% -0.2

100 convind + -5.0% -4.1 -3.1% -5.0 -2.7% -2.8 -1.4% -1.6

All firms, 13-36 month ahead returns

Unidimensional MultidimensionalUnidimensional Multidimensional


# abs{t-stat} 1.96 48 47

37 26

Mean # obs. per regression

Mean adjusted R2

Sharpe ratio on portfolio of RPS with abs{t-stat} 3

# abs{t-stat} 3.0

2.98 2.03

6,362

7.4%

5,035

0.4%

4,930

6.5%

9 8

5,048

0.4%

27 21

Table 6 unidim vs. multidim (partial view)

20

● Our missing value data resets add noise.

● Our RPS missing value resets add noise.

● We use mixture of pre- and post-publication data.

● Our monthly RPS remeasurement choice often distances us from methods in originating papers.

● Ditto for calendar alignment and return holding period.

● We use scaled decile ranked RPS, not unscaled RPS, or just extreme top/bottom RPS deciles.

39

We think 26 multidimensionally priced RPS is likely an underestimate:

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Multidim pricing of famous RPS

RPS Pred. sign MALSRet t-stat. MALSRet t-stat.

1 beta + -3.9% -0.8 0.1% 0.1

3 ep + 6.6% 1.2 6.4% 4.3

4 mve - -6.8% -1.8 12.1% 3.8

6 sue + 18.4% 12.1 10.2% 13.2

7 chfeps + 10.8% 3.6 2.4% 1.2

8 bm + 15.1% 4.6 10.8% 5.4

9 mom36m - 8.7% 5.2 0.8% 1.9

11 lev + 6.6% 1.6 7.1% 3.3

22 mom1m - 4.2% 4.5 -1.4% -3.7

23 mom6m + 8.6% 5.4

24 mom12m + 9.8% 6.0 0.7% 1.5

36 acc - -8.0% -4.1 -3.3% -2.8

37 turn + 21.9% 9.1 25.2% 11.1

44 indmom + 25.8% 7.3 7.2% 6.0

45 ps + 5.6% 2.5 -1.3% -1.6

46 dolvol - 1.0% 1.5 -10.0% -10.1

49 sfe + -6.0% -1.4 -16.1% -8.6

68 retvol - -5.8% -1.1 -13.9% -6.7

74 aeavol + 7.7% 6.2 3.3% 6.1

76 agr - -15.8% -5.9 -6.9% -4.2

80 ear + 16.5% 16.6 9.4% 13.8

87 roaq + 13.6% 3.3 10.8% 7.7

100 convind + -5.0% -4.1 -3.1% -5.0

Unidimensional Multidimensional


21

41

Top 10 t-stats (1-month ahead returns)

# RPS Pred. sign MALSRet t-stat. MALSRet t-stat.

1 ear + 16.5% 16.6 9.4% 13.8

2 sue + 18.4% 12.1 10.2% 13.2

3 turn + 21.9% 9.1 25.2% 11.1

4 dolvol - 1.0% 1.5 -10.0% -10.1

5 sfe + -6.0% -1.4 -16.1% -8.6

6 roaq + 13.6% 3.3 10.8% 7.7

7 rsup + 7.9% 3.5 7.4% 7.5

8 retvol - -5.8% -1.1 -13.9% -6.7

9 aeavol + 7.7% 6.2 3.3% 6.1

10 saleinv + 3.1% 2.2 5.4% 5.1

11 bm + 15.1% 4.6 10.8% 5.4

20 mve - -6.8% -1.8 12.1% 3.8

56 mom12m + 9.8% 6.0 0.8% 1.9

Unidimensional Multidimensional

All firms, 1 month ahead returns10 largest multidimensional t-stats

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Table 7 – Additional multidim results

RET horizon 1980-2012 1980-1989 1990-1999 2000-2012

1 month 47, 26 24, 15 32, 19 36, 22

Estimation decade

Panel A: By decade: Number of multidimensional RPS abs{t-stat} 3.0, 1.96

Panel D: By firm size: Mean FM multidimensional RPS regression adj. R 2

RET horizon All firms Large-Cap Mid-Cap Small-Cap

1 month 6.5% 16.8% 8.7% 4.4%

2-12 months 9.0% 21.0% 12.6% 7.1%

13-36 months 7.4% 16.5% 10.4% 4.2%

Panel C: By firm size: Number of multidimensional RPS abs{t-stat} 3.0, 1.96

RET horizon All firms Large-Cap Mid-Cap Small-Cap

1 month 47, 26 16, 5 35, 17 34, 21

2-12 months 30, 13 13, 5 23, 6 22, 4

13-36 months 21, 8 15, 4 23, 11 18, 5

22

Fig. 2A – MALSRet attenuation Multidim = 0.34 x unidim

43

Unidimensional MALSRet

Multidimensional MALSRet

44

-15

-10

-5

0

5

10

15

-10 -5 0 5 10 15 20

1-month ahead returns 2-12 month ahead returns 13-36 months ahead returns

Fig. 2A – t-stat{MALSRet} attenuation Multidim = [0.59, 0.38] x unidim

Multidimensional t-stat{MALSRet}

Unidimensional t-stat{MALSRet}

23

45

Fig. 3 – MALSRet attenuation by pub Post-pub = 0.72 x pre-pub Post-pub = 0.63 x pre-pub

● A hard nut to crack – we offer one perspective.

● We hypothesize that mispricing is more likely to manifest in short-length near-term returns, while the rational pricing of economic risks is more likely to be seen in longer-length further-away returns.

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What might multidimensionality say about rational pricing vs. mispricing?

1-month

ahead

returns

13-36 month

ahead returns

Date RPS is

measured

2-12 months

ahead returns

24

Table 9 – Our estimation of the RPS that likely capture economic risks vs.

RPS that likely reflect mispricing

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Rational pricing of economic risks Mispricing

sue #6 pchcapx_ia #40 dy #5 turn #37 fgr5yr #10 chfeps #7

bm #8 ill #62 ep #3 dolvol #46 mom1m #22 pchsaleinv #19

lev #11 mve #4 saleinv #18 aeavol #74 nincr #43 mve_ia #27

sfe #49 agr #76 indmom #44 nanalyst #50

retvol #68 ear #80 std_dolvol #47 tb #57

rsup #81 std_turn #48 lgr #60

roaq #87 idiovol #53 ms #64

convind #100 zerotrade #71 stdcf #82

chtx #92 absacc #90

cash #95

MispricingRational pricing of economic risks

Next most likely Most likelyMost likely Next most likely Next most likely Next most likely

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Implications that we see

1. The 26-dimensionality of U.S. stock returns is likely understated, not overstated.

2. Controlling for only firm size, book-to-market and 12-month mom is low powered, maybe also biased.

3. NPV of investing in understanding why returns are so multidimensional >> NPV of finding another RPS.

4. How much the estimation of dimensionality has changed over 20+ years means that it is reasonable to take the inferences/conclusions of our study, and future studies, more cautiously than ever.

25

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Conclusions & future work

We are the first to state that our paper raises more questions than it answers. For example:

Why are returns so multidimensional?

Exactly which RPS reflect rational economic pricing, and which reflect mispricing, and why?

If there really are close to 20 RPS that each reflects mispricing, where does such diverse mispricing come from in the first place?

Do multidimensioned factors work better or worse than RPS?

Do U.S. multidimensioned RPS price outside U.S. and non-equity?

How well do multidimensioned RPS explain the cross-section of higher moments of returns, and why?

Do our results mean that equity portfolio managers have been mis-evaluated over the past 30 years?

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This concludes my talk. Thank you for inviting me.

I look forward to hearing your views.

Documents

SQA Nov. 15 , 2013 GOALS OF MY TALK