Jie Zhang, HKPU

Forecasted Earnings per Share and the Cross Section of

Expected Returns

Ling CenK.C. John Wei

Hong Kong University of Science and TechnologyJie Zhang

The Hong Kong Polytechnic University

Jie Zhang, HKPU 2

Outline

Major Findings Motivations Data and Sample Empirical Results Potential Explanations

Risk vs. Mispricing Conclusions and Contributions

Jie Zhang, HKPU 3

Major Findings

This paper finds a surprisingly strong positive relation between the levels of analysts’ forecasted earnings per share (FEPS) and future stock returns

The FEPS anomaly survives a number of well-known cross-sectional effects, such as the size, value and earnings-to-price effects, and price and earnings momentum

Jie Zhang, HKPU 4

Motivations

Cross-sectional behavior of stock returns Related to market beta or systematic risk

CAPM --- Sharpe (1964); Lintner (1965) ICAPM --- Merton (1973) CCAPM --- Lucas (1978) etc.

Asset-pricing anomalies --- FF (1992, 1996) Value strategies based on E/P, C/P, B/M etc. Long-term contrarian and medium-term momentum

Fama’s (1976) joint hypothesis problem

Jie Zhang, HKPU 5

Motivations(continued)

Why asset-pricing anomalies are interesting? Because they help us to understand more deeply about risk and return! To identify unknown risk factors

e.g. liquidity risk or volatility risk To understand market efficiency

e.g. market friction, limits of arbitrage

Jie Zhang, HKPU 6

Motivations(continued)

The role of FEPS in predicting future returns Prior empirical studies investigating the

information content of earnings focus mainly on earnings surprises

The return predictability based on either EPS or FEPS per se is ignored

Jie Zhang, HKPU 7

Data and Sample

The basic sample: all NYSE, AMEX and Nasdaq-listed common stocks in the intersection of (a) the CRSP stock file, (b) the merged Compustat annual industrial file, and (c) the I/B/E/S unadjusted summary historical file

Sample period: Jan. 1983 – Dec. 2004 Criteria for each month-stock:

Sufficient data on price, size, B/M, return (including past six months), and FEPS

Price higher than $5 Positive Book value

Jie Zhang, HKPU 8

Data and Sample(continued)

712,563 stock-month observations, or an average of 2,699 stocks per month

Summary statistics (Table I) FEPS is highly correlated with Price, FE/P, and BPS

Jie Zhang, HKPU 9

Table I: Summary Statistics

Jie Zhang, HKPU 10

Empirical Results

Trading strategies based on FEPS 10 FEPS-sorted decile portfolios (Table II)

Future stock returns increase across deciles as FEPS increases

The profits mainly come from the short side High FEPS firms are large in size, high price,

greater analyst coverage, higher FE/P, higher FROE => less risky

FEPS is not related to B/M or past returns

Jie Zhang, HKPU 11

Table II: Portfolio Characteristics for Equally Weighted Forecasted Earnings Per Share Deciles

Jie Zhang, HKPU 12

Empirical Results(continued)

Trading strategies based on FEPS Cumulative returns to the FEPS anomaly

(Figure 1) Accumulated at a diminishing speed Not reversal up to 36 months

Monthly returns for different holding periods (Figure 2A&B) The abnormal return spreads disappear after 6

months

Jie Zhang, HKPU 13

Figure 1: Cumulative Returns to a Hedge Strategy of Buying the Highest FEPS Stocks and Selling the lowest FEPS Stocks

0%

5%

10%

15%

20%

25%

30%

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Holding Period (in Month)

Cu

mu

lati

ve H

edge

Por

tfol

io R

etu

rns

(in

%)

Jie Zhang, HKPU 14

Figure 2A: Raw Monthly Returns to a Hedge Strategy of Buying the Highest FEPS Stocks and Selling the Lowest FEPS Stocks for Different Holding Periods

-0.5

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10 11 12

Hodling Period (in Month)

Raw

Mon

thly

Hed

ge P

ortf

olio

Ret

urns

(in

%)

Jie Zhang, HKPU 15

Figure 2B: Risk-Adjusted Monthly Returns to a Hedge Strategy of Buying the Highest FEPS Stocks and Selling the Lowest FEPS Stocks for Different Holding Periods

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10 11 12

Hodling Period (in Month)

Ris

k-A

dju

sted

Mon

thly

Hed

ge P

ortf

olio

Ret

urn

s(i

n %

)

Jie Zhang, HKPU 16

Empirical Results(continued)

Trading strategies based on FEPS FEPS strategies within five Size groups (Table IV) FEPS strategies within five Price groups (Table V) Overall, the abnormal returns to FEPS strategies are

robust after controlling for firm size, stock price (and analyst coverage)

The FEPS anomaly is greatest in stocks with small firm size, low price (and low analyst coverage)

Jie Zhang, HKPU 17

Table IV: Mean Portfolio Returns by Size and Forecasted Earnings Per Share

Jie Zhang, HKPU 18

Table V: Mean Portfolio Returns by Price and Forecasted Earnings Per Share

Jie Zhang, HKPU 19

Empirical Results(continued)

Trading strategies based on FEPS FEPS Strategies within 3×3 Size and Book-to-

Market Groups (Table VI) FEPS Strategies within 3×3 Size and

Momentum Groups (Table VII) The FEPS anomaly survives the book-to-

market effect and the price momentum The FEPS anomaly decreases with past

returns

Jie Zhang, HKPU 20

Table VI: Mean Portfolio Returns by Size, Book-to-Market, and Forecasted Earnings Per Share

Jie Zhang, HKPU 21

Table VII: Mean Portfolio Returns by Size, Momentum, and Forecasted Earnings Per Share

Jie Zhang, HKPU 22

Empirical Results(continued)

Regression tests Time-series regressions (Table III)

Risk-adjusted returns (Alpha) increase across FEPS decile portfolios as FEPS increases

Mixed risk profile The highest FEPS stocks behave like big, value stocks The lowest FEPS stocks behave like small, growth and loser

stocks

Fama-Macbeth cross-sectional regressions (Table IX) None of identified cross-sectional effects in returns captures

the FEPS effect Not driven by specific industries

Jie Zhang, HKPU 23

Table III: Time-Series Tests of Four-Factor Models for Equally Weighted Forecasted Earnings Per Share Deciles

Jie Zhang, HKPU 24

Table IX: Fama-MacBeth Regressions: Explaining the Cross-Section of Individual Stock Returns

Jie Zhang, HKPU 25

Empirical Results(continued)

Evidence on mispricing (Table VIII) Larger analyst forecast errors for low FEPS

stocks relative to high FEPS stocks Subsequent earnings surprises explain a

substantial proportion of the abnormal returns to FEPS strategies

Jie Zhang, HKPU 26

Table VIII: Forecast Errors and Earnings Surprises for Portfolios Classified by Size and Forecasted Earnings Per Share

Jie Zhang, HKPU 27

Empirical Results(continued)

Robustness checks Seasonality and subperiod analysis (Table X)

Similar January effect with momentum Countercyclical

Various measures of earnings Historical EPS; Time-weighted average of

forecasted EPS from the IBES detail file (similar results!)

total earnings (much weak!) Outliers? (No)

Jie Zhang, HKPU 28

Table X: Seasonality and Subperiod Analysis for Equally Weighted Forecasted Earnings Per Share Deciles

Jie Zhang, HKPU 29

Potential Explanations

Risk? Not easy to reconcile the FEPS anomaly with

an existing risk framework Firm characteristics Four-factor model Time-series pattern of the FEPS anomaly

However, strictly speaking, we cannot rule out the possibility that there is some unknown risk factor.

Jie Zhang, HKPU 30

Potential Explanations(continued)

Mispricing? The FEPS anomaly might capture systematic

errors-in-expectations of investors on EPS Ex ante forecast errors, i.e. (FEPS – Actual)/|Actual| Abnormal returns around future earnings

announcements Two key prerequisites

Psychological behavior of investors Limits of arbitrage

Jie Zhang, HKPU 31

Conclusions

Forecasted earnings per share (FEPS) has strong predictive power on future stock returns.

In particular, stocks with higher FEPS earn substantially higher future returns than stocks with lower FEPS, even after controlling for the market risk, the size, value, and earnings-to-price effects, and price and earnings momentum.

Time-series and cross-sectional patterns of the FEPS anomaly, as well as further evidence on forecast errors and abnormal returns around future earnings announcements supports the errors-in-expectations explanation that investors overvalue (undervalue) stocks when their expectations about EPS are low (high).

Jie Zhang, HKPU 32

Contributions of This Paper

This paper documents a novel asset-pricing anomaly that can be predicted by FEPS

This paper would open up a new field for scholars to study unknown risk factors and market efficiency