Table 9 Open in new tab Disaggregated...

Panel A: $R_{oos}^{2} \times 100$ for quintile portfolios
		Book-to-market	Earnings-to-price
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Valuation ratios	MW	8.1	7.1	8.7	9.1	12.6	8.9	7.3	8.8	10.1	11.6
ANN	14.7	17.1	11.9	14.0	12.1	13.1	14.6	16.8	13.4	14.1
RF	6.7	16.2	9.4	17.8	15.4	8.0	13.0	17.7	16.1	16.7
MW+ANN	14.9	15.7	10.8	13.4	14.9	13.1	13.8	16.7	14.5	15.5
MW+RF	8.9	19.0	13.4	21.8	21.4	10.1	17.0	22.4	20.4	22.5

		Dollar trading volume	Amihud illiquidity
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Liquidity	MW	15.7	10.5	10.2	6.2	−0.9	−1.0	4.1	7.3	10.7	14.9
ANN	17.2	13.1	14.5	15.8	8.0	8.2	12.4	12.8	16.0	16.5
RF	21.8	16.0	16.8	14.0	−11.3	−8.9	4.8	12.4	19.4	20.1
MW+ANN	19.6	13.9	15.7	16.2	2.9	4.1	10.2	12.7	17.3	18.7
MW+RF	27.5	20.0	20.7	17.1	−11.2	−7.5	8.1	15.1	23.3	25.0

		12-month momentum	Industry momentum
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Momentum	MW	13.9	9.4	7.5	5.9	5.8	7.7	11.1	10.3	10.3	6.4
ANN	13.9	11.1	14.8	13.2	15.9	13.0	17.4	15.3	14.0	10.8
RF	15.2	12.7	13.1	15.3	7.2	13.1	18.9	19.6	11.1	0.5
MW+ANN	17.0	10.8	13.1	12.2	14.3	11.9	17.8	16.1	16.2	9.5
MW+RF	21.4	18.1	16.3	18.4	7.4	15.6	23.4	23.6	17.5	1.8

Panel A:

R_{oos}^{2} \times 100

for quintile portfolios

Book-to-market

Earnings-to-price

Valuation ratios

8.1

7.1

8.7

9.1

12.6

8.9

7.3

8.8

10.1

11.6

ANN

14.7

17.1

11.9

14.0

12.1

13.1

14.6

16.8

13.4

14.1

6.7

16.2

9.4

17.8

15.4

8.0

13.0

17.7

16.1

16.7

MW+ANN

14.9

15.7

10.8

13.4

14.9

13.1

13.8

16.7

14.5

15.5

MW+RF

8.9

19.0

13.4

21.8

21.4

10.1

17.0

22.4

20.4

22.5

Dollar trading volume

Amihud illiquidity

Liquidity

15.7

10.5

10.2

6.2

−0.9

−1.0

4.1

7.3

10.7

14.9

ANN

17.2

13.1

14.5

15.8

8.0

8.2

12.4

12.8

16.0

16.5

21.8

16.0

16.8

14.0

−11.3

−8.9

4.8

12.4

19.4

20.1

MW+ANN

19.6

13.9

15.7

16.2

2.9

4.1

10.2

12.7

17.3

18.7

MW+RF

27.5

20.0

20.7

17.1

−11.2

−7.5

8.1

15.1

23.3

25.0

12-month momentum

Industry momentum

Momentum

13.9

9.4

7.5

5.9

5.8

7.7

11.1

10.3

6.4

ANN

13.9

11.1

14.8

13.2

15.9

13.0

17.4

15.3

14.0

10.8

15.2

12.7

13.1

15.3

7.2

13.1

18.9

19.6

11.1

0.5

MW+ANN

17.0

10.8

13.1

12.2

14.3

11.9

17.8

16.1

16.2

9.5

MW+RF

21.4

18.1

16.3

18.4

7.4

15.6

23.4

23.6

17.5

1.8

Panel A: $R_{oos}^{2} \times 100$ for quintile portfolios
		Book-to-market	Earnings-to-price
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Valuation ratios	MW	8.1	7.1	8.7	9.1	12.6	8.9	7.3	8.8	10.1	11.6
ANN	14.7	17.1	11.9	14.0	12.1	13.1	14.6	16.8	13.4	14.1
RF	6.7	16.2	9.4	17.8	15.4	8.0	13.0	17.7	16.1	16.7
MW+ANN	14.9	15.7	10.8	13.4	14.9	13.1	13.8	16.7	14.5	15.5
MW+RF	8.9	19.0	13.4	21.8	21.4	10.1	17.0	22.4	20.4	22.5

		Dollar trading volume	Amihud illiquidity
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Liquidity	MW	15.7	10.5	10.2	6.2	−0.9	−1.0	4.1	7.3	10.7	14.9
ANN	17.2	13.1	14.5	15.8	8.0	8.2	12.4	12.8	16.0	16.5
RF	21.8	16.0	16.8	14.0	−11.3	−8.9	4.8	12.4	19.4	20.1
MW+ANN	19.6	13.9	15.7	16.2	2.9	4.1	10.2	12.7	17.3	18.7
MW+RF	27.5	20.0	20.7	17.1	−11.2	−7.5	8.1	15.1	23.3	25.0

		12-month momentum	Industry momentum
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Momentum	MW	13.9	9.4	7.5	5.9	5.8	7.7	11.1	10.3	10.3	6.4
ANN	13.9	11.1	14.8	13.2	15.9	13.0	17.4	15.3	14.0	10.8
RF	15.2	12.7	13.1	15.3	7.2	13.1	18.9	19.6	11.1	0.5
MW+ANN	17.0	10.8	13.1	12.2	14.3	11.9	17.8	16.1	16.2	9.5
MW+RF	21.4	18.1	16.3	18.4	7.4	15.6	23.4	23.6	17.5	1.8

Panel B: $R_{oos}^{2} \times 100$ for industry portfolios (one digit SIC code)
MW	6.6	5.4	11.9	8.0	9.0	8.7	12.0	8.0	16.9	2.1
ANN	23.9	12.7	12.2	15.8	16.6	8.1	12.0	17.3	3.6	12.9
RF	29.3	15.6	10.8	13.2	16.5	7.7	11.9	11.4	9.5	15.2
MW+ANN	22.7	8.3	13.4	14.3	19.2	8.6	15.6	16.5	11.0	18.4
MW+RF	31.6	18.1	14.6	16.0	22.5	12.5	18.1	12.4	21.5	12.6

Panel B:

R_{oos}^{2} \times 100

for industry portfolios (one digit SIC code)

6.6

5.4

11.9

8.0

9.0

8.7

12.0

8.0

16.9

2.1

ANN

23.9

12.7

12.2

15.8

16.6

8.1

12.0

17.3

3.6

12.9

29.3

15.6

10.8

13.2

16.5

7.7

11.9

11.4

9.5

15.2

MW+ANN

22.7

8.3

13.4

14.3

19.2

8.6

15.6

16.5

11.0

18.4

MW+RF

31.6

18.1

14.6

16.0

22.5

12.5

18.1

12.4

21.5

12.6

Panel B: $R_{oos}^{2} \times 100$ for industry portfolios (one digit SIC code)
MW	6.6	5.4	11.9	8.0	9.0	8.7	12.0	8.0	16.9	2.1
ANN	23.9	12.7	12.2	15.8	16.6	8.1	12.0	17.3	3.6	12.9
RF	29.3	15.6	10.8	13.2	16.5	7.7	11.9	11.4	9.5	15.2
MW+ANN	22.7	8.3	13.4	14.3	19.2	8.6	15.6	16.5	11.0	18.4
MW+RF	31.6	18.1	14.6	16.0	22.5	12.5	18.1	12.4	21.5	12.6

Table 9

Open in new tab

Disaggregated performance comparison, one-year horizon, monthly frequency

Panel A: $R_{oos}^{2} \times 100$ for quintile portfolios
		Book-to-market					Earnings-to-price
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Valuation ratios	MW	8.1	7.1	8.7	9.1	12.6	8.9	7.3	8.8	10.1	11.6
	ANN	14.7	17.1	11.9	14.0	12.1	13.1	14.6	16.8	13.4	14.1
	RF	6.7	16.2	9.4	17.8	15.4	8.0	13.0	17.7	16.1	16.7
	MW+ANN	14.9	15.7	10.8	13.4	14.9	13.1	13.8	16.7	14.5	15.5
	MW+RF	8.9	19.0	13.4	21.8	21.4	10.1	17.0	22.4	20.4	22.5

		Dollar trading volume					Amihud illiquidity
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Liquidity	MW	15.7	10.5	10.2	6.2	−0.9	−1.0	4.1	7.3	10.7	14.9
	ANN	17.2	13.1	14.5	15.8	8.0	8.2	12.4	12.8	16.0	16.5
	RF	21.8	16.0	16.8	14.0	−11.3	−8.9	4.8	12.4	19.4	20.1
	MW+ANN	19.6	13.9	15.7	16.2	2.9	4.1	10.2	12.7	17.3	18.7
	MW+RF	27.5	20.0	20.7	17.1	−11.2	−7.5	8.1	15.1	23.3	25.0

		12-month momentum					Industry momentum
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Momentum	MW	13.9	9.4	7.5	5.9	5.8	7.7	11.1	10.3	10.3	6.4
	ANN	13.9	11.1	14.8	13.2	15.9	13.0	17.4	15.3	14.0	10.8
	RF	15.2	12.7	13.1	15.3	7.2	13.1	18.9	19.6	11.1	0.5
	MW+ANN	17.0	10.8	13.1	12.2	14.3	11.9	17.8	16.1	16.2	9.5
	MW+RF	21.4	18.1	16.3	18.4	7.4	15.6	23.4	23.6	17.5	1.8

Panel A: $R_{oos}^{2} \times 100$ for quintile portfolios
		Book-to-market					Earnings-to-price
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Valuation ratios	MW	8.1	7.1	8.7	9.1	12.6	8.9	7.3	8.8	10.1	11.6
	ANN	14.7	17.1	11.9	14.0	12.1	13.1	14.6	16.8	13.4	14.1
	RF	6.7	16.2	9.4	17.8	15.4	8.0	13.0	17.7	16.1	16.7
	MW+ANN	14.9	15.7	10.8	13.4	14.9	13.1	13.8	16.7	14.5	15.5
	MW+RF	8.9	19.0	13.4	21.8	21.4	10.1	17.0	22.4	20.4	22.5

		Dollar trading volume					Amihud illiquidity
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Liquidity	MW	15.7	10.5	10.2	6.2	−0.9	−1.0	4.1	7.3	10.7	14.9
	ANN	17.2	13.1	14.5	15.8	8.0	8.2	12.4	12.8	16.0	16.5
	RF	21.8	16.0	16.8	14.0	−11.3	−8.9	4.8	12.4	19.4	20.1
	MW+ANN	19.6	13.9	15.7	16.2	2.9	4.1	10.2	12.7	17.3	18.7
	MW+RF	27.5	20.0	20.7	17.1	−11.2	−7.5	8.1	15.1	23.3	25.0

		12-month momentum					Industry momentum
		Q1	Q2	Q3	Q4	Q5	Q1	Q2	Q3	Q4	Q5

Momentum	MW	13.9	9.4	7.5	5.9	5.8	7.7	11.1	10.3	10.3	6.4
	ANN	13.9	11.1	14.8	13.2	15.9	13.0	17.4	15.3	14.0	10.8
	RF	15.2	12.7	13.1	15.3	7.2	13.1	18.9	19.6	11.1	0.5
	MW+ANN	17.0	10.8	13.1	12.2	14.3	11.9	17.8	16.1	16.2	9.5
	MW+RF	21.4	18.1	16.3	18.4	7.4	15.6	23.4	23.6	17.5	1.8

Panel B: $R_{oos}^{2} \times 100$ for industry portfolios (one digit SIC code)
	0	1	2	3	4	5	6	7	8	9
MW	6.6	5.4	11.9	8.0	9.0	8.7	12.0	8.0	16.9	2.1
ANN	23.9	12.7	12.2	15.8	16.6	8.1	12.0	17.3	3.6	12.9
RF	29.3	15.6	10.8	13.2	16.5	7.7	11.9	11.4	9.5	15.2
MW+ANN	22.7	8.3	13.4	14.3	19.2	8.6	15.6	16.5	11.0	18.4
MW+RF	31.6	18.1	14.6	16.0	22.5	12.5	18.1	12.4	21.5	12.6

Panel B: $R_{oos}^{2} \times 100$ for industry portfolios (one digit SIC code)
	0	1	2	3	4	5	6	7	8	9
MW	6.6	5.4	11.9	8.0	9.0	8.7	12.0	8.0	16.9	2.1
ANN	23.9	12.7	12.2	15.8	16.6	8.1	12.0	17.3	3.6	12.9
RF	29.3	15.6	10.8	13.2	16.5	7.7	11.9	11.4	9.5	15.2
MW+ANN	22.7	8.3	13.4	14.3	19.2	8.6	15.6	16.5	11.0	18.4
MW+RF	31.6	18.1	14.6	16.0	22.5	12.5	18.1	12.4	21.5	12.6

Notes: To obtain the results in Panel A, we sort the sample stocks into quintiles, according to the size of stock-specific valuation ratios (book-to-market and earnings-to-price), liquidity (Amihud illiquidity and dollar trading volume), and momentum (industry and 12-month). The sorting is renewed each month, taking into account the availability conditions outlined in Section 2. The pooled $R_{oos}^{2} \times 100$ according to Equation (15) is reported for each quintile portfolio and the approaches of interest, namely, MW, pure ML (ANN and RF), and theory assisted by machine learning (MW+RF and MW+ANN). Panel B shows the pooled $R_{oos}^{2} \times 100$ for each of the 10 industry portfolios based on the one-digit SIC code. The RPE are computed at the monthly (EOM) frequency. The machine learning results are obtained using the short training scheme depicted in Figure 3.

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