long-term return reversal: overreaction or taxes?

Long-Term Return Reversal:Overreaction or Taxes?

Thomas J. George

University of Houston

and

Chuan-Yang Hwang

Hong Kong University of Science and Technology

The Empirical Cornerstones of Behavioral Finance

•Jegadeesh and Titman (1993) show that A self-financing strategy that buys the top 10% and sells the bottom 10% of stocks ranked by returns during the past 6 months, and holds the positions for 6 months, produces profits of 1% per month.

•DeBondt and Thaler (1985) document long-term reversals in stock returns. Stocks that perform poorly in the past perform better over the next 3 to 5 years than stocks that perform well in the past.

Behavior Models

•Barberis, Shleifer and Vishny (1998)

momentum occurs because traders are slow to revise their priors when new information arrive---cognitive bias. Long-term reversals occur because when traders finally do adjust, they over-react. •Daniel, Hirshleifer and Subrahmanyam (1998)

momentum occurs because traders over-react to prior information when new information confirms it---self attribution bias. Long-term reversals occur as the over-reaction is corrected in the long run.

Behavior Models (Cont’d)

•Hong and Stein (1999)

There are two type of traders: fundamental analysts and trend chasers. Information diffuses slowly which results in momentum. Trend chasers push prices beyond the level justified by the fundamentals.

•These models links short term momentum with long term reversal.

•Short run momentum and long term reversal are viewed as the same phenomenon in the literature.

Recent Findings

• Moskowitz and Grinblatt (1999) argue that momentum in individual stock returns is driven by momentum in industry returns.

• Grundy and Martin (2001) show that neither industry effect nor cross-sectional difference in the expected returns are the primary source of momentum profit.

• Cooper, Gutierrez and Hameed (2004)Test Daniel, Hirshleifer and Subrahmanyam and find that momentum profits are larger following an UP market.

• Lee and Swaminathan (2000) propose a “momentum life cycle” hypothesis and show that winners with high volume and losers with low volume have smaller momentum and will reverse sooner.

A Common Conception • Short-term momentum and long-term reversal are

connected.

• They are a sequence of the same phenomenon.

Recent Findings (continued)• George and Hwang (2004)

52-week high measure-- A measure that gauges how close a stock’s current price is near its 52 week high.

• This measure strongly dominates all of the existing measures in predicting momentum.

• Propose adjustment and anchoring bias as the explanation. • The momentum captured by 52-week high measure does not

reverse.• This indicates momentum and reversal in returns are separate

phenomena.

Gorge and Hwang (2004)

Raw Returns Risk Adjusted Returns

Raw Returns Risk Adjusted Returns

Monthly return to (6,6) strategy




Jan. Incl. Jan.Excl. Jan. Incl. Jan.Excl. Jan. Incl. Jan. Excl. Jan. Incl. Jan. Excl. 52–Wk High Momentum

0.65 (4.08)

1.06 (7.64)

0.86 (7.29)

1.13 (11.35)

0.39 (2.63)

0.78 (6.14)

0.60 (5.61)

0.85 (9.73)

JT 6-month Return Momentum

0.38 (3.71)

0.46 (4.39)

0.38 (4.02)

0.46 (5.13)

0.24 (2.74)

0.29 (3.25)

0.27 (3.77)

0.32 (4.65)

MG 6-month Industry Momentum

0.25 (2.83)

0.22 (2.45)

0.25 (2.92)

0.24 (2.72)

0.17 (2.23)

0.15 (1.81)

0.22 (3.11)

0.20 (2.66)

Monthly return to (6,~12,12)strategy




Jan. Incl. Jan. Excl. Jan. Incl. Jan. Excl. Jan. Incl. Jan. Excl. Jan. Incl. Jan. Excl 52–Wk High Momentum

-0.02 (-0.23)

0.16 (1.93)

-0.06 (-0.70)

0.08 (1.00)

-0.07 (-0.82)

0.04 (0.60)

-0.01 (-0.15)

0.07 (1.11)

JT 6-month Return Momentum

-0.13 (-2.65)

-0.12 (-2.66)

-0.06 (-1.24)

-0.07 (-1.62)

-0.05 (-1.29)

-0.08 (-1.85)

-0.10 (-2.20)

-0.14 (-3.16)

MG 6-month Industry Momentum

-0.08 (-1.33)

-0.11 (-1.91)

0.02 (0.45)

0.01 (0.16)

0.04 (0.91)

0.02 (0.39)

0.09 (1.76)

0.08 (1.54)

An Open Question

• If momentum and reversal in returns are separate phenomena and if momentum can indeed be explained by anchoring bias, how do we explain the long term reversal?

What Explain the Long Term Return Reversal

In this paper, we examine two possible

explanations:

1. Overreaction

2. Capital gain lock in effect

Evidences are more consistent with lock in effect.

Overreaction • Stocks which are close to long term low should

rebound– The loser classification based on the nearness

to 60-month low is better in predicting the loser reversal than what is based on the traditional measure such as past 60 month return.

• Stocks which are close to long term high should head south

– The winner classification based on the nearness to 60-month high is better in predicting the winner reversal than what is based on the traditional measure such as past 60 month return.

Why Are 60-month High/Low Better Measures Than Past Return?

•When a stock is near it 60-month high/low, it signals the information has just arrived and overreaction may have occurred as implied by the models.

•Flexible length window vs. fixed length window

Why Are 60-month High/Low Better Measures Than Past Return? (Cont’d)

• Example: Stock price was $30 five years ago and was also $30 two years ago, since then a stream of good news have pushed the stock to reach its 60-month high of $70 one year ago (with overreaction of $10.) The current price is $60.

• With fixed window, this stock is still classified as a winner (with past five year return of $100%.) even though the reversal process has been complete.

Why Are 60-month High/Low Better Measures Than Past Return? (Cont’d)

• Another example: Stock price was $30 five years ago fell to $10 two years ago and is now $35 due to overreaction to a series of good information (under the overreaction hypothesis).

• With fixed window, this stock is not classified as a candidate for reversal since the five-year return is “small”

• With flexible window, the current price is near its 60 month high and is correctly identified as the candidate for overreaction

Capital Gain Lock- in Hypothesis

• Klein (1998, 1999, 2001) presents a model in which stocks with higher accrued capital gain will have lower future pre-tax return; this result implies a slowly dissipating return reversal.

– The reservation price for a seller of high accrual capital gain is higher than the “fundamental price” by the amount of the benefit of deferral.

Capital Gain Lock-in Hypothesis (Cont’d)

– The benefit of deferral depends positively on the capital gain, tax rate as well as the expected horizon of holding the stock which is in turn increases with the accrued capital gain.

– The magnitude of the deferral benefit is only part of the accrued gain. Thus, there will still be an accrued capital gain hence benefit of deferral in the stock price next period. This explains why the reversal is slowly dissipating

Capital Gain Lock-in Hypothesis (Cont’d)

• In this paper, we recognize the asymmetric nature of the lock-in effect associated with capital gain and capital loss.

– The lock in effect of capital gain (loss) increases (decreases) the reservation price for the seller. However in the case of capital loss, the “fundamental price” is higher than seller’s reservation price. As long as there are buyers willing to buy the stocks at the “fundamental price”, the lock in effect of the capital loss would be minimal. Out tests of the lock-in effect are built around this observation.

Data and Methodology

• Monthly data for all NYSE, AMEX and NASDAQ firms covered by CRSP from 1962 through 2001.

• HKSE monthly data from 1980 through 2000

Data and Methodology (cont’d)

One innovation in our methodology is to estimate winner and loser portfolio returns via the following regression.

, 0 1 , 1 2 , 1 3 , 4 ,

5 , 6 , 7 , 8 ,

52 52

1 1 2 2

i t jt jt i t jt i t jt i t j jt i t j

jt i t j jt i t j jt i t j jt i t j

R b b R b size b wkhW b wkhL

b M W b M L b M W b M L

According to Fama(1976), these coefficients are the minimum variance portfolio return

0 jtb is the month t return a “neutral” portfolio that was

formed in month t-j and has hedged (zeroed out) the effects

of size, bid-ask bounce and momentum, as well as the effects

of measure 1 and 2 dummies.

b5jt can be viewed as the return in excess of b0jt earned by

taking a long position j months ago in a “pure” measure-1

winner portfolio.

Data and Methodology (Cont’d)

, 0 1 , 1 2 , 1 3 , 4 ,

5 , 6 , 7 , 8 ,

52 52

1 1 2 2

i t jt jt i t jt i t jt i t j jt i t j

jt i t j jt i t j jt i t j jt i t j

R b b R b size b wkhW b wkhL

b M W b M L b M W b M L

A strategy to buy Measure-1 winner portfolio every months and hold on to it for T months will generate the following portfolio return in month t.

5 51

1 T

t jtj

S bT

Unlike traditional approach which uses only winner (losers) stocks to estimate winner (loser) portfolio returns, we use all stocks.

Our methodology allows us to control for other effects.


With a 60 month price history Pt-1, Pt-2,…, Pt-60 We construct the

following measures to classify stocks into winners and losers.

1. Traditional Return Measure (TR): Past five-year return:

60

60

t t

t

P PP

plus the return from reinvesting dividends.

2. Five-Year High Measure (FYH): This measures the nearness

of the month-t price to the stock’s five-year high:

60

6011

1FYH t t n

t t nt nnt nn

P Pw

Pw

where wt-n = 1 if Pt-n = max{Pt, Pt-1,…, Pt-60} and wt-n = 0

otherwise.


3. Five-year low measure (FYL): This measures

the nearness of the month-t price to the stock’s 5-

year low: 60

6011

1FYL t t n

t t nt nnt nn

P Pw

Pw

where wt-n = 1 if Pt-n = min{Pt, Pt-1,…, Pt-60} and

wt-n = 0 otherwise.

4. Equal-Weighted Gain and Loss Measure

(EWGL): This measures the average embedded

percentage capital gain net of capital losses,

60

1

1EWGL

60t t n

tt nn

P P

P


5. Equal-Weighted Gain Only measure (EWGO):

60

6011

1EWGO t t n

t t nt nnt nn

P Pw

Pw

where wt-n = 1 if Pt > Pt-n and wt-n = 0 otherwise.

This measure employed specifically recognizes the

asymmetry between capital gain and loss, i.e., that

that capital losses do not generate negative deferral

benefits.

Implications of Overreaction Hypothesis

• FYH dominates TR in predicting winner reversal

• FYL dominates TR in predicting loser reversal

Implications of Capital Lock-in Hypothesis

• EWGO dominates TR and FYH in predicting winner reversal.

• FYL dominates TR and FYH in predicting winner reversal.

• EWGO and FYL don’t predict loser reversal.

• No loser reversal except in January due to tax loss selling hypothesis.

Monthly return (1,12)


Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded



Jan. excluded

2.47 0.72 2.02 0.10 2.50 0.47 2.65 0.60 2.66 0.77 Intercept (4.03) (1.34) (3.14) (0.18) (3.79) (0.85) (4.00) (1.10) (4.13) (1.42) -6.82 -5.83 -6.81 -5.65 -6.82 -5.62 -6.73 -5.51 -6.62 -5.43 Ri,t-1

(-15.04) (-14.47) (-13.83) (-13.04) (-13.50) (-12.68) (-13.20) (-12.28) (-12.94) (-12.21) -0.10 0.02 -0.06 0.07 -0.09 0.05 -0.10 0.04 -0.10 0.02 Size

(-2.48) (0.42) (-1.41) (1.86) (-2.05) (1.24) (-2.26) (0.97) (-2.39) (0.60) 0.32 0.43 -0.14 -0.05 -0.08 -0.02 -0.09 -0.06 -0.01 0.05 52-Wk High

Winner (4.76) (6.52) (-2.87) (-1.10) (-1.75) (-0.37) (-2.11) (-1.48) (-0.28) (2.01) -0.40 -0.96 0.19 -0.21 -0.01 -0.28 0.09 -0.16 0.02 -0.34 52-Wk High

Loser (-2.02) (-6.09) (1.21) (-1.64) (-0.04) (-2.03) (0.60) (-1.13) (0.12) (-2.78) -0.33 -0.27 -0.39 -0.42 -0.29 -0.37 -0.17 -0.28 -0.26 -0.32 Five-Year

Return Winner (-2.61) (-2.09) (-3.62) (-3.77) (-2.84) (-3.61) (-1.57) (-2.66) (-2.58) (-3.11) 0.66 0.19 0.43 0.15 0.13 -0.06 0.13 0.02 0.30 0.06 Five-Year

Return Loser (3.99) (1.37) (2.97) (1.13) (1.05) (-0.49) (1.20) (0.19) (2.61) (0.60)

Long Term Reversal with Traditional Measure (10%)



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.

excluded 3.00 1.05 2.78 0.79 2.56 0.56 2.36 0.27 2.63 0.58 Intercept

(4.54) (1.82) (4.17) (1.37) (3.82) (0.98) (3.44) (0.46) (3.88) (1.02) -6.78 -5.79 -6.62 -5.55 -6.73 -5.62 -6.78 -5.58 -6.84 -5.69 Ri,t-1

(-15.35) (-15.16) (-14.32) (-13.91) (-14.06) (-13.49) (-13.57) (-12.80) (-14.00) (-13.56) -0.15 -0.01 -0.12 0.02 -0.10 0.04 -0.09 0.06 -0.11 0.03 Size

(-3.24) (-0.33) (-2.64) (0.46) (-2.23) (0.93) (-1.87) (1.44) (-2.28) (0.87) 0.35 0.46 -0.11 -0.02 -0.08 -0.01 -0.11 -0.07 0.00 0.06 52-Wk High

Winner (5.63) (7.63) (-2.39) (-0.46) (-1.66) (-0.15) (-2.47) (-1.63) (-0.08) (2.20) -0.26 -0.88 0.30 -0.11 0.04 -0.21 0.12 -0.14 0.07 -0.30 52-Wk High

Loser (-1.19) (-5.21) (1.80) (-0.76) (0.27) (-1.43) (0.73) (-0.94) (0.44) (-2.14) -0.42 -0.41 -0.55 -0.60 -0.39 -0.50 -0.25 -0.37 -0.33 -0.43 Five-Year Low

Winner (-2.89) (-2.75) (-4.47) (-4.87) (-3.36) (-4.37) (-2.09) (-3.20) (-2.77) (-3.56) 0.04 -0.13 0.12 0.00 0.09 0.03 0.02 0.03 0.04 -0.01 Five-Year Low

Loser (0.48) (-1.64) (1.59) (-0.01) (1.24) (0.43) (0.26) (0.48) (0.84) (-0.09)

Long Term Reversal with FYL Measure (10%)



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded



Jan. excluded

2.79 1.20 1.99 0.25 2.45 0.55 2.65 0.69 2.69 0.93 Intercept (4.99) (2.43) (3.38) (0.50) (3.97) (1.06) (4.23) (1.36) (4.52) (1.86) -6.93 -5.93 -6.89 -5.71 -6.91 -5.70 -6.80 -5.57 -6.70 -5.49 Ri,t-1

(-15.42) (-14.94) (-13.97) (-13.25) (-13.69) (-12.94) (-13.44) (-12.58) (-13.12) (-12.45) -0.13 -0.02 -0.06 0.06 -0.09 0.04 -0.10 0.03 -0.11 0.01 Size

(-3.25) (-0.52) (-1.47) (1.67) (-2.07) (1.15) (-2.36) (0.86) (-2.59) (0.32) 0.25 0.31 -0.07 -0.01 -0.02 0.02 -0.03 -0.02 0.02 0.06 52-Wk High

Winner (4.58) (5.75) (-1.86) (-0.37) (-0.62) (0.53) (-0.72) (-0.47) (0.90) (2.29) -0.41 -0.74 0.07 -0.20 0.00 -0.20 0.02 -0.15 -0.05 -0.28 52-Wk High

Loser (-3.43) (-7.31) (0.70) (-2.21) (0.01) (-2.06) (0.18) (-1.51) (-0.51) (-3.12) -0.17 -0.13 -0.19 -0.21 -0.13 -0.18 -0.10 -0.17 -0.12 -0.16 Five-Year

Return Winner (-2.19) (-1.66) (-2.74) (-2.99) (-1.92) (-2.71) (-1.49) (-2.55) (-1.97) (-2.54) 0.31 0.07 0.21 0.06 0.12 0.04 0.10 0.06 0.18 0.06 Five-Year

Return Loser (3.32) (0.82) (2.64) (0.83) (1.81) (0.57) (1.75) (0.90) (3.05) (1.14)

Long Term Reversal with Traditional Measure (10%)



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(5.40) (2.82) (4.49) (1.77) (4.06) (1.26) (3.64) (0.68) (4.26) (1.47) -6.94 -5.93 -6.72 -5.64 -6.82 -5.71 -6.87 -5.67 -6.94 -5.79 Ri,t-1

(-15.95) (-15.92) (-14.63) (-14.31) (-14.40) (-13.92) (-13.91) (-13.22) (-14.38) (-14.04) -0.17 -0.05 -0.12 0.01 -0.10 0.03 -0.09 0.05 -0.11 0.02 Size

(-3.95) (-1.19) (-2.77) (0.23) (-2.33) (0.77) (-1.98) (1.32) (-2.51) (0.57) 0.26 0.33 -0.04 0.02 -0.02 0.03 -0.04 -0.02 0.02 0.06 52-Wk High

Winner (4.79) (6.41) (-1.12) (0.51) (-0.49) (0.75) (-0.97) (-0.40) (0.63) (2.10) -0.36 -0.72 0.11 -0.17 0.03 -0.17 0.04 -0.13 -0.03 -0.27 52-Wk High

Loser (-2.74) (-6.51) (1.00) (-1.63) (0.25) (-1.58) (0.39) (1.21) (-0.27) (-2.67) -0.23 -0.22 -0.32 -0.35 -0.21 -0.27 -0.15 -0.23 -0.20 -0.25 Five-year Low

Winner (-2.50) (-2.32) (-4.08) (-4.38) (-3.01) (-3.90) (-2.08) (-3.05) (-2.63) (-3.31) 0.00 -0.06 0.03 -0.01 0.04 0.03 0.04 0.07 0.02 0.01 Five-year Low

Loser (0.03) (-1.02) (0.60) (-0.21) (0.70) (0.47) (0.86) (1.31) (0.32) (0.19)

Long Term Reversal with FYL Measure (30%)



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded



Jan. excluded

2.80 1.35 2.02 0.37 2.45 0.61 2.62 0.70 2.68 0.99 Intercept (5.34) (2.88) (3.58) (0.77) (4.13) (1.23) (4.29) (1.41) (4.70) (2.08) -7.04 -6.05 -6.98 -5.80 -6.99 -5.78 -6.86 -5.63 -6.77 -5.57 Ri,t-1

(-15.83) (-15.39) (-14.32) (-13.64) (-14.00) (-13.31) (-13.64) (-12.80) (-13.40) (-12.78) -0.13 -0.03 -0.06 0.05 -0.09 0.04 -0.10 0.03 -0.11 0.01 Size

(3.50) (-0.96) (-1.59) (1.42) (-2.11) (1.09) (-2.33) (0.90) (-2.67) (0.19) -0.19 -0.18 -0.18 -0.21 -0.10 -0.16 -0.09 -0.16 -0.12 -0.16 Five-Year

Return Winner (-2.44) (-2.17) (-2.52) (-2.92) (-1.45) (-2.20) (-1.27) (-2.22) (-1.75) (-2.37) 0.27 0.15 0.15 0.10 0.06 0.05 0.10 0.09 0.14 0.10 Five-Year

Return Loser (4.35) (2.58) (2.70) (1.85) (1.12) (0.90) (1.87) (1.64) (3.78) (2.69) 0.18 0.21 -0.12 -0.09 -0.03 -0.01 -0.03 -0.02 0.00 0.02 52-Wk High

Winner (3.89) (4.34) (-3.53) (-2.61) (-1.13) (-0.36) (-0.89) (-0.72) (-0.05) (0.87) -0.41 -0.63 0.07 -0.11 0.00 -0.14 0.01 -0.13 -0.06 -0.23 52-Wk High

Loser (-4.51) (-8.51) (1.07) (-1.89) (-0.02) (-1.98) (0.10) (-1.67) (-0.91) (-3.96) 0.16 0.22 0.07 0.11 -0.03 -0.02 -0.01 -0.02 0.04 0.06 Five-Year

High Winner (2.88) (3.95) (1.42) (1.99) (-0.61) (-0.28) (-0.12) (-0.34) (0.87) (1.23) 0.09 -0.20 0.07 -0.17 0.05 -0.12 0.04 -0.07 0.07 -0.11 Five-Year

High Loser (0.79) (-1.90) (0.59) (-1.60) (0.53) (-1.26) (0.50) (-0.75) (0.78) (-1.17)

Test of Overreaction Hypothesis :TR vs. FYH

Test of Overreaction Hypothesis :TR vs. FYL



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(5.14) (2.57) (3.59) (0.70) (4.13) (1.22) (4.34) (1.48) (4.65) (2.00) -7.00 -6.01 -6.99 -5.81 -7.01 -5.81 -6.89 -5.66 -6.78 -5.58 Ri,t-1

(-15.91) (-15.57) (-14.45) (-13.83) (-14.08) (-13.42) (-13.76) (-12.95) (-13.49) (-12.90) -0.13 -0.02 -0.07 0.06 -0.09 0.04 -0.10 0.03 -0.11 0.01 Size

(-3.32) (-0.57) (-1.60) (1.56) (-2.16) (1.09) (-2.41) (0.79) (-2.65) (0.26) -0.08 -0.02 0.00 0.02 -0.01 -0.01 -0.04 -0.03 -0.04 -0.02 Five-Year

Return Winner (-1.71) (-0.49) (-0.01) (0.50) (-0.28) (-0.14) (-0.86) (-0.64) (-1.03) (-0.44) 0.32 0.09 0.19 0.05 0.08 -0.01 0.06 -0.01 0.16 0.03 Five-Year

Return Loser (3.34) (1.00) (2.28) (0.62) (1.08) (-0.16) (1.01) (-0.12) (2.26) (0.42) 0.26 0.33 -0.05 0.01 -0.01 0.03 -0.03 -0.01 0.03 0.07 52-Wk High

Winner (4.91) (6.21) (-1.28) (0.31) (-0.33) (0.83) (-0.75) (-0.35) (0.91) (2.24) -0.40 -0.73 0.07 -0.20 0.00 -0.20 0.02 -0.15 -0.05 -0.27 52-Wk High

Loser (-3.32) (-7.07) (0.64) (-2.16) (-0.02) (-2.03) (0.24) (-1.47) (-0.44) (-2.96) -0.17 -0.19 -0.29 -0.35 -0.17 -0.25 -0.09 -0.18 -0.14 -0.21 Five-Year Low

Winner (-1.69) (-1.88) (-3.25) (-3.86) (-2.10) (-3.06) (-1.01) (-2.11) (-1.67) (-2.51) -0.05 -0.06 -0.01 -0.02 0.01 0.01 -0.01 0.04 -0.02 0.00 Five-Year Low

Loser (-0.77) (-0.82) (-0.21) (-0.34) (0.14) (0.21) (-0.11) (0.67) (-0.38) (0.01)

Test of Capital Gain Lock-in Hypothesis TR vs. FYL



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(5.14) (2.57) (3.59) (0.70) (4.13) (1.22) (4.34) (1.48) (4.65) (2.00) -7.00 -6.01 -6.99 -5.81 -7.01 -5.81 -6.89 -5.66 -6.78 -5.58 Ri,t-1

(-15.91) (-15.57) (-14.45) (-13.83) (-14.08) (-13.42) (-13.76) (-12.95) (-13.49) (-12.90) -0.13 -0.02 -0.07 0.06 -0.09 0.04 -0.10 0.03 -0.11 0.01 Size

(-3.32) (-0.57) (-1.60) (1.56) (-2.16) (1.09) (-2.41) (0.79) (-2.65) (0.26) -0.08 -0.02 0.00 0.02 -0.01 -0.01 -0.04 -0.03 -0.04 -0.02 Five-Year

Return Winner (-1.71) (-0.49) (-0.01) (0.50) (-0.28) (-0.14) (-0.86) (-0.64) (-1.03) (-0.44) 0.32 0.09 0.19 0.05 0.08 -0.01 0.06 -0.01 0.16 0.03 Five-Year

Return Loser (3.34) (1.00) (2.28) (0.62) (1.08) (-0.16) (1.01) (-0.12) (2.26) (0.42) 0.26 0.33 -0.05 0.01 -0.01 0.03 -0.03 -0.01 0.03 0.07 52-Wk High

Winner (4.91) (6.21) (-1.28) (0.31) (-0.33) (0.83) (-0.75) (-0.35) (0.91) (2.24) -0.40 -0.73 0.07 -0.20 0.00 -0.20 0.02 -0.15 -0.05 -0.27 52-Wk High


Winner (-1.69) (-1.88) (-3.25) (-3.86) (-2.10) (-3.06) (-1.01) (-2.11) (-1.67) (-2.51) -0.05 -0.06 -0.01 -0.02 0.01 0.01 -0.01 0.04 -0.02 0.00 Five-Year Low

Loser (-0.77) (-0.82) (-0.21) (-0.34) (0.14) (0.21) (-0.11) (0.67) (-0.38) (0.01)

Test of Capital Gain Lock-in Hypothesis TR vs. EWGO



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(5.08) (2.50) (3.57) (0.68) (4.12) (1.21) (4.32) (1.46) (4.61) (1.96) -7.00 -6.00 -6.98 -5.80 -7.01 -5.80 -6.88 -5.65 -6.78 -5.57 Ri,t-1

(-15.86) (-15.50) (-14.38) (-13.74) (-14.04) (-13.36) (-13.73) (-12.91) (-13.45) (-12.85) -0.13 -0.02 -0.06 0.06 -0.09 0.04 -0.10 0.03 -0.11 0.01 Size

(-3.28) (-0.51) (-1.59) (1.59) (-2.17) (1.08) (-2.39) (0.81) (-2.63) (0.29) -0.11 -0.06 -0.02 -0.01 -0.04 -0.04 -0.05 -0.05 -0.06 -0.04 Five-Year Return

Winner (-2.44) (-1.33) (-0.49) (-0.14) (-0.76) (-0.85) (-1.03) (-1.03) (-1.66) (-1.29) 0.33 0.10 0.21 0.07 0.08 -0.01 0.06 -0.01 0.16 0.04 Five-Year Return

Loser (3.45) (1.13) (2.51) (0.84) (1.08) (-0.15) (0.99) (-0.13) (2.38) (0.54) 0.26 0.33 -0.05 0.01 -0.02 0.03 -0.03 -0.02 0.03 0.07 52-Wk High

Winner (4.94) (6.23) (-1.29) (0.28) (-0.38) (0.81) (-0.87) (-0.43) (0.91) (2.27) -0.41 -0.73 0.07 -0.19 0.00 -0.20 0.03 -0.14 -0.04 -0.27 52-Wk High

Loser (-3.37) (-7.19) (0.70) (-2.13) (0.02) (-2.01) (0.27) (-1.43) (-0.44) (-2.99) -0.13 -0.14 -0.28 -0.32 -0.15 -0.22 -0.08 -0.16 -0.12 -0.18 Equal-Weighted

Gain Winner (-1.39) (-1.46) (-3.56) (-4.09) (-2.11) (-3.05) (-1.06) (-2.19) (-1.74) (-2.55) -0.06 -0.06 -0.05 -0.05 0.01 0.02 -0.01 0.03 -0.03 -0.01 Equal-Weighted

Gain Loser (-0.93) (-0.87) (-0.74) (-0.79) (0.21) (0.29) (-0.22) (0.53) (-0.60) (-0.17)

Test of Capital Gain Lock-in Hypothesis EWGL vs. EWGO



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(5.47) (2.93) (4.52) (1.81) (4.01) (1.17) (3.65) (0.66) (4.45) (1.68) -7.01 -6.01 -6.79 -5.71 -6.88 -5.78 -6.95 -5.75 -7.03 -5.88 Ri,t-1

(-16.18) (-16.13) (-14.80) (-14.50) (-14.56) (-14.07) (-14.11) (-13.46) (-14.60) (-14.29) -0.16 -0.05 -0.11 0.01 -0.10 0.03 -0.09 0.05 -0.11 0.02 Size

(-3.89) (-1.24) (-2.68) (0.30) (-2.21) (0.93) (-1.92) (1.40) (-2.52) (0.54) 0.06 0.18 -0.06 0.00 -0.06 -0.05 -0.05 -0.05 -0.02 0.02 Equal-Weighted

Gain/Loss Winner (1.05) (3.21) (-0.98) (0.02) (-1.25) (-0.98) (-1.14) (-1.10) (-0.52) (0.48) 0.27 -0.01 0.18 -0.02 0.07 -0.05 0.08 0.01 0.15 -0.01 Equal-Weighted

Gain/Loss Loser (2.68) (-0.06) (1.92) (-0.21) (0.92) (-0.61) (1.23) (0.12) (1.94) (-0.13) 0.29 0.33 -0.02 0.02 -0.01 0.03 -0.03 -0.01 0.04 0.07 52-Wk High

Winner (5.99) (6.77) (-0.55) (0.62) (-0.22) (0.91) (-0.79) (-0.29) (1.49) (2.58) -0.44 -0.72 0.06 -0.16 0.00 -0.17 0.01 -0.14 -0.07 -0.27 52-Wk High

Loser (-4.13) (-7.89) (0.69) (-1.98) (-0.03) (-1.85) (0.13) (-1.47) (-0.80) (-3.26) -0.25 -0.34 -0.28 -0.37 -0.17 -0.25 -0.10 -0.18 -0.16 -0.25 Equal-Weighted

Gain Winner (-2.91) (-3.93) (-3.39) (-4.40) (-2.30) (-3.40) (-1.36) (-2.42) (-2.12) (-3.29) -0.07 -0.01 -0.05 -0.01 0.02 0.07 0.02 0.08 -0.04 0.02 Equal-Weighted

Gain Loser (-0.95) (-0.16) (-0.68) (-0.13) (0.34) (0.92) (0.33) (1.16) (-0.61) (0.25)

Test of Capital Gain Lock-in Hypothesis EWGL vs. FYL



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(5.54) (3.01) (4.56) (1.85) (4.04) (1.20) (3.69) (0.70) (4.50) (1.73) -7.03 -6.02 -6.81 -5.73 -6.90 -5.79 -6.96 -5.76 -7.04 -5.89 Ri,t-1

(-16.28) (-16.25) (-14.91) (-14.63) (-14.62) (-14.15) (-14.15) (-13.51) (-14.67) (-14.38) -0.16 -0.05 -0.11 0.01 -0.09 0.03 -0.09 0.05 -0.11 0.02 Size

(-3.92) (-1.28) (-2.70) (0.27) (-2.21) (0.93) (-1.95) (1.37) (-2.54) (0.51) 0.01 0.12 -0.10 -0.05 -0.10 -0.10 -0.07 -0.08 -0.05 -0.02 Equal-Wtd

Gain/Loss Winner (0.15) (2.16) (-1.84) (-0.88) (-2.11) (-1.97) (-1.57) (-1.82) (-1.42) (-0.59) 0.27 -0.01 0.16 -0.04 0.07 -0.06 0.08 0.00 0.14 -0.02 Equal-Wtd

Gain/Loss Loser (2.58) (-0.12) (1.62) (-0.48) (0.87) (-0.68) (1.11) (-0.02) (1.71) (-0.32) 0.29 0.33 -0.02 0.02 -0.01 0.03 -0.03 -0.01 0.04 0.07 52-Wk High

Winner (6.00) (6.81) (-0.54) (0.70) (-0.17) (0.95) (-0.73) (-0.24) (1.50) (2.60) -0.44 -0.72 0.06 -0.16 -0.01 -0.17 0.01 -0.14 -0.07 -0.27 52-Wk High


Winner (-2.25) (-3.23) (-2.64) (-3.59) (-1.71) (-2.68) (-1.10) (-1.99) (-1.62) (-2.71) -0.07 -0.02 -0.02 0.01 0.01 0.06 0.03 0.09 -0.03 0.03 Five-Year Low

Loser (-0.98) (-0.25) (-0.33) (0.17) (0.20) (0.83) (0.39) (1.24) (-0.47) (0.39)

Monthly

return (1,12)


Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(2.73) (2.73) (2.56) (2.35) (2.07) (1.96) (2.12) (1.90) (2.19) (2.05) 2.86 3.26 2.35 2.68 2.57 3.02 1.39 1.57 2.59 3.06 Ri,t-1

(1.44) (1.54) (1.31) (1.43) (1.36) (1.52) (0.64) (0.68) (1.24) (1.38) -0.30 -0.27 -0.36 -0.30 -0.37 -0.18 -0.39 -0.28 -0.47 -0.33 Size

(-1.97) (-1.85) (-2.27) (-1.94) (-1.56) (-1.10) (-1.96) (-1.52) (-2.13) (-1.72) -0.28 -0.16 0.09 0.14 0.70 0.28 0.68 0.69 0.51 0.42 Five-Year Return

Winner (-1.39) (-0.79) (0.41) (0.62) (1.47) (1.29) (2.40) (2.28) (2.01) (1.91) 0.40 0.38 0.30 0.29 -0.13 -0.06 0.71 0.36 0.44 0.22 Five-Year Return

Loser (1.50) (1.67) (1.09) (1.31) (-0.50) (-0.23) (1.28) (1.05) (1.16) (0.98) 0.05 0.06 -0.05 0.02 0.10 -0.06 -0.06 -0.31 0.07 -0.04 52-Wk High

Winner (0.29) (0.34) (-0.29) (0.10) (0.45) (-0.34) (-0.25) (-1.59) (0.51) (-0.32) 0.14 0.18 0.10 0.05 0.08 0.17 0.34 0.41 0.32 0.28 52-Wk High

Loser (0.62) (0.71) (0.31) (0.16) (0.34) (0.68) (1.16) (1.35) (1.40) (1.20) 0.18 0.22 -0.04 0.05 0.06 -0.01 0.42 0.38 0.27 0.23 Five-Year High

Winner (0.92) (1.08) (-0.18) (0.22) (0.30) (-0.05) (2.01) (1.78) (1.50) (1.26) -0.19 -0.07 0.02 0.21 0.23 0.08 0.14 -0.46 0.21 0.07 Five-Year High

Loser (-0.65) (-0.27) (0.05) (0.74) (0.60) (0.25) (0.23) (-1.43) (0.67) (0.26)

Test with Data from a Regime Without Taxes TR vs. FYH



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(2.58) (2.56) (2.52) (2.34) (2.02) (1.93) (1.84) (1.61) (1.73) (1.54) 3.09 3.56 3.10 3.58 1.77 2.19 2.25 2.76 0.15 0.39 Ri,t-1

(1.60) (1.73) (1.66) (1.83) (0.92) (1.09) (0.98) (1.13) (0.09) (0.23) -0.27 -0.24 -0.38 -0.32 -0.42 -0.23 -0.46 -0.32 -0.50 -0.33 Size

(-1.73) (-1.60) (-2.25) (-1.97) (-1.66) (-1.30) (-1.99) (-1.57) (-2.00) (-1.61) -0.16 -0.04 0.11 0.12 0.56 0.15 0.36 0.34 0.29 0.12 Five-Year Return

Winner (-0.73) (-0.18) (0.39) (0.38) (1.32) (0.64) (1.34) (1.21) (1.23) (0.54) 0.34 0.38 0.20 0.26 0.16 0.10 1.18 0.31 0.72 0.31 Five-Year Return

Loser (1.24) (1.39) (0.62) (0.84) (0.45) (0.31) (1.12) (0.79) (1.13) (0.98) 0.04 0.08 -0.11 0.00 0.18 0.01 0.05 -0.13 0.18 0.11 52-Wk High

Winner (0.21) (0.41) (-0.54) (0.01) (0.79) (0.07) (0.22) (-0.59) (1.17) (0.70) 0.14 0.20 0.17 0.19 0.12 0.26 0.61 0.38 0.36 0.23 52-Wk High

Loser (0.55) (0.73) (0.53) (0.54) (0.43) (0.93) (1.35) (1.06) (1.10) (0.79) -0.18 -0.15 -0.10 -0.11 0.18 0.07 0.51 0.66 0.41 0.51 Five-Year Low

Winner (-0.63) (-0.54) (-0.32) (-0.35) (0.51) (0.23) (1.34) (1.67) (1.34) (1.68) -0.12 -0.04 -0.06 -0.18 -0.34 -0.28 -0.41 0.09 -0.24 -0.01 Five-Year Low

Loser (-0.42) (-0.15) (-0.24) (-0.78) (-1.09) (-0.85) (-0.68) (0.25) (-0.77) (-0.03)

Test with Data from a Regime Without Taxes TR vs. FYL



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(2.68) (2.66) (2.52) (2.35) (2.07) (1.97) (1.92) (1.67) (2.12) (1.98) 2.93 3.34 2.40 2.69 2.60 3.12 1.50 1.79 2.64 3.12 Ri,t-1

(1.47) (1.57) (1.36) (1.46) (1.35) (1.54) (0.67) (0.75) (1.26) (1.40) -0.29 -0.27 -0.37 -0.31 -0.36 -0.19 -0.37 -0.24 -0.47 -0.33 Size

(-1.95) (-1.84) (-2.31) (-2.02) (-1.57) (-1.16) (-1.78) (-1.31) (-2.09) (-1.70) -0.16 -0.09 0.01 0.00 0.51 0.09 0.43 0.44 0.30 0.20 Five-Year Return

Winner (-0.77) (-0.42) (0.05) (0.01) (1.28) (0.39) (1.61) (1.53) (1.34) (0.93) 0.36 0.39 0.24 0.31 0.14 0.09 0.98 0.26 0.63 0.28 Five-Year Return

Loser (1.39) (1.51) (0.83) (1.13) (0.43) (0.30) (1.08) (0.73) (1.16) (1.02) 0.09 0.13 -0.10 -0.01 0.11 -0.04 0.05 -0.13 0.13 0.06 52-Wk High

Winner (0.46) (0.66) (-0.56) (-0.03) (0.51) (-0.21) (0.22) (-0.62) (0.95) (0.41) 0.15 0.21 0.11 0.12 0.10 0.20 0.43 0.27 0.41 0.33 52-Wk High Loser

(0.60) (0.77) (0.35) (0.37) (0.41) (0.79) (1.08) (0.83) (1.40) (1.18) -0.13 -0.06 0.18 0.20 0.18 0.10 0.34 0.37 0.28 0.29 Equal-Weighted

Gain Winner (-0.54) (-0.23) (0.65) (0.70) (0.58) (0.37) (1.18) (1.18) (1.23) (1.27) -0.14 -0.05 0.12 -0.01 -0.34 -0.30 -0.39 -0.12 -0.25 -0.09 Equal-Weighted

Gain Loser (-0.57) (-0.19) (0.51) (-0.05) (-1.25) (-1.07) (-0.88) (-0.38) (-1.00) (-0.52)

Test with Data from a Regime Without Taxes TR vs. EWGO

Test of Capital Gain Lock-in Hypothesis TR vs. EWGO



Jan. excluded

Monthly return

(13,24)

Monthly return

(13,24) Jan.

excluded

Monthly return

(25,36)

Monthly return

(25,36) Jan.

excluded

Monthly return

(37,48)

Monthly return

(37,48) Jan.

excluded


Monthly return

(1,60) Jan.


(5.08) (2.50) (3.57) (0.68) (4.12) (1.21) (4.32) (1.46) (4.61) (1.96) -7.00 -6.00 -6.98 -5.80 -7.01 -5.80 -6.88 -5.65 -6.78 -5.57 Ri,t-1

(-15.86) (-15.50) (-14.38) (-13.74) (-14.04) (-13.36) (-13.73) (-12.91) (-13.45) (-12.85) -0.13 -0.02 -0.06 0.06 -0.09 0.04 -0.10 0.03 -0.11 0.01 Size

(-3.28) (-0.51) (-1.59) (1.59) (-2.17) (1.08) (-2.39) (0.81) (-2.63) (0.29) -0.11 -0.06 -0.02 -0.01 -0.04 -0.04 -0.05 -0.05 -0.06 -0.04 Five-Year Return

Winner (-2.44) (-1.33) (-0.49) (-0.14) (-0.76) (-0.85) (-1.03) (-1.03) (-1.66) (-1.29) 0.33 0.10 0.21 0.07 0.08 -0.01 0.06 -0.01 0.16 0.04 Five-Year Return

Loser (3.45) (1.13) (2.51) (0.84) (1.08) (-0.15) (0.99) (-0.13) (2.38) (0.54) 0.26 0.33 -0.05 0.01 -0.02 0.03 -0.03 -0.02 0.03 0.07 52-Wk High

Winner (4.94) (6.23) (-1.29) (0.28) (-0.38) (0.81) (-0.87) (-0.43) (0.91) (2.27) -0.41 -0.73 0.07 -0.19 0.00 -0.20 0.03 -0.14 -0.04 -0.27 52-Wk High

Loser (-3.37) (-7.19) (0.70) (-2.13) (0.02) (-2.01) (0.27) (-1.43) (-0.44) (-2.99) -0.13 -0.14 -0.28 -0.32 -0.15 -0.22 -0.08 -0.16 -0.12 -0.18 Equal-Weighted

Gain Winner (-1.39) (-1.46) (-3.56) (-4.09) (-2.11) (-3.05) (-1.06) (-2.19) (-1.74) (-2.55) -0.06 -0.06 -0.05 -0.05 0.01 0.02 -0.01 0.03 -0.03 -0.01 Equal-Weighted

Gain Loser (-0.93) (-0.87) (-0.74) (-0.79) (0.21) (0.29) (-0.22) (0.53) (-0.60) (-0.17)

Conclusion• Lock- in effect motivated measures subsume the existing measure in

predicting long term reversal.• Overreaction motivated measures do not predict long term reversal. • Evidences suggest that long term reversal reflects investors’ rational

decision of tax avoidance rather than their irrational overreaction. • Losers reverse only in January which is consistent with tax loss

selling. • No winner or loser reversal in Hong Kong. These are further

evidences for capital gain lock-in hypothesis as an explanation for the long term reversal observed in the US market.

long-term return reversal: overreaction or taxes?

Documents

momentum profits

smaller momentum

predicting momentum

short term momentum

short run momentum

momentum life cycle

industry returns

longterm return reversal