The characteristics of the factor payoffs to the candidate style attributes are demonstrated in Table 1. PANEL (A) and PANEL (B). Table 1 displays the univariate test results of the style attributes in the Fundamental values relative to the share price and Solvency and Liquidity respectively. Each panel consists of the time-series means of the factor payoffs to the style attributes within the category, their respective t-statistics, and the results of the sign test on the time-series median of the payoffs to each attribute.
Examining PANEL (A) and PANEL (B) of Table 1, there are 2 (out of 9) style attributes in total that exhibit significant t-statistics for the time-series mean of their factor payoffs over the entire examination period. Both these attributes are from the Solvency and Liquidity categories. None of the attributes in the Fundamental values relative to the share price category demonstrate their abilities to explain the cross-sectional equity returns in their individual capacities. However, this observation does not entail that the attributes that are statistically not significant in these two categories are unimportant in explaining cross-sectional equity returns since the attributes are examined in isolation. Certain style attributes may not be able to distinguish cross-sectional equity returns in isolation, yet receive significant payoffs when employed with their complimentary counterparts (Hodnett 2010).
Examining the results of the median tests on the factor payoffs of the style attributes reveals that only one attribute in the Solvency and Liquidity category is associated with a significant sign. The payoffs to style attributes are deemed to be fair if the signs associated with them correspond to their theoretical expectations. However, their payoffs are considered overvalued/undervalued when the style attributes possess signs that are unexpected.
Another way of assessing the style consistency of the candidate style attributes is to determine whether the magnitudes and the directions of the style payoffs are consistent over time. This objective is achieved by observing the geometric cumulative factor payoffs of the Style Attributes and the Cross-Section of Equity Returns: Univariate Linear Approach from quarter to quarter. The geometric cumulative factor payoffs over the entire examination period (March 2001 to March 2021) for the 9 candidate style attributes are computed and depicted in Fig. 1. The cumulative factor payoffs to style attributes in both categories are depicted in CHART (A) and CHART (B) respectively to facilitate the comparison between the rewards to the style attributes within the same category.
Fundamental values relative to the share price
The t-statistics of the mean factor payoffs to the style attributes in PANEL (A) of Table 1 demonstrate that all style attributes in this category (BVTP, CFTP, EY and INCTMKT) do not have significant mean payoffs over the examination period. In addition, all style attributes in this category do not possess significant positive signs from the Fundamental values relative to the share price category. This means that during the examination period the firms did not have significant Fundamental values relative to the share price which could reward these firms with higher payoffs.
Examining the cumulative geometric factor payoffs to the attributes in CHART (A) of Fig. 1, shows that amongst all other fundamental indicators, the mean payoffs from INCTMKT are the most volatile over the examination period. The mean factor payoff of INCTMKT reduces from 3.8157 in December 2007 to -2.045 in September 2020.
Table 1 Characteristics of Factor Payoffs to Style Attributes
PANEL (A) Fundamental Values Relative to Share Price
|
BVTP
|
CFTP
|
EY
|
INCTMKT
|
Examination period: March 2001 to March 2021
|
|
|
|
|
Factor Payoffs
|
-0.0005
|
-7.75919E-05
|
0.0735
|
0.0075
|
Mean Tests:
|
|
|
|
|
t-statistic
|
-0.0616
|
-1.6865
|
1.6630
|
0.0874
|
P-Value
|
0.951
|
0.096
|
0.100
|
0.931
|
Median Test:
|
|
|
|
|
Wilcoxon Signed Rank Test
|
1608
|
1259
|
1939
|
1636
|
P-value
|
0.807
|
0.059
|
0.191
|
0.910
|
Table 1 displays the time-series means of the factor payoffs to the style attributes, their respective t-statistics, and the test results of the sign test on the time-series median of the payoffs to each attribute in the Fundamental values relative to the share price category over the entire examination period. The style attributes under examination are BVTP, CFTP, EY and INCTMKT. Both the sizes and the signs of the factor payoffs to the candidate style attributes must be estimated in order to determine the relative consistency of the factor payoff to each style attribute. The t-statistic of the attribute’s mean payoff determines the size of the factor payoff to a particular attribute. On the other hand, to determine the consistency of the signs associated with the factor payoffs Wilcoxon signed ranks test is employed on the medians of the factor payoffs. The null hypothesis of the sign test is that a particular factor payoff does not exhibit a consistent sign. Therefore, the rejection of the null hypothesis for a particular sign test means that there is a consistent positive/negative reward to the style attribute in question. Values that are statistically significant at the 5 percent significance level are highlighted in bold.
The geometric cumulative payoffs to the style attributes in the Fundamental values relative to the share price category over the entire examination period from March 2001 to March 2021 are computed and depicted. Style attributes under examination are BVTP, CFTP, EY and INCTMKT. The factor payoffs to the style attributes are estimated by the Fama-MacBeth (1973) single factor model.
Solvency and Liquidity
Examining the characteristics of the payoffs to style attributes in the Solvency and Liquidity category (PANEL (B) of Table 1), 3 (out of 5) attributes in their individual merits have failed to explain the cross-sectional returns over the examination period. CFTCURRLIABS and CURRENTRATIO are the only 2 attributes that exhibit significant payoffs in the examination period. The significant positive payoffs to CFTCURRLIABS and CURRENTRATIO over the overall examination period reveal that firms with a high CFTCURRLIABS and CURRENTRATIO are rewarded with a higher payoff. The CFTCURRLIABS (operating cash flow ratio) and CURRENTRATIO (liquidity ratio) are a measure of a company’s liquidity in the short term. Investors prefer firms with steady cash flows as compared to cash-strapped firms.
The cumulative geometric factor payoffs to style attribute demonstrated in CHART (B) of Fig. 1 indicate that the payoffs to CFTCURRLIABS and CURRENTRATIO exhibit significant negative payoffs. CURRENTRATIO is the only style attribute in this category to exhibit a consistent sign. CFTDEBT, DEBTEQ and ICBT do not add value in forecasting equity returns unless these are compliments to attributes in other categories in explaining cross-sectional equity returns. Except for the factor payoffs to ICBT and CURRENTRATIO all other style attributes exhibit extreme volatility over the examination period.
Table 1 Characteristics of Factor Payoffs to Style Attributes
PANEL (B) Solvency and Liquidity
|
CFTCURRLIABS
|
CFTDEBT
|
CURRENTRATIO
|
DEBTEQ
|
ICBT
|
Examination period: March 2001 to March 2021
|
|
|
|
|
|
Factor Payoffs
|
-0.0477
|
-0.01537
|
-0.02703
|
-0.00108
|
-3.3E-05
|
Mean Tests:
|
|
|
|
|
|
t-statistic
|
-2.1506
|
-1.5372
|
-2.8892
|
-0.0674
|
-0.6886
|
p-value
|
0.035
|
0.128
|
0.005
|
-0.0674
|
0.493
|
Median Test:
|
|
|
|
|
|
Wilcoxon Signed Rank Test
|
1263
|
1540
|
945
|
1637
|
1414
|
p-value
|
0.062
|
0.572
|
< .001
|
0.914
|
0.247
|
This table displays the time-series means of the factor payoffs to the style attributes, their respective t-statistics, and the test results of the sign test on the time-series median of the payoffs to each attribute in the Solvency and Liquidity category over the entire examination period. The style attributes under examination are CFTCURRLIABS, CFTDEBT, CURRENTRATIO, DEBTTEQ and ICBT. Values that are statistically significant at the 5 percent significance level are highlighted in bold. In order to determine the relative consistency of the factor payoff to each style attribute, both the sizes and the signs of the factor payoffs to the candidate style attributes must be estimated. The size of the factor payoff to a particular attribute is determined by the t-statistic of the attribute’s mean payoff. On the other hand, a Wilcoxon signed ranks test is employed to determine the consistency of the signs associated with the factor payoffs. Sign tests are tests on the medians of the factor payoffs, and the null hypothesis is that a particular factor payoff does not exhibit a consistent sign. Therefore, the rejection of the null hypothesis for a particular sign test (highlighted in bold) means that there is a consistent positive/negative reward to the style attribute in question.
CHART (B) Solvency and Liquidity
The geometric cumulative payoffs to the style attributes in the solvency and liquidity category over the entire examination period from March 2001 to March 2021 are computed and depicted. Style attributes under examination are CFTCURRLIABS, CFTDEBT, CURRENTRATIO, DEBTEQ and ICBT. The factor payoffs to the candidate style attributes are estimated by the Fama-MacBeth (1973) single factor model.