When did our field stop being “asset pricing” and become “asset expected returning?” … Market-to-book ratios should be our left-hand variable, the thing we are trying to explain, not a sorting characteristic for expected returns.– John Cochrane, Presidential Address, American Finance Association, 2011
1 Introduction
2 The price of quality: dynamic model
2.1 A dynamic model of firm quality: time-varying profits, growth, and risk
2.2 Valuation: the price of quality
3 Data, quality measures, and preliminary analysis
3.1 Data sources
3.2 Quality score
3.3 Portfolios
3.4 Ex ante quality forecasts fundamentals
P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 | P10 | H-L | H-L | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(Low) | (High) | t-stat | |||||||||||
Panel A: Long Sample (U.S.), 6/1975 –12/2016
| |||||||||||||
Quality | t | −1.44 | −0.83 | −0.53 | −0.29 | −0.07 | 0.15 | 0.38 | 0.65 | 0.99 | 1.64 |
3.07
| 54.21 |
Quality | t + 12 M | −0.86 | −0.51 | −0.33 | −0.20 | −0.01 | 0.16 | 0.36 | 0.54 | 0.83 | 1.46 |
2.34
| 40.31 |
Quality | t + 36 M | −0.50 | −0.32 | −0.23 | −0.16 | −0.02 | 0.11 | 0.23 | 0.41 | 0.65 | 1.22 |
1.73
| 19.33 |
Quality | t + 60 M | −0.23 | −0.17 | −0.14 | −0.12 | −0.04 | 0.06 | 0.18 | 0.31 | 0.52 | 1.07 |
1.31
| 13.96 |
Quality | t + 120 M | −0.23 | −0.18 | −0.14 | −0.09 | −0.04 | 0.07 | 0.16 | 0.33 | 0.48 | 0.91 |
1.14
| 12.96 |
Profit | t + 120 M | −0.37 | −0.23 | −0.12 | −0.02 | 0.10 | 0.13 | 0.26 | 0.33 | 0.53 | 1.08 |
1.47
| 22.42 |
Growth | t + 120 M | −0.15 | −0.11 | −0.13 | −0.11 | −0.13 | −0.08 | −0.05 | 0.02 | 0.23 | 0.41 |
0.56
| 5.96 |
Safety | t + 120 M | −0.43 | −0.27 | −0.14 | −0.04 | 0.04 | 0.13 | 0.23 | 0.37 | 0.60 | 0.75 |
1.18
| 14.38 |
Panel B: Broad Sample (Global), 6/1989 – 12/2016
| |||||||||||||
Quality | t | −1.63 | −0.91 | −0.57 | −0.31 | −0.08 | 0.15 | 0.39 | 0.66 | 1.01 | 1.59 |
3.22
| 44.10 |
Quality | t + 12 M | −1.16 | −0.60 | −0.38 | −0.20 | −0.03 | 0.13 | 0.32 | 0.52 | 0.82 | 1.34 |
2.50
| 28.49 |
Quality | t + 36 M | −0.81 | −0.43 | −0.28 | −0.17 | −0.04 | 0.07 | 0.22 | 0.39 | 0.63 | 1.07 |
1.88
| 17.56 |
Quality | t + 60 M | −0.53 | −0.24 | −0.17 | −0.12 | −0.03 | 0.03 | 0.15 | 0.29 | 0.47 | 0.86 |
1.39
| 13.43 |
Quality | t + 120 M | −0.41 | −0.22 | −0.13 | −0.05 | 0.00 | 0.05 | 0.13 | 0.26 | 0.42 | 0.65 |
1.06
| 16.76 |
Profit | t + 120 M | −0.29 | −0.14 | −0.03 | 0.05 | 0.16 | 0.18 | 0.29 | 0.37 | 0.52 | 0.93 |
1.23
| 17.20 |
Growth | t + 120 M | −0.12 | −0.06 | −0.10 | −0.08 | −0.05 | −0.05 | −0.06 | 0.03 | 0.15 | 0.21 |
0.32
| 6.21 |
Safety | t + 120 M | −0.51 | −0.34 | −0.21 | −0.12 | −0.01 | 0.04 | 0.15 | 0.30 | 0.46 | 0.57 |
1.08
| 12.67 |
4 The price of quality
4.1 The price of quality in the United States and globally
Panel A
|
Long Sample (U.S., 6/1975 – 12/2016)
|
Broad Sample (Global, 6/1989–12/2016)
| ||||||||||
(1)
|
(2)
|
(3)
|
(4)
|
(5)
|
(6)
|
(7)
|
(8)
|
(9)
|
(10)
|
(11)
|
(12)
| |
Quality |
0.22
|
0.24
|
0.24
|
0.22
|
0.22
|
0.24
|
0.17
|
0.20
|
0.17
|
0.17
|
0.17
|
0.20
|
(10.07) | (20.92) | (10.06) | (11.78) | (10.07) | (20.92) | (14.06) | (26.38) | (13.59) | (20.67) | (14.06) | (24.97) | |
Firm size |
0.34
| . . |
0.33
| . . |
0.34
| . . |
0.34
| . . |
0.33
|
0.32
| ||
(20.92) | (18.87) | (20.92) | (12.81) | (12.49) | (10.83) | |||||||
1-year return |
0.21
|
0.21
| . |
0.21
|
0.26
|
0.26
|
0.26
| |||||
(12.59) | (12.39) | (12.59) | (24.04) | (27.48) | (23.68) | |||||||
Firm age |
−0.18
| . |
−0.17
| . |
−0.18
| . |
−0.12
| . |
−0.11
| . |
−0.13
| |
(−7.60) | (−6.81) | (−7.60) | (−5.23) | (−4.92) | (−7.23) | |||||||
Profit Uncertainty | . |
0.38
| . |
0.35
| . |
0.38
| . |
0.41
| . |
0.35
| . |
0.41
|
(15.54) | (15.15) | (15.54) | (28.36) | (19.92) | (27.67) | |||||||
Dividend payer | . |
−0.16
| . |
−0.07
| . |
−0.16
| . |
−0.20
| . |
−0.10
| . |
−0.20
|
(−7.68) | (−3.50) | (−7.68) | (−6.64) | (−2.93) | (−4.74) | |||||||
Profit Uncertainty | . |
−0.20
| . |
−0.20
| . |
−0.20
| . |
−0.22
| . |
−0.20
| . |
−0.23
|
x Dividend payer | . | (−10.88) | . | (−7.78) | . | (−10.88) | . | (−15.13) | . | (−8.05) | . | (−13.98) |
Average AdjR2 | 0.09 | 0.41 | 0.26 | 0.49 | 0.09 | 0.41 | 0.09 | 0.36 | 0.20 | 0.43 | 0.03 | 0.34 |
Nobs (years) | 60 | 54 | 60 | 54 | 60 | 54 | 28 | 28 | 28 | 28 | 28 | 28 |
Industry FE | X | X | X | X | ||||||||
Country FE | X | X | X | X | ||||||||
Firm FE | X | X | X | X | ||||||||
Panel B
|
Long Sample (U.S., 6/1975 – 12/2016)
|
Broad Sample (Global, 6/1989 – 12/2016)
| ||||||||||
(1)
|
(2)
|
(3)
|
(4)
|
(5)
|
(6)
|
(7)
|
(8)
|
(9)
|
(10)
| |||
Profitability |
0.19
| . | . |
0.11
|
0.14
|
0.13
| . | . |
0.06
|
0.08
| ||
(10.31) | . | . | (6.65) | (9.67) | (19.74) | . | . | (8.75) | (11.68) | |||
Growth |
0.18
| . |
0.12
|
0.13
| . |
0.14
| . |
0.11
|
0.13
| |||
(12.37) | . | (14.73) | (24.76) | . | (20.23) | . | (13.33) | (22.76) | ||||
Safety | . |
0.13
|
0.04
|
0.02
| . | . |
0.10
|
0.04
|
0.04
| |||
. | (8.23) | (3.69) | (2.17) | . | . | (9.89) | (3.86) | (3.05) | ||||
Firm size |
0.34
|
0.33
|
0.38
|
0.33
|
0.32
|
0.33
|
0.33
|
0.36
|
0.33
|
0.31
| ||
(17.42) | (19.28) | (22.79) | (18.36) | (18.56) | (11.82) | (12.56) | (14.23) | (11.90) | (9.94) | |||
1-year return |
0.22
|
0.22
|
0.23
|
0.21
|
0.21
|
0.27
|
0.27
|
0.27
|
0.26
|
0.26
| ||
(12.42) | (11.89) | (13.58) | (11.87) | (11.99) | (26.44) | (26.13) | (28.28) | (28.17) | (24.70) | |||
Firm age |
−0.18
|
−0.16
|
−0.20
|
−0.17
|
−0.18
|
−0.12
|
−0.11
|
−0.12
|
−0.11
|
−0.14
| ||
(−6.79) | (−6.30) | (−7.07) | (−7.04) | (−7.41) | (−4.84) | (−4.30) | (−5.14) | (−4.96) | (−6.77) | |||
Profit Uncertainty |
0.31
|
0.31
|
0.36
|
0.33
|
0.35
|
0.32
|
0.31
|
0.35
|
0.34
|
0.39
| ||
(11.48) | (13.33) | (12.68) | (14.27) | (13.53) | (17.53) | (16.24) | (23.77) | (23.32) | (36.38) | |||
Dividend payer |
−0.08
| −0.01 |
−0.06
|
−0.06
|
−0.13
|
−0.10
| −0.05 |
−0.09
|
−0.08
|
−0.17
| ||
(−3.77) | (−0.55) | (−2.80) | (−3.18) | (−6.31) | (−3.08) | (−1.61) | (−2.76) | (−2.64) | (−4.30) | |||
Profit Uncertainty x Dividend payer |
−0.19
|
−0.21
|
−0.20
|
−0.21
|
−0.20
|
−0.20
|
−0.20
|
−0.20
|
−0.20
|
−0.23
| ||
(−6.52) | (−8.02) | (−6.27) | (−8.13) | (−10.93) | (−8.03) | (−7.40) | (−8.10) | (−8.31) | (−13.63) | |||
Average AdjR2 | 0.48 | 0.48 | 0.45 | 0.50 | 0.43 | 0.42 | 0.43 | 0.42 | 0.44 | 0.35 | ||
Nobs (years) | 54 | 54 | 54 | 54 | 54 | 28 | 28 | 28 | 28 | 28 | ||
Industry FE | X | X | ||||||||||
Country FE | X | X | X | X | ||||||||
Firm FE | X | X |
4.2 The price of quality sub-components
4.3 The price of quality across subsets of stocks
5 Understanding the price of quality: the return of quality stocks
5.1 The returns of quality-sorted portfolios
P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 | P10 | H-L | |
---|---|---|---|---|---|---|---|---|---|---|---|
(Low) | (High) | ||||||||||
Panel A: Long Sample U.S., 7/1957 – 12/2016
| |||||||||||
Excess return | 0.28 |
0.43
|
0.43
|
0.51
|
0.55
|
0.53
|
0.48
|
0.62
|
0.52
|
0.70
|
0.42
|
(1.09) | (2.10) | (2.29) | (2.88) | (3.14) | (3.18) | (2.94) | (3.71) | (3.11) | (4.11) | (2.56) | |
CAPM alpha |
−0.44
|
−0.17
| −0.13 | −0.02 | 0.03 | 0.03 | −0.01 |
0.12
| 0.01 |
0.20
|
0.64
|
(−3.72) | (−2.29) | (−1.94) | (−0.29) | (0.55) | (0.60) | (−0.19) | (2.36) | (0.28) | (3.11) | (4.26) | |
3-factor alpha |
−0.57
|
−0.28
|
−0.21
| −0.10 | −0.03 | −0.02 | −0.02 |
0.10
| 0.05 |
0.31
|
0.88
|
(−6.52) | (−4.45) | (−3.68) | (−1.89) | (−0.60) | (−0.41) | (−0.39) | (1.99) | (1.01) | (5.90) | (8.23) | |
4-factor alpha |
−0.59
|
−0.39
|
−0.28
|
−0.19
| −0.11 |
−0.12
| −0.10 |
0.11
| 0.07 |
0.46
|
1.05
|
(−6.30) | (−5.90) | (−4.56) | (−3.58) | (−1.91) | (−2.41) | (−1.79) | (2.10) | (1.55) | (8.59) | (9.31) | |
Beta | 1.28 | 1.16 | 1.10 | 1.06 | 1.04 | 1.00 | 0.97 | 0.97 | 0.97 | 0.92 | −0.36 |
Sharpe Ratio | 0.14 | 0.27 | 0.30 | 0.37 | 0.41 | 0.41 | 0.38 | 0.48 | 0.40 | 0.53 | 0.33 |
Information Ratio | −0.88 | −0.83 | −0.64 | −0.50 | −0.27 | −0.34 | −0.25 | 0.29 | 0.22 | 1.20 | 1.31 |
Adjusted R2 | 0.88 | 0.91 | 0.91 | 0.92 | 0.90 | 0.92 | 0.91 | 0.91 | 0.93 | 0.91 | 0.59 |
Panel B: Broad Sample Global, 7/1998 – 12/2016
| |||||||||||
Excess return | 0.11 | 0.33 | 0.39 | 0.46 | 0.46 |
0.46
|
0.57
|
0.59
|
0.55
|
0.63
|
0.52
|
(0.32) | (1.11) | (1.43) | (1.81) | (1.88) | (1.99) | (2.52) | (2.65) | (2.45) | (2.80) | (2.49) | |
CAPM alpha |
−0.41
| −0.13 | −0.03 | 0.06 | 0.08 | 0.10 |
0.21
|
0.25
|
0.20
|
0.29
|
0.71
|
(−2.50) | (−1.01) | (−0.31) | (0.64) | (0.84) | (1.11) | (2.57) | (2.76) | (2.21) | (2.76) | (4.05) | |
3-factor alpha |
−0.51
| −0.21 | −0.11 | 0.01 | 0.01 | 0.04 |
0.19
|
0.23
|
0.25
|
0.40
|
0.91
|
(−3.40) | (−1.84) | (−1.06) | (0.10) | (0.07) | (0.45) | (2.34) | (2.56) | (2.72) | (4.20) | (6.66) | |
4-factor alpha |
−0.43
|
−0.27
| −0.17 | −0.06 | −0.05 | −0.04 | 0.11 | 0.19 |
0.27
|
0.56
|
0.99
|
(−2.63) | (−2.16) | (−1.60) | (−0.62) | (−0.57) | (−0.43) | (1.20) | (1.93) | (2.73) | (5.57) | (6.67) | |
Beta | 1.20 | 1.08 | 1.02 | 0.97 | 0.92 | 0.89 | 0.87 | 0.85 | 0.83 | 0.79 | −0.41 |
Sharpe Ratio | 0.06 | 0.21 | 0.27 | 0.34 | 0.36 | 0.38 | 0.48 | 0.51 | 0.47 | 0.53 | 0.47 |
Information Ratio | −0.55 | −0.45 | −0.34 | −0.13 | −0.12 | −0.09 | 0.25 | 0.40 | 0.57 | 1.17 | 1.40 |
Adjusted R2 | 0.82 | 0.85 | 0.87 | 0.86 | 0.88 | 0.87 | 0.87 | 0.84 | 0.84 | 0.84 | 0.58 |
5.2 Quality minus junk
Panel A: Long Sample (U.S., 7/1957 – 12/2016) | Panel B: Broad Sample (Global, 7/1998 – 12/2016) | |||||||
---|---|---|---|---|---|---|---|---|
QMJ | Profitability | Safety | Growth | QMJ | Profitability | Safety | Growth | |
Excess Returns |
0.29
|
0.25
|
0.23
|
0.17
|
0.38
|
0.39
| 0.23 |
0.15
|
(3.62) | (3.69) | (2.44) | (2.46) | (3.33) | (4.34) | (1.72) | (1.96) | |
CAPM-alpha |
0.39
|
0.32
|
0.40
|
0.16
|
0.51
|
0.48
|
0.40
|
0.16
|
(5.43) | (4.75) | (5.52) | (2.28) | (5.76) | (6.88) | (4.49) | (2.05) | |
3-factor alpha |
0.51
|
0.40
|
0.52
|
0.28
|
0.61
|
0.51
|
0.51
|
0.24
|
(8.90) | (6.97) | (9.06) | (5.17) | (8.75) | (8.11) | (7.91) | (3.63) | |
4-factor alpha |
0.60
|
0.50
|
0.51
|
0.46
|
0.61
|
0.47
|
0.39
|
0.40
|
(9.95) | (8.32) | (8.39) | (8.29) | (8.07) | (6.89) | (5.73) | (5.78) | |
MKT |
−0.20
|
−0.12
|
−0.32
|
−0.04
|
−0.27
|
−0.19
|
−0.35
|
−0.03
|
(−14.35) | (−8.47) | (−22.30) | (−2.81) | (−15.78) | (−12.73) | (−22.74) | (−2.06) | |
SMB |
−0.26
|
−0.22
|
−0.30
| −0.04 |
−0.32
|
−0.28
|
−0.23
|
−0.12
|
(−11.92) | (−10.01) | (−13.55) | (−1.76) | (−8.71) | (−8.32) | (−6.79) | (−3.56) | |
HML |
−0.37
|
−0.29
|
−0.28
|
−0.49
|
−0.30
| −0.06 |
−0.25
|
−0.38
|
(−15.85) | (−12.57) | (−11.91) | (−23.09) | (−8.59) | (−1.83) | (−7.98) | (−12.17) | |
UMD |
−0.09
|
−0.10
| 0.01 |
−0.16
| 0.00 | 0.04 |
0.11
|
−0.14
|
(−4.34) | (−4.87) | (0.32) | (−9.17) | (−0.02) | (1.56) | (4.63) | (−5.86) | |
Sharpe Ratio | 0.47 | 0.48 | 0.32 | 0.32 | 0.64 | 0.83 | 0.33 | 0.37 |
Information Ratio | 1.40 | 1.17 | 1.18 | 1.16 | 1.70 | 1.45 | 1.21 | 1.22 |
Adjusted R2 | 0.50 | 0.34 | 0.62 | 0.46 | 0.65 | 0.52 | 0.78 | 0.34 |
5.3 Robustness of QMJ performance
Panel A: Long Sample (U.S.,7/1963–12/2016) | Panel B: Broad Sample (Global, 11/1990–12/2016) | |||||||
---|---|---|---|---|---|---|---|---|
QMJ | Profitability | Safety | Growth | QMJ | Profitability | Safety | Growth | |
Excess Returns |
0.29
|
0.29
|
0.20
|
0.15
|
0.32
|
0.37
| 0.19 | 0.12 |
(3.30) | (3.92) | (2.04) | (2.02) | (2.70) | (4.07) | (1.36) | (1.51) | |
5-factor alpha |
0.38
|
0.29
|
0.38
|
0.30
|
0.33
|
0.29
|
0.27
|
0.19
|
(7.71) | (6.85) | (5.75) | (6.60) | (5.06) | (5.83) | (3.48) | (3.34) | |
6-factor alpha |
0.33
|
0.28
|
0.29
|
0.27
|
0.28
|
0.28
|
0.16
|
0.18
|
(6.81) | (6.54) | (4.49) | (5.85) | (4.46) | (5.58) | (2.42) | (3.12) | |
MKT |
−0.17
|
−0.08
|
−0.28
|
−0.05
|
−0.24
|
−0.15
|
−0.32
|
−0.06
|
(−14.07) | (−7.72) | (−17.60) | (−4.47) | (−13.92) | (−10.84) | (−17.79) | (−3.84) | |
SMB |
−0.11
|
−0.07
|
−0.19
| 0.03 |
−0.17
|
−0.17
|
−0.17
|
−0.08
|
(−6.51) | (−4.57) | (−8.89) | (1.83) | (−5.41) | (−6.84) | (−5.03) | (−2.61) | |
HML |
−0.26
|
−0.29
|
−0.19
|
−0.26
|
−0.25
|
−0.10
|
−0.25
|
−0.11
|
(−10.85) | (−13.80) | (−6.26) | (−11.88) | (−6.42) | (−3.05) | (−6.10) | (−2.93) | |
CMA | −0.05 |
0.09
| 0.04 |
−0.36
| 0.05 | 0.06 |
0.13
|
−0.41
|
(−1.39) | (3.04) | (0.97) | (−11.46) | (0.99) | (1.57) | (2.54) | (−9.10) | |
RMW |
0.55
|
0.58
|
0.32
|
0.33
|
0.65
|
0.59
|
0.46
|
0.32
|
(24.07) | (28.37) | (10.67) | (15.70) | (13.63) | (15.49) | (9.28) | (7.24) | |
UMD |
0.07
| 0.01 |
0.13
|
0.05
|
0.08
| 0.02 |
0.19
| 0.02 |
(5.68) | (1.25) | (8.87) | (4.37) | (4.92) | (1.32) | (11.30) | (1.29) | |
Sharpe Ratio | 0.45 | 0.54 | 0.28 | 0.28 | 0.53 | 0.80 | 0.27 | 0.30 |
Information Ratio | 1.00 | 0.96 | 0.66 | 0.86 | 0.97 | 1.21 | 0.52 | 0.68 |
Adjusted R2 | 0.72 | 0.70 | 0.63 | 0.67 | 0.77 | 0.75 | 0.81 | 0.54 |
5.4 The risk of quality stocks
Return | t-statistics | Number of months | |||||||
---|---|---|---|---|---|---|---|---|---|
Excess Return | CAPM Alpha | 3-Factor Alpha | 4-Factor Alpha | Excess Return | CAPM Alpha | 3-Factor Alpha | 4-Factor Alpha | ||
Panel A: Long Sample U.S., 7/1957 – 12/2016
| |||||||||
All Periods |
0.29
|
0.39
|
0.51
|
0.60
| 3.62 | 5.43 | 8.90 | 9.95 | 714 |
Recession |
0.50
|
0.48
|
0.74
|
0.82
| 2.00 | 2.16 | 4.47 | 4.96 | 110 |
Expansion |
0.25
|
0.38
|
0.49
|
0.56
| 3.03 | 4.99 | 8.26 | 8.69 | 604 |
Severe bear market | 0.03 | 0.30 | 0.82 | 0.78 | 0.03 | 0.40 | 1.69 | 1.50 | 21 |
Severe bull Market | 0.18 |
0.18
|
0.32
|
0.50
| 1.14 | 1.21 | 2.46 | 3.56 | 144 |
Low volatility |
0.43
|
0.63
|
0.71
|
0.77
| 2.41 | 4.21 | 5.78 | 6.16 | 245 |
High volatility | 0.13 |
0.21
|
0.41
|
0.56
| 1.24 | 1.92 | 5.70 | 7.16 | 227 |
Spike up in volatility |
0.48
|
0.56
|
0.58
|
0.72
| 3.20 | 4.15 | 5.18 | 6.32 | 240 |
Spike down in volatility | 0.00 |
0.23
|
0.48
|
0.47
| −0.04 | 1.80 | 5.06 | 4.58 | 238 |
Panel B: Broad Sample Global, 7/1989 – 12/2016
| |||||||||
All Periods |
0.38
|
0.51
|
0.61
|
0.61
| 3.33 | 5.76 | 8.75 | 8.07 | 330 |
Recession | 0.91 |
0.59
|
1.22
|
1.23
| 1.84 | 1.70 | 5.18 | 5.15 | 37 |
Expansion |
0.32
|
0.50
|
0.59
|
0.56
| 2.80 | 5.56 | 8.44 | 7.24 | 293 |
Severe bear market | 0.57 |
0.93
|
1.23
|
1.30
| 0.53 | 1.78 | 5.33 | 4.64 | 15 |
Severe bull Market |
0.65
|
0.59
|
0.71
|
0.89
| 2.38 | 2.38 | 3.98 | 3.97 | 38 |
Low volatility |
0.53
|
0.65
|
0.81
|
0.79
| 2.31 | 4.09 | 6.65 | 6.29 | 139 |
High volatility | 0.10 |
0.19
|
0.38
|
0.50
| 0.67 | 1.48 | 3.22 | 3.72 | 92 |
Spike up in volatility |
0.53
|
0.64
|
0.61
|
0.64
| 2.40 | 3.86 | 4.79 | 4.81 | 115 |
Spike down in volatility | 0.17 |
0.39
|
0.65
|
0.61
| 0.88 | 2.47 | 5.02 | 4.27 | 116 |
5.5 Market (in)efficiency: analysts’ expectations of the price of quality
P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 | P10 | H-L | H-L | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
(Low) | (High) | t-statistics | ||||||||||
Panel A: United States
| ||||||||||||
Price (scaled by book) | 2.69 | 2.29 | 2.46 | 2.80 | 3.10 | 3.02 | 3.30 | 3.81 | 4.58 | 7.05 |
4.36
| 4.20 |
Mean price target (scaled by book) | 3.45 | 2.79 | 2.94 | 3.31 | 3.64 | 3.50 | 3.85 | 4.43 | 5.28 | 8.26 |
4.82
| 3.83 |
Median price target (scaled by book) | 3.43 | 2.78 | 2.93 | 3.31 | 3.63 | 3.49 | 3.85 | 4.42 | 5.28 | 8.28 |
4.85
| 3.85 |
Mean Implied Expected Return | 0.26 | 0.20 | 0.19 | 0.17 | 0.17 | 0.16 | 0.16 | 0.16 | 0.15 | 0.15 |
−0.11
| −3.71 |
Median Implied Expected Return | 0.25 | 0.19 | 0.19 | 0.17 | 0.16 | 0.16 | 0.16 | 0.16 | 0.16 | 0.16 |
−0.10
| −3.80 |
Dispersion | 0.83 | 0.90 | 0.95 | 0.96 | 0.97 | 0.97 | 0.97 | 0.97 | 0.97 | 0.95 |
0.13
| 6.06 |
Number of estimates | 9.10 | 10.67 | 12.08 | 12.04 | 12.41 | 13.12 | 14.31 | 13.37 | 14.47 | 17.43 |
8.33
| 8.48 |
Mean Forecast Error | −0.030 | −0.019 | −0.015 | −0.011 | −0.011 | −0.010 | −0.008 | −0.008 | −0.007 | −0.005 |
0.03
| 3.46 |
Dispersion (EPS) | 0.551 | 0.328 | 0.224 | 0.141 | 0.109 | 0.091 | 0.084 | 0.059 | 0.053 | 0.034 |
−0.52
| −8.07 |
Number of estimates (EPS) | 15.36 | 18.05 | 19.30 | 20.22 | 20.78 | 20.88 | 22.04 | 23.06 | 21.79 | 25.56 |
10.20
| 10.28 |
Realized future 12-month return | 0.024 | 0.059 | 0.067 | 0.067 | 0.071 | 0.097 | 0.065 | 0.093 | 0.079 | 0.068 | 0.054 | 1.82 |
Panel B: Global
| ||||||||||||
Price (scaled by book) | 2.74 | 2.37 | 2.47 | 2.78 | 3.06 | 2.98 | 3.26 | 3.75 | 4.48 | 6.85 |
4.11
| 4.08 |
Mean price target (scaled by book) | 3.56 | 2.92 | 2.97 | 3.29 | 3.59 | 3.45 | 3.80 | 4.36 | 5.16 | 8.03 |
4.46
| 3.63 |
Median price target (scaled by book) | 3.54 | 2.91 | 2.96 | 3.29 | 3.58 | 3.44 | 3.80 | 4.35 | 5.16 | 8.04 |
4.50
| 3.65 |
Mean Implied Expected Return | 0.28 | 0.22 | 0.20 | 0.17 | 0.17 | 0.16 | 0.16 | 0.16 | 0.15 | 0.15 |
−0.13
| −5.02 |
Median Implied Expected Return | 0.27 | 0.21 | 0.19 | 0.17 | 0.16 | 0.15 | 0.16 | 0.16 | 0.15 | 0.16 |
−0.11
| −5.22 |
Dispersion | 0.82 | 0.90 | 0.95 | 0.96 | 0.97 | 0.97 | 0.98 | 0.97 | 0.97 | 0.95 |
0.13
| 6.75 |
Number of estimates | 8.72 | 10.41 | 11.84 | 11.86 | 12.26 | 12.98 | 14.12 | 13.32 | 14.34 | 16.85 |
8.13
| 8.76 |
Mean Forecast Error | −0.030 | −0.019 | −0.016 | −0.011 | −0.011 | −0.008 | −0.006 | −0.007 | −0.007 | −0.005 |
0.02
| 3.34 |
Dispersion (EPS) | 0.548 | 0.338 | 0.305 | 0.348 | 0.172 | 0.121 | 0.104 | 0.101 | 0.063 | 0.045 |
−0.50
| −7.31 |
Number of estimates (EPS) | 15.18 | 16.95 | 18.33 | 19.27 | 19.86 | 20.21 | 21.25 | 22.21 | 20.85 | 23.40 |
8.23
| 7.55 |
Realized future 12-month return | 0.025 | 0.055 | 0.065 | 0.067 | 0.074 | 0.098 | 0.069 | 0.094 | 0.083 | 0.070 |
0.058
| 2.00 |
5.6 Linking prices and returns: the price of quality predicts QMJ
Left-hand side | Panel A: Long Sample (U.S., 7/1957 – 12/2016) | Panel B: Broad Sample (Global, 7/1989 – 12/2016) | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Return (t) | Return (t, t + 12) | Return (t, t + 36) | Return (t, t + 60) | Return (t) | Return (t, t + 12) | Return (t, t + 36) | Return (t, t + 60) | |||||||||
Ret-Rf | Alpha | Ret-Rf | Alpha | Ret-Rf | Alpha | Ret-Rf | Alpha | Ret-Rf | Alpha | Ret-Rf | Alpha | Ret-Rf | Alpha | Ret-Rf | Alpha | |
QMJ |
−0.03
| −0.01 |
−0.46
|
−0.27
|
−1.52
|
−1.03
|
−2.35
|
−2.87
| −0.03 | 0.02 |
−0.82
| 0.10 |
−1.91
| 0.17 |
−1.40
|
−3.57
|
(−3.18) | (−1.76) | (−2.82) | (−2.50) | (−3.60) | (−2.78) | (−3.59) | (−4.32) | (−1.38) | (1.49) | (−2.65) | (0.56) | (−2.99) | (0.30) | (−4.09) | (−6.32) | |
Profitability |
−0.04
|
−0.02
|
−0.49
|
−0.34
|
−1.51
|
−1.19
|
−2.27
|
−2.69
| −0.04 | 0.02 |
−1.08
| −0.14 |
−2.14
| −0.59 |
−2.88
|
−4.64
|
(−3.28) | (−2.14) | (−2.95) | (−2.41) | (−3.61) | (−2.84) | (−3.18) | (−4.16) | (−1.58) | (1.13) | (−4.55) | (−0.95) | (−3.60) | (−1.37) | (−4.93) | (−6.16) | |
Growth |
−0.03
| −0.01 |
−0.33
| −0.08 | −0.99 | −0.11 | −0.41 | −1.70 | −0.03 | 0.01 |
−0.65
| −0.06 |
−2.35
| −0.74 |
−2.68
|
−2.59
|
(−3.42) | (−0.81) | (−2.26) | (−0.70) | (−1.76) | (−0.34) | (−0.61) | (−1.80) | (−1.70) | (0.51) | (−3.78) | (−0.31) | (−4.05) | (−1.09) | (−2.20) | (−3.86) | |
Safety | −0.01 | 0.00 | −0.11 | −0.07 |
−0.97
| −0.73 |
−2.28
|
−2.52
| −0.02 | 0.00 | −0.34 | 0.04 | −0.61 |
0.64
|
0.69
|
−1.33
|
(−0.63) | (−0.12) | (−0.61) | (−0.48) | (−1.99) | (−1.65) | (−2.39) | (−3.41) | (−1.07) | (0.11) | (−1.22) | (0.27) | (−1.42) | (4.06) | (3.17) | (−2.79) | |
Average Adj R2 | 0.06 | 0.04 | 0.07 | 0.04 | 0.17 | 0.08 | 0.16 | 0.31 | 0.05 | 0.02 | 0.09 | 0.01 | 0.20 | 0.07 | 0.19 | 0.36 |
6 Further asset pricing applications
6.1 Quality at a reasonable price
6.2 QMJ on the right-hand-side of a factor model
Left-hand side | Panel A: Long Sample (U.S., 7/1957–12/2016) | Panel B: Broad Sample (Global, 7/1989–12/2016) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
SMB | SMB | HML | HML | UMD | UMD | SMB | SMB | HML | HML | UMD | UMD | |
Excess Returns | 0.15 | 0.16 |
0.30
|
0.30
|
0.71
|
0.71
| 0.02 | 0.02 |
0.35
|
0.35
|
0.66
|
0.66
|
(1.55) | (1.55) | (2.39) | (2.39) | (4.77) | (4.77) | (0.23) | (0.23) | (2.19) | (2.19) | (3.05) | (3.05) | |
Alpha | 0.13 |
0.49
|
0.79
|
1.01
|
1.07
|
1.22
| 0.08 |
0.43
|
0.76
|
1.00
|
1.08
|
1.08
|
(1.26) | (4.97) | (8.52) | (12.47) | (9.76) | (10.75) | (0.71) | (3.87) | (6.82) | (9.51) | (7.57) | (6.81) | |
MKT |
0.17
| 0.01 |
−0.16
|
−0.26
|
−0.20
|
−0.25
|
0.06
|
−0.11
|
−0.10
|
−0.25
|
−0.22
|
−0.22
|
(7.15) | (0.38) | (−7.18) | (−13.03) | (−7.52) | (−8.76) | (2.57) | (−3.51) | (−3.83) | (−8.44) | (−6.87) | (−5.02) | |
SMB | . | . | −0.04 |
−0.22
| −0.08 |
−0.16
| . | . |
−0.13
|
−0.30
| −0.12 | −0.12 |
. | . | (−1.26) | (−6.76) | (−1.92) | (−3.50) | . | . | (−2.16) | (−5.33) | (−1.64) | (−1.49) | |
HML | −0.05 |
−0.28
| . | . |
−0.81
|
−0.91
|
−0.11
|
−0.27
| . | . |
−0.94
|
−0.94
|
(−1.26) | (−6.76) | . | . | (−24.87) | (−23.45) | (−2.16) | (−5.33) | . | . | (−19.14) | (−15.72) | |
UMD | −0.06 |
−0.11
|
−0.57
|
−0.48
| . | . | −0.07 | −0.05 |
−0.56
|
−0.46
| . | . |
(−1.92) | (−3.50) | (−24.87) | (−23.45) | . | . | (−1.64) | (−1.49) | (−19.14) | (−15.72) | . | . | |
QMJ | . |
−0.64
| . |
−0.71
| . |
−0.31
| . |
−0.59
| . |
−0.62
| . | 0.00 |
. | (−11.92) | . | (−15.85) | . | (−4.34) | . | (−8.71) | . | (−8.59) | . | (−0.02) | |
Sharpe Ratio | 0.20 | 0.20 | 0.31 | 0.31 | 0.62 | 0.62 | 0.04 | 0.04 | 0.42 | 0.42 | 0.58 | 0.58 |
Information Ratio | 0.18 | 0.73 | 1.14 | 1.69 | 1.28 | 1.49 | 0.15 | 0.87 | 1.34 | 1.94 | 1.47 | 1.47 |
Adjusted R2 | 0.09 | 0.24 | 0.47 | 0.61 | 0.48 | 0.49 | 0.04 | 0.22 | 0.53 | 0.62 | 0.57 | 0.57 |