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Revisiting the price effect in US stocks
Finance Research Letters 30 (2019) 139–144
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Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Revisiting the price effect in US stocks Paul Geertsema
⁎,1
, Helen Lu1
T
Department of Accounting and Finance, University of Auckland Business School, Owen G Glenn Building, 12 Grafton Road, Auckland, New Zealand
ARTICLE INFO
ABSTRACT
Keywords: Return predictability Price effect Benchmark models
Nominal price does not predict average stock returns in the cross-section of US stocks using the NYSE break-pointed, value-weighted portfolio formation approach adopted in the recent assetpricing literature. The evidence in support of return predictability is largely constrained to small stocks, with a “low price effect” more prevalent up to the 1970’s and a “high price effect” more prevalent from 1980 onwards. Among the six asset-pricing models tested in our study, only the Fama–French 3-factor model consistently yields positive alphas for trading strategies based on nominal stock prices.
JEL classification: G12 G14
1. Introduction and literature The price anomaly is one of the earliest documented anomalies, with some of the first evidence dating back to a study by Fritzemeier (1936). Since then a number of studies have documented a relationship between stock price and subsequent realised return in the US stock market. The early literature mostly documents a “low price effect” in which stocks with low nominal prices earn higher than average subsequent returns (Fritzemeier, 1936; Blume and Husic, 1973; Bachrach and Galai, 1979; Edmister and Greene, 1980; Goodman and Peavy, 1986), but a recent working paper by Singal and Tayal (2017) find evidence supporting a “high price effect” in US stock return data from 1962 to 2015, such that stocks with high nominal prices outperform stocks with low nominal prices. We explain the conflicting findings in the literature by examining fine-grained sub-samples in the US data. Our results show that the predictive power of nominal prices are concentrated in small stocks (consistent with Singal and Tayal, 2017) but also that the direction of return predictability flipped signs after the 1970s. Specifically, when we partition stocks by size quintile and decade we find that statistically meaningful price hedge portfolio returns are concentrated in the small stock quintiles and that the direction of return predictability changes from mostly negative (a low price effect) in the early decades spanning 1930 to 1970 to mostly positive (a high price effect) from 1980 onwards. Our work is closely related to chapter 7 of Zaremba and Shemer (2018) which includes a comprehensive review of the price anomaly literature, in addition to cross-country empirical tests of the price effect. Their chapter opens with the observation that “the evidence on the precise direction of the price impact on future returns remains to a large extent confusing” (page 213). While Zaremba and Shemer (2018) documents a low-price effect in several countries based on CAPM alphas of equal-weighted portfolios, we take a different approach by applying more recent techniques to US data. Specifically, we use portfolios based on NYSE breakpoints and value-weighted returns which has emerged as the norm for recent empirical asset pricing research (for example, see Asness et al., 2017; Ball et al., 2015; Fama and French, 2015; Hou et al., 2015). This approach seeks to mitigate the influence from micro-cap stocks which can otherwise swamp price-sorted quantiles. The other point of difference is that we incorporate the latest generation of benchmark models in our analysis. In addition to the CAPM model used by Zaremba and Shemer (2018) and the commonly used Corresponding author. E-mail addresses: [email protected] (P. Geertsema), [email protected] (H. Lu). 1 Postal address: The University of Auckland Business School, Private Bag 92019, Auckland 1142, New Zealand. ⁎
https://doi.org/10.1016/j.frl.2019.03.017 Received 18 October 2018; Received in revised form 7 January 2019; Accepted 6 March 2019 Available online 09 March 2019 1544-6123/ © 2019 Elsevier Inc. All rights reserved.
Finance Research Letters 30 (2019) 139–144
P. Geertsema and H. Lu
Fama and French (1993) 3-factor model, we also apply the Carhart model (Carhart, 1997), the q-factor model of Hou et al. (2015) and the five- and six-factor models of Fama and French (2015, 2018). Contrary to both the earlier literature and the recent work by Singal and Tayal (2017) and Zaremba and Shemer (2018), we conclude that the US evidence is insufficient to support the notion of a stable price effect in either direction. Specifically, returns to trading strategies based on prices only consistently generate significant and positive alphas under the Fama and French (1993) 3-factor model. However, this price effect disappears when using the more recent Carhart model (Carhart, 1997), q-factor model of Hou et al. (2015) or the five- and six-factor models of Fama and French (2015, 2018). Attempts have been made to explain the empirical relationship between stock prices and subsequent stock returns. Brown and Pfeiffer (2007) find that survivorship bias accounts for about half the returns to their price hedge strategy.2 Green and Hwang (2009) demonstrate that stocks with similar prices co-move and argue that this is as a result of investors categorising stocks based on price. It is possible that some investors believe that stocks with lower prices have more “potential upside”. Building on this intuition (Kumar, 2009) shows that individual investors appear to prefer lottery-type stocks (which tend also to be stocks with lower prices) and that this preference is strongest in lower socio-economic groups. Baker et al. (2009) show that firms respond to the demand for low priced stocks via stock splits. In robustness checks (Bandi et al., 2009) consider whether price proxies for stock-splits, which may convey information (as a signalling device by management), but find no evidence to suggest that this is the case. Our study does not aim at explaining the price anomaly. Instead, we show that the evidence for a stable price effect is lacking in the US stocks because the direction of the price effect is sample specific, primarily present in small stocks and hedge portfolio alphas obtained from the more recent asset-pricing models are generally insignificant. 2. Data and tests For empirical tests we turn to CRSP/Compustat merged monthly US stock return data and annual accounting data. We consider two samples. The first sample, which we term the “full sample”, starts in December 1925 and ends in December 2017 (inclusive).3 The second sample, which we term the “recent sample”, starts in January 1967 and ends in December 2017 (inclusive). The recent sample reflects the availability of benchmark factors used in time-series alpha tests. In particular, the 5 and 6-factor Fama–French models becomes available in July of 1963 (limited by the availability of Compustat data required for the construction of those factors) while the Hou et al. (2015) q-factors are only available starting in January of 1967 – which we take as the starting point of our “recent sample”. The dependent variable r is the monthly CRSP total return (CRSP variable RET) adjusted for delisting returns less the risk free rate (RF, sourced from Ken French’s data library as described below). If delisting returns are missing and the delisting code is greater than 200 we substitute a delisting return of −55% for NASDAQ stocks (Shumway and Warther, 1999) and a delisting return of −30% for all other stocks (Shumway, 1997). Our main explanatory variable is price, which is equal to the absolute value of CRSP variable PRC. (1)
pricet = |PRCt |
In constructing equal weighted portfolios we only include common US stocks (share code 10 or 11) in CRSP with lagged market capitalisations above the 10th percentile of common stocks listed on the NYSE in each month and with lagged prices equal to or above $1 in each month. Value weighted portfolios include all common US stocks (share code 10 or 11) in CRSP but use NYSE breakpoints such that each decile contains an equal number of NYSE common stocks in each month. In hedge portfolio time series tests we control for the market excess return (MKTRF) as well as the time-series factors formed by sorting on size (SMB), book-to-market (HML), momentum (UMD), investment (CMA) and profitability (RMW). We use the risk free rate (RF) to calculate excess returns. The original Fama and French (1993) factors are identified by post-fixing them with “ff3” (SMBff3 and HMLff3) to distinguish them from the factors used in the other Fama and French factor models.4 In addition we make use the Hou et al. (2015) q-factor model consisting of the market factor (MKT), a size factor (ME), an investment factor (I2A) and a profitability factor (ROE).5 The decile portfolio returns for price using the recent sample are summarised in Table 1. The first panel summarises value weighted portfolio decile returns and the second panel summarises equal weighted portfolio decile returns. For brevity we discuss the value weighted results, noting the equal weighted results (in parenthesis) only when they are significantly different from the value weighted results. It is evident that unadjusted portfolio returns are not monotonically related to the price deciles. In fact, the highest returns are clustered around the middle portfolios. The lowest decile portfolio, corresponding to the lowest price stocks, produces notably lower returns than the other portfolios. The hedge portfolio formed by taking a long position in the decile 10 portfolio and a short position 2 In this paper all realised returns are delisting adjusted, thus mitigating the potential impact of survivorship bias. See the Data section for more detail. 3 In tests that rely on the Fama and French (1993) factors the full sample starts in July 1926 rather than December 1925, reflecting the availability of the factors. 4 These factors were sourced from Ken French’s data library at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. The factor time series starts in July 1926 and ends in December 2017. 5 A special thanks to Lu Zhang for kindly making available the q-factor data. The q-factor time series starts in January 1967 and ends in December 2017.
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Table 1 Price sorted portfolio summary (recent sample). The results below are calculated using monthly CRSP stock return data starting in January 1967 and ending in December 2017 (612 months, the recent sample). Decile portfolios are formed by sorting on lagged price. The first panel is based on value weighted (by lagged market capitalisation) mean monthly decile portfolio returns incorporating all common stocks (share code 10 or 11). The decile breakpoints in the first panel are based on monthly sorts of all common stock listed on the NYSE into deciles with an equal number of NYSE stocks (NYSE breakpoints). The second panel is based on equal weighted mean monthly decile portfolio returns incorporating all common stocks (share code 10 or 11) with lagged price equal to or above $1 in each month and lagged market capitalisations above the 10th percentile of common stocks on the NYSE in each month, with decile breakpoints set to ensure an equal number of stocks in each month. Decile returns in both tables are calculated using delisting-adjusted excess returns. The row labelled “p10m1” is the hedge portfolio formed by taking a long position in the decile 10 portfolio and a short position in the decile 1 portfolio. The last row, labelled “t-stat” contains t-statistics for the hedge portfolio mean return and time-series alphas. The Sharpe ratio is reported under the heading “SHARPE” and is annualised. All other measures are reported on a monthly basis. The geometric return is reported under heading “GEO”. The maximum drawdown is reported under the heading “MDD”. The t-statistics reported are based on Newey–West HAC robust standard errors with a lag of 12 months. Significance levels are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01). The monthly time-series alphas reported are estimated as follows: CAPM-α: rthedge = + (MKTRFt ) + t . FF3-α: rthedge = + 1 (MKTRFt ) + 2 (SMBff 3t ) + 3 (HMLff 3t ) + t . FFC4-α: rthedge = + 1 (MKTRFt ) + 2 (SMBff 3t ) + 3 (HMLff 3t ) + 4 (UMDt ) + t . HXZ4α: rthedge = + 1 (MKTt ) + 2 (MEt ) + 3 (I 2A) + 4 (ROE ) + t . FF5-α: rthedge = + 1 (MKTRFt ) + 2 (SMBt ) + 3 (HMLt ) + 4 (RMWt ) + 5 (CMAt ) + t . FF6-α: rthedge = + 1 (MKTRFt ) + 2 (SMBt ) + 3 (HMLt ) + 4 (RMWt ) + 5 (CMAt ) + 6 (UMDt ) + t . Value weighted price hedge portfolio timeseries statistics
p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p10m1 t−stat
N
MEAN
GEO
SD
SHARPE
MDD
MIN
CAPM-α
FF3-α
FFC4-α
HXZ4-α
FF5-α
FF6-α
612 612 612 612 612 612 612 612 612 612 612
0.0046 0.0067 0.0067 0.0077 0.0065 0.0062 0.0053 0.0057 0.0058 0.0051 0.0005 (0.17)
0.0009 0.0042 0.0048 0.0061 0.0052 0.0050 0.0041 0.0046 0.0048 0.0041 −0.0022
0.0867 0.0711 0.0629 0.0569 0.0521 0.0496 0.0481 0.0456 0.0442 0.0431 0.0693
0.19 0.34 0.39 0.49 0.45 0.45 0.39 0.44 0.47 0.42 0.03
0.90 0.77 0.68 0.62 0.63 0.57 0.69 0.55 0.55 0.57 0.88
−0.3269 −0.3042 −0.3028 −0.2283 −0.2256 −0.2149 −0.2389 −0.2309 −0.2185 −0.2225 −0.5762
−0.0034 −0.0006 0.0000 0.0015 0.0007 0.0006 −0.0003 0.0004 0.0006 0.0001 0.0035 (1.29)
−0.0060 −0.0030 −0.0021 −0.0001 −0.0007 −0.0005 −0.0011 −0.0001 0.0006 0.0013 0.0073*** (4.59)
−0.0010 0.0009 0.0008 0.0026 0.0011 0.0010 −0.0003 0.0002 0.0004 −0.0001 0.0009 (0.49)
0.0029 0.0024 0.0020 0.0034 0.0009 0.0007 −0.0009 −0.0008 −0.0002 0.0002 −0.0027 (−0.95)
−0.0024 −0.0009 −0.0006 0.0012 −0.0006 −0.0004 −0.0013 −0.0007 −0.0000 0.0011 0.0035 (1.47)
0.0015 0.0021 0.0016 0.0033 0.0009 0.0008 −0.0007 −0.0004 −0.0001 −0.0000 −0.0015 (−0.79)
Equal weighted price hedge portfolio timeseries statistics
p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p10m1 t−stat
N
MEAN
GEO
SD
SHARPE
MDD
MIN
CAPM-α
FF3-α
FFC4-α
HXZ4-α
FF5-α
FF6-α
612 612 612 612 612 612 612 612 612 612 612
0.0043 0.0068 0.0072 0.0077 0.0079 0.0077 0.0077 0.0068 0.0066 0.0069 0.0025 (1.02)
0.0007 0.0043 0.0052 0.0060 0.0063 0.0063 0.0064 0.0056 0.0055 0.0057 0.0006
0.0857 0.0701 0.0639 0.0585 0.0560 0.0525 0.0503 0.0490 0.0476 0.0484 0.0596
0.18 0.35 0.41 0.48 0.51 0.53 0.55 0.50 0.50 0.51 0.15
0.89 0.76 0.70 0.73 0.71 0.68 0.63 0.65 0.61 0.57 0.80
−0.3420 −0.3256 −0.3206 −0.2830 −0.2847 −0.2612 −0.2494 −0.2671 −0.2478 −0.2406 −0.4853
−0.0040 −0.0005 0.0004 0.0013 0.0017 0.0018 0.0020 0.0012 0.0011 0.0015 0.0055** (2.44)
−0.0066 −0.0026 −0.0015 −0.0004 0.0001 0.0005 0.0008 0.0005 0.0008 0.0021 0.0087*** (5.34)
−0.0022 −0.0000 0.0002 0.0007 0.0009 0.0008 0.0006 −0.0001 −0.0002 0.0001 0.0023 (1.34)
0.0010 0.0010 0.0009 0.0011 0.0004 0.0002 0.0004 −0.0001 −0.0001 0.0012 0.0002 (0.07)
−0.0034 −0.0014 −0.0006 0.0000 −0.0001 0.0002 0.0005 0.0002 0.0008 0.0026 0.0059** (2.39)
−0.0000 0.0007 0.0006 0.0009 0.0005 0.0004 0.0004 −0.0003 −0.0000 0.0009 0.0009 (0.48)
in the decile 1 portfolio yields 5 basis points per month (25 basis points per month equal weighted). The hedge portfolio returns are not significantly different from zero. For the value weighted price hedge portfolio the time series alphas obtained from benchmark risk models are all small and statistically insignificant, with the notable exception of the Fama and French (1993) 3-factor model which yields a monthly alpha of 73 basis points per month (t-statistic 4.59). The results diverge when we consider the equal weighted hedge portfolio. Of the six benchmark models, half yield statistically significant alpha’s (CAPM, FF3 and FF5). Overall the time series evidence is too weak to reject the null hypothesis that price is not predictive of realised returns. While there is some evidence for return predictability, it is generally limited to the Fama–French 3-factor model or equal weighted returns (under some benchmark models). In particular, the value weighted time-series alphas are small, statistically insignificant and of variable sign under the more recent q-factor model of Hou et al. (2015) and the five- and six-factor models of Fama and French (2015; 2018). In Table 2 we collate the mean returns and benchmark time-series alphas (organised by rows) for the recent sample as well as the full sample, reporting value weighted and equal weighted results for price-sorted hedge portfolios. Since the factors for the q-factor model of Hou et al. (2015) and the five- and six-factor models of Fama and French (2015; 2018) are only available in the recent sample, we do not report full sample results for these more recent benchmark models. 141
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Table 2 Summary of price hedge portfolio means and time-series alphas. The table below is based on monthly CRSP stock return data starting in January 1967 and ending in December 2017 (612 months) for the recent sample and starting in July 1926 and ending in December 2017 for the full sample (1098 months). The full sample omits the Hou et al. (2015) q-factor model and the later Fama and French (2015) models since we lack factor returns for the full sample. The coefficients and t-statistics reported are for price decile hedge portfolio means and time-series alphas from benchmark models. Coefficients are reported in basis points per month. The hedge portfolios are constructed as detailed in Table 1. The t-statistics reported are based on Newey–West HAC robust standard errors with a lag of 12 months. Significance levels are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01). Recent sample
Full sample
Value weighted Coefficients (basis points/month)
Equal weighted
Value weighted
Equal weighted
Mean CAPM-α FF3-α FFC4-α HXZ4-α FF5-α FF6-α t-statistics
5 35 73*** 9 −27 35 −15
25 55*** 87*** 23 2 59*** 9
−35 16 55*** 0
−12 38** 71*** 17
Mean CAPM-α FF3-α FFC4-α HXZ4-α FF5-α FF5-α
(0.17) (1.29) (4.59) (0.49) (−0.95) (1.47) (−0.79)
(1.02) (2.44) (5.34) (1.34) (0.07) (2.39) (0.48)
(−1.10) (0.65) (3.60) (0.01)
(−0.47) (2.01) (5.57) (1.34)
Table 3 Two-way sort on size and price (full sample). The table below is based on monthly CRSP stock return data in starting in December 1926 and ending in December 2017 for the full sample. The table shows a two-way sort of all common stocks (share code 10 or 11) by size (the primary sorting variable) and then within each size quintile by the secondary sorting variable, price. The size quintiles are based on monthly sorts of all common stocks into 5 quintiles with an equal number of NYSE common stocks in each month. Within each size quintile stocks are again sorted into NYSE breakpointed price quintiles. The tables report the value weighted mean monthly return (in basis points) for intersections of size quintiles and “within” secondary sort variable (price) quintiles. Returns are delisting-adjusted total returns. The row labelled HML reports the difference between the secondary sorting variable quintile 5 and quintile 1. Standard errors for hedge portfolio returns are calculated using a weighted robust OLS regression. Standard errors are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01) respectively. Value weighted mean returns Size quintile Price quintile
1
2
3
4
5
All
1 2 3 4 5 HML All
−14 22 52 62 83 97*** 47
36 63 78 72 79 43*** 67
51 78 70 71 64 13 67
62 73 68 67 73 11 69
55 48 58 55 58 3 55
53 53 61 58 61 8 58
The Fama and French (1993) 3-factor model invariably produces economically and statistically significant time-series alphas, ranging from 55 basis points to 87 basis points per month. If we only consider equal weighted portfolios the CAPM model and the Fama and French (2015) 5-factor model also yield statistically significant alphas, albeit lower in economic terms. Cremers et al. (2012) shows that the Fama and French (1993) 3-factor model produces statistically and economically significant positive alphas even for benchmark indices such as the S&P 500 index. In contrast, the more recent benchmark models yield insignificant alphas of variable sign (with the exception of the Fama and French (2015) 5-factor equal weighted price alpha). The mean hedge portfolio return based on raw returns (the row labelled Mean in Table 2) is never statistically or economically significant and is of variable sign. Singal and Tayal (2017) argues that it is necessary to control for the effect of size in order to make the price effect apparent. In Table 3 we conduct a two-way sort by size and then, within each size quintile, by price using the full sample. We use NYSE breakpoints for both size and price quintiles. The price (high-minus-low) quintile hedge portfolio is positive and significant for the first and second size quintiles, suggesting a high price effect in the smaller stocks. However, the price hedge portfolio is not significant 142
Finance Research Letters 30 (2019) 139–144
P. Geertsema and H. Lu
Table 4 Two-way sort on decade and price (full sample). The table below is based on monthly CRSP stock return data in December 1925 and ending in December 2017 for the full sample. The table shows a two-way sort of all common stocks (share code 10 or 11) by decade (the primary sorting variable) and then within each decade by price. The decade is based on the decade of the realised stock return. Within each decade stocks are again sorted into NYSE breakpointed price. The tables report the value weighted mean monthly return (in basis points) for intersections of decade and “within” price quintiles. Returns are delisting-adjusted total returns. The row labelled HML reports the difference between the secondary sorting variable quintile 5 and quintile 1. Standard errors for hedge portfolio returns are calculated using a weighted robust OLS regression. Standard errors are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01) respectively. Value weighted mean returns Decade Price
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
All
1 2 3 4 5 HML All
−81 11 54 37 123 204 *** 81
−9 −56 −22 −19 −38 −29 −33
111 100 92 89 64 −47 ** 76
112 99 96 87 113 1 105
56 25 22 17 24 −32 *** 24
33 35 29 16 0 −33 *** 10
−47 47 68 58 50 97 *** 49
52 85 77 78 139 87 *** 115
−8 19 −17 −12 −49 −41 *** −27
102 107 117 116 113 11 114
39 62 59 59 57 19 ** 58
Table 5 Price quintile hedge portfolio performance in size-decade sub-samples. The tables below are based on monthly panel data from the full sample spanning December 1925 to December 2017 (inclusive) using common stocks (share codes 10 or 11). The columns contain results pertaining to quintiles sorted by size. The size quintiles are based on NYSE breakpoints such that each quintile contains an equal number of NYSE listed common stocks in each month. The rows contain results relating to consecutive decades. Each intersection of size quintile and decade contains the price quintile hedge portfolio (P5-P1) mean return (in basis points) calculated using observations within that size quintile and decade. Price quintiles within each intersection are calculated using NYSE breakpoints in each month. Panel A tabulates value weighted (by lagged market capitalisation) price hedge portfolio returns and Panel B tabulates the count of observations. Standard errors for hedge portfolio returns are calculated using a weighted robust OLS regression. Standard errors are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01) respectively. Panel A: Value weighted mean returns Size quintiles (NYSE breakpoints) Decade
1
2
3
4
5
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
−170 −145* −52 −11 −56*** 10 214*** 90*** 72*** 102***
121* −54 −15 −4 47** −6 132*** 51*** 41** 14
59 −66 −46** 21 25 −31* 80*** 43** −35* 21
130** −27 −50** 27* −1 −15 28* 69*** −38* 23
133** 17 −35* 42** 14 −17 −21 83*** −45* −1
Panel B: Count of observations Size quintiles (NYSE breakpoints) Decade
1
2
3
4
5
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
4920 16,899 20,090 24,432 94,216 292,265 446,591 501,145 358,092 183,967
4953 17,002 20,226 24,586 34,875 64,966 86,318 116,792 92,391 61,439
5003 17,071 20,244 24,626 31,350 49,278 56,509 70,258 61,693 42,129
4966 17,070 20,254 24,627 29,466 39,662 40,570 53,548 49,820 36,627
5095 17,312 20,309 24,707 28,731 35,231 34,451 43,697 43,752 33,171
in the 3rd, 4th and 5th size quintiles. The evidence in favour of a high price effect is concentrated in the first two size quintiles that together account for only 7% of market capitalisation, with no significant predictability evident in the remaining 93% of market capitalisation. 143
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Next we consider the predictive power of price in sequential chronological sub-samples, each a decade in length. Table 4 presents the results of sorting by price within each decade. A very strong high price effect is evident in the 1920’s. The statistically significant price hedge portfolio returns are negative or insignificant from 1930 to 1970 inclusive. From 1980 to 2010 the significant price hedge portfolios are positive, with the notable exception of the 2000’s. To gain a better understanding of the prevalence of the price effect across time and within different size groupings, we construct a two-way tabulation of mean price hedge portfolio returns within the intersection of decade and size quintiles. This is effectively a sequential three-way sort by decade, then (within each decade) by size quintile, then (within each decade and size quintile intersection) by price quintile. The results for mean quintile hedge portfolio returns sorted on price are collated in Table 5. In Table 5 the columns contain results pertaining to quintiles sorted by size. The size quintiles are based on NYSE breakpoints. The rows contain results relating to consecutive decades. Each intersection of size quintile and decade contains the price quintile hedge portfolio mean return (in basis points) calculated using only observations within that size quintile and decade. Price quintiles within each intersection are constructed using NYSE breakpoints. Panel A tabulates value weighted (by lagged market capitalisation) price hedge portfolio returns and Panel B tabulates the count of observations. We find that the pattern of value weighted hedge portfolio returns detailed in Panel A of Table 5 are not uniform. While hedge portfolio returns are significant in some size and decade intersections, the sign varies. It appears that there was a broadly positive relationship between price quintile and realised return in the 1980’s and the 1990’s (a high price effect). In the other decades the significant hedge portfolio returns are sparser. The relationship is predominantly negative up to 1980 (a low price effect). This may explain the findings in Blume and Husic (1973) and Bachrach and Galai (1979), who both document a low price effect. From the 1980’s onwards a positive relationship between price and return is evident in most of the significant hedge portfolio returns, with the notable exception of the 2000’s, where a negative relationship is evident in the three largest size quintiles. 3. Conclusion We re-examine the price effect in US data from 1925 to 2017. Value weighted (NYSE breakpointed) and equal weighted hedge portfolios yield mean returns that are statistically and economically insignificant. We do find modest evidence of a positive relationship between price and subsequent return (a high price effect) when using the Fama and French (1993) 3-factor model. In contrast, value weighted time-series alpha’s calculated using the CAPM, the Carhart (1997) 4-factor model, the Hou et al. (2015) qfactor model and the five- and six-factor models of Fama and French (2015; 2018) are all statistically and economically insignificant. When hedge portfolio returns based on sorting by price are calculated in sub-samples within the intersection of size quintiles and decades, we find that the predictive power is mostly concentrated in the lowest size quintiles, consistent with Singal and Tayal (2017). In addition, this predictability is predominantly negative (a low price effect) in the decades up to the 1970’s or 1980’s but predominantly positive (a high price effect) thereafter. We conclude that the evidence does not support the notion of a pervasive and stable price effect in US stocks. References Asness, C., Frazzini, A., Pedersen, L.H., 2017. Quality Minus Junk. Bachrach, B., Galai, D., 1979. The risk-return relationship and stock prices. J. Financ. Quant. Anal. 14 (2), 421–441. Baker, M., Greenwood, R., Wurgler, J., 2009. Catering through nominal share prices. J. Finance 64 (6), 2559–2590. Ball, R., Gerakos, J., Linnainmaa, J.T., Nikolaev, V.V., 2015. Deflating profitability. J. Financ. Econ. 117 (2), 225–248. Bandi, F.M., Russell, J.R., Sabbaghi, O., 2009. The Price Level Puzzle. Working Paper. Blume, M.E., Husic, F., 1973. Price, beta, and exchange listing. J. Finance 28 (2), 283–299. Brown, W.D., Pfeiffer, R.J., 2007. Causes and consequences of the relation between split-adjusted share prices and subsequent stock returns. J. Bus. Finance Acc. 34 (1–2), 292–312. https://doi.org/10.1111/j.1468-5957.2006.00645.x. Carhart, M.M., 1997. On persistence in mutual fund performance. J. Finance 52 (1), 57–82. Cremers, M., Petajisto, A., Zitzewitz, E., 2012. Should benchmark indices have alpha? Revisiting performance evaluation. Technical Report. National Bureau of Economic Research. Edmister, R.O., Greene, J.B., 1980. Performance of super-low-price stocks. J. Portf. Manage. 7 (1), 36–41. Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 33 (1), 3–56. Fama, E.F., French, K.R., 2015. A five-factor asset pricing model. J. Financ. Econ. 116 (1), 1–22. https://doi.org/10.1016/j.jfineco.2014.10.010. Fama, E.F., French, K.R., 2018. Choosing factors. J. Financ. Econ. 128 (2), 234–252. Fritzemeier, L.H., 1936. Relative price fluctuations of industrial stocks in different price groups. J. Bus. Univ. Chic. 133–154. Goodman, D.A., Peavy, J.W., 1986. The low price effect: relationship with other stock market anomalies. Rev. Bus. Econ. Res. 22 (1), 18. Green, T.C., Hwang, B.-H., 2009. Price-based return comovement. J. Financ. Econ. 93 (1), 37–50. https://doi.org/10.1016/j.jfineco.2008.09.002. Hou, K., Xue, C., Zhang, L., 2015. Digesting anomalies: an investment approach. Rev. Financ. Stud. 28, 650–705. Kumar, A., 2009. Who gambles in the stock market? J. Finance 64 (4), 1889–1933. Shumway, T., 1997. The delisting bias in CRSP data. J. Finance 52 (1), pp.327–340. Shumway, T., Warther, V.A., 1999. The delisting bias in crsp’s NASDAQ data and its implications for the size effect. J. Finance 54 (6), 2361–2379. Singal, V., Tayal, J., 2017. Stock Prices Matter. SSRN. Zaremba, A., Shemer, J., 2018. Price-based Investment Strategies. Palgrave Macmillan, pp. 213–225. Chapter 7
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Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Revisiting the price effect in US stocks Paul Geertsema
⁎,1
, Helen Lu1
T
Department of Accounting and Finance, University of Auckland Business School, Owen G Glenn Building, 12 Grafton Road, Auckland, New Zealand
ARTICLE INFO
ABSTRACT
Keywords: Return predictability Price effect Benchmark models
Nominal price does not predict average stock returns in the cross-section of US stocks using the NYSE break-pointed, value-weighted portfolio formation approach adopted in the recent assetpricing literature. The evidence in support of return predictability is largely constrained to small stocks, with a “low price effect” more prevalent up to the 1970’s and a “high price effect” more prevalent from 1980 onwards. Among the six asset-pricing models tested in our study, only the Fama–French 3-factor model consistently yields positive alphas for trading strategies based on nominal stock prices.
JEL classification: G12 G14
1. Introduction and literature The price anomaly is one of the earliest documented anomalies, with some of the first evidence dating back to a study by Fritzemeier (1936). Since then a number of studies have documented a relationship between stock price and subsequent realised return in the US stock market. The early literature mostly documents a “low price effect” in which stocks with low nominal prices earn higher than average subsequent returns (Fritzemeier, 1936; Blume and Husic, 1973; Bachrach and Galai, 1979; Edmister and Greene, 1980; Goodman and Peavy, 1986), but a recent working paper by Singal and Tayal (2017) find evidence supporting a “high price effect” in US stock return data from 1962 to 2015, such that stocks with high nominal prices outperform stocks with low nominal prices. We explain the conflicting findings in the literature by examining fine-grained sub-samples in the US data. Our results show that the predictive power of nominal prices are concentrated in small stocks (consistent with Singal and Tayal, 2017) but also that the direction of return predictability flipped signs after the 1970s. Specifically, when we partition stocks by size quintile and decade we find that statistically meaningful price hedge portfolio returns are concentrated in the small stock quintiles and that the direction of return predictability changes from mostly negative (a low price effect) in the early decades spanning 1930 to 1970 to mostly positive (a high price effect) from 1980 onwards. Our work is closely related to chapter 7 of Zaremba and Shemer (2018) which includes a comprehensive review of the price anomaly literature, in addition to cross-country empirical tests of the price effect. Their chapter opens with the observation that “the evidence on the precise direction of the price impact on future returns remains to a large extent confusing” (page 213). While Zaremba and Shemer (2018) documents a low-price effect in several countries based on CAPM alphas of equal-weighted portfolios, we take a different approach by applying more recent techniques to US data. Specifically, we use portfolios based on NYSE breakpoints and value-weighted returns which has emerged as the norm for recent empirical asset pricing research (for example, see Asness et al., 2017; Ball et al., 2015; Fama and French, 2015; Hou et al., 2015). This approach seeks to mitigate the influence from micro-cap stocks which can otherwise swamp price-sorted quantiles. The other point of difference is that we incorporate the latest generation of benchmark models in our analysis. In addition to the CAPM model used by Zaremba and Shemer (2018) and the commonly used Corresponding author. E-mail addresses: [email protected] (P. Geertsema), [email protected] (H. Lu). 1 Postal address: The University of Auckland Business School, Private Bag 92019, Auckland 1142, New Zealand. ⁎
https://doi.org/10.1016/j.frl.2019.03.017 Received 18 October 2018; Received in revised form 7 January 2019; Accepted 6 March 2019 Available online 09 March 2019 1544-6123/ © 2019 Elsevier Inc. All rights reserved.
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Fama and French (1993) 3-factor model, we also apply the Carhart model (Carhart, 1997), the q-factor model of Hou et al. (2015) and the five- and six-factor models of Fama and French (2015, 2018). Contrary to both the earlier literature and the recent work by Singal and Tayal (2017) and Zaremba and Shemer (2018), we conclude that the US evidence is insufficient to support the notion of a stable price effect in either direction. Specifically, returns to trading strategies based on prices only consistently generate significant and positive alphas under the Fama and French (1993) 3-factor model. However, this price effect disappears when using the more recent Carhart model (Carhart, 1997), q-factor model of Hou et al. (2015) or the five- and six-factor models of Fama and French (2015, 2018). Attempts have been made to explain the empirical relationship between stock prices and subsequent stock returns. Brown and Pfeiffer (2007) find that survivorship bias accounts for about half the returns to their price hedge strategy.2 Green and Hwang (2009) demonstrate that stocks with similar prices co-move and argue that this is as a result of investors categorising stocks based on price. It is possible that some investors believe that stocks with lower prices have more “potential upside”. Building on this intuition (Kumar, 2009) shows that individual investors appear to prefer lottery-type stocks (which tend also to be stocks with lower prices) and that this preference is strongest in lower socio-economic groups. Baker et al. (2009) show that firms respond to the demand for low priced stocks via stock splits. In robustness checks (Bandi et al., 2009) consider whether price proxies for stock-splits, which may convey information (as a signalling device by management), but find no evidence to suggest that this is the case. Our study does not aim at explaining the price anomaly. Instead, we show that the evidence for a stable price effect is lacking in the US stocks because the direction of the price effect is sample specific, primarily present in small stocks and hedge portfolio alphas obtained from the more recent asset-pricing models are generally insignificant. 2. Data and tests For empirical tests we turn to CRSP/Compustat merged monthly US stock return data and annual accounting data. We consider two samples. The first sample, which we term the “full sample”, starts in December 1925 and ends in December 2017 (inclusive).3 The second sample, which we term the “recent sample”, starts in January 1967 and ends in December 2017 (inclusive). The recent sample reflects the availability of benchmark factors used in time-series alpha tests. In particular, the 5 and 6-factor Fama–French models becomes available in July of 1963 (limited by the availability of Compustat data required for the construction of those factors) while the Hou et al. (2015) q-factors are only available starting in January of 1967 – which we take as the starting point of our “recent sample”. The dependent variable r is the monthly CRSP total return (CRSP variable RET) adjusted for delisting returns less the risk free rate (RF, sourced from Ken French’s data library as described below). If delisting returns are missing and the delisting code is greater than 200 we substitute a delisting return of −55% for NASDAQ stocks (Shumway and Warther, 1999) and a delisting return of −30% for all other stocks (Shumway, 1997). Our main explanatory variable is price, which is equal to the absolute value of CRSP variable PRC. (1)
pricet = |PRCt |
In constructing equal weighted portfolios we only include common US stocks (share code 10 or 11) in CRSP with lagged market capitalisations above the 10th percentile of common stocks listed on the NYSE in each month and with lagged prices equal to or above $1 in each month. Value weighted portfolios include all common US stocks (share code 10 or 11) in CRSP but use NYSE breakpoints such that each decile contains an equal number of NYSE common stocks in each month. In hedge portfolio time series tests we control for the market excess return (MKTRF) as well as the time-series factors formed by sorting on size (SMB), book-to-market (HML), momentum (UMD), investment (CMA) and profitability (RMW). We use the risk free rate (RF) to calculate excess returns. The original Fama and French (1993) factors are identified by post-fixing them with “ff3” (SMBff3 and HMLff3) to distinguish them from the factors used in the other Fama and French factor models.4 In addition we make use the Hou et al. (2015) q-factor model consisting of the market factor (MKT), a size factor (ME), an investment factor (I2A) and a profitability factor (ROE).5 The decile portfolio returns for price using the recent sample are summarised in Table 1. The first panel summarises value weighted portfolio decile returns and the second panel summarises equal weighted portfolio decile returns. For brevity we discuss the value weighted results, noting the equal weighted results (in parenthesis) only when they are significantly different from the value weighted results. It is evident that unadjusted portfolio returns are not monotonically related to the price deciles. In fact, the highest returns are clustered around the middle portfolios. The lowest decile portfolio, corresponding to the lowest price stocks, produces notably lower returns than the other portfolios. The hedge portfolio formed by taking a long position in the decile 10 portfolio and a short position 2 In this paper all realised returns are delisting adjusted, thus mitigating the potential impact of survivorship bias. See the Data section for more detail. 3 In tests that rely on the Fama and French (1993) factors the full sample starts in July 1926 rather than December 1925, reflecting the availability of the factors. 4 These factors were sourced from Ken French’s data library at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. The factor time series starts in July 1926 and ends in December 2017. 5 A special thanks to Lu Zhang for kindly making available the q-factor data. The q-factor time series starts in January 1967 and ends in December 2017.
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Table 1 Price sorted portfolio summary (recent sample). The results below are calculated using monthly CRSP stock return data starting in January 1967 and ending in December 2017 (612 months, the recent sample). Decile portfolios are formed by sorting on lagged price. The first panel is based on value weighted (by lagged market capitalisation) mean monthly decile portfolio returns incorporating all common stocks (share code 10 or 11). The decile breakpoints in the first panel are based on monthly sorts of all common stock listed on the NYSE into deciles with an equal number of NYSE stocks (NYSE breakpoints). The second panel is based on equal weighted mean monthly decile portfolio returns incorporating all common stocks (share code 10 or 11) with lagged price equal to or above $1 in each month and lagged market capitalisations above the 10th percentile of common stocks on the NYSE in each month, with decile breakpoints set to ensure an equal number of stocks in each month. Decile returns in both tables are calculated using delisting-adjusted excess returns. The row labelled “p10m1” is the hedge portfolio formed by taking a long position in the decile 10 portfolio and a short position in the decile 1 portfolio. The last row, labelled “t-stat” contains t-statistics for the hedge portfolio mean return and time-series alphas. The Sharpe ratio is reported under the heading “SHARPE” and is annualised. All other measures are reported on a monthly basis. The geometric return is reported under heading “GEO”. The maximum drawdown is reported under the heading “MDD”. The t-statistics reported are based on Newey–West HAC robust standard errors with a lag of 12 months. Significance levels are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01). The monthly time-series alphas reported are estimated as follows: CAPM-α: rthedge = + (MKTRFt ) + t . FF3-α: rthedge = + 1 (MKTRFt ) + 2 (SMBff 3t ) + 3 (HMLff 3t ) + t . FFC4-α: rthedge = + 1 (MKTRFt ) + 2 (SMBff 3t ) + 3 (HMLff 3t ) + 4 (UMDt ) + t . HXZ4α: rthedge = + 1 (MKTt ) + 2 (MEt ) + 3 (I 2A) + 4 (ROE ) + t . FF5-α: rthedge = + 1 (MKTRFt ) + 2 (SMBt ) + 3 (HMLt ) + 4 (RMWt ) + 5 (CMAt ) + t . FF6-α: rthedge = + 1 (MKTRFt ) + 2 (SMBt ) + 3 (HMLt ) + 4 (RMWt ) + 5 (CMAt ) + 6 (UMDt ) + t . Value weighted price hedge portfolio timeseries statistics
p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p10m1 t−stat
N
MEAN
GEO
SD
SHARPE
MDD
MIN
CAPM-α
FF3-α
FFC4-α
HXZ4-α
FF5-α
FF6-α
612 612 612 612 612 612 612 612 612 612 612
0.0046 0.0067 0.0067 0.0077 0.0065 0.0062 0.0053 0.0057 0.0058 0.0051 0.0005 (0.17)
0.0009 0.0042 0.0048 0.0061 0.0052 0.0050 0.0041 0.0046 0.0048 0.0041 −0.0022
0.0867 0.0711 0.0629 0.0569 0.0521 0.0496 0.0481 0.0456 0.0442 0.0431 0.0693
0.19 0.34 0.39 0.49 0.45 0.45 0.39 0.44 0.47 0.42 0.03
0.90 0.77 0.68 0.62 0.63 0.57 0.69 0.55 0.55 0.57 0.88
−0.3269 −0.3042 −0.3028 −0.2283 −0.2256 −0.2149 −0.2389 −0.2309 −0.2185 −0.2225 −0.5762
−0.0034 −0.0006 0.0000 0.0015 0.0007 0.0006 −0.0003 0.0004 0.0006 0.0001 0.0035 (1.29)
−0.0060 −0.0030 −0.0021 −0.0001 −0.0007 −0.0005 −0.0011 −0.0001 0.0006 0.0013 0.0073*** (4.59)
−0.0010 0.0009 0.0008 0.0026 0.0011 0.0010 −0.0003 0.0002 0.0004 −0.0001 0.0009 (0.49)
0.0029 0.0024 0.0020 0.0034 0.0009 0.0007 −0.0009 −0.0008 −0.0002 0.0002 −0.0027 (−0.95)
−0.0024 −0.0009 −0.0006 0.0012 −0.0006 −0.0004 −0.0013 −0.0007 −0.0000 0.0011 0.0035 (1.47)
0.0015 0.0021 0.0016 0.0033 0.0009 0.0008 −0.0007 −0.0004 −0.0001 −0.0000 −0.0015 (−0.79)
Equal weighted price hedge portfolio timeseries statistics
p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p10m1 t−stat
N
MEAN
GEO
SD
SHARPE
MDD
MIN
CAPM-α
FF3-α
FFC4-α
HXZ4-α
FF5-α
FF6-α
612 612 612 612 612 612 612 612 612 612 612
0.0043 0.0068 0.0072 0.0077 0.0079 0.0077 0.0077 0.0068 0.0066 0.0069 0.0025 (1.02)
0.0007 0.0043 0.0052 0.0060 0.0063 0.0063 0.0064 0.0056 0.0055 0.0057 0.0006
0.0857 0.0701 0.0639 0.0585 0.0560 0.0525 0.0503 0.0490 0.0476 0.0484 0.0596
0.18 0.35 0.41 0.48 0.51 0.53 0.55 0.50 0.50 0.51 0.15
0.89 0.76 0.70 0.73 0.71 0.68 0.63 0.65 0.61 0.57 0.80
−0.3420 −0.3256 −0.3206 −0.2830 −0.2847 −0.2612 −0.2494 −0.2671 −0.2478 −0.2406 −0.4853
−0.0040 −0.0005 0.0004 0.0013 0.0017 0.0018 0.0020 0.0012 0.0011 0.0015 0.0055** (2.44)
−0.0066 −0.0026 −0.0015 −0.0004 0.0001 0.0005 0.0008 0.0005 0.0008 0.0021 0.0087*** (5.34)
−0.0022 −0.0000 0.0002 0.0007 0.0009 0.0008 0.0006 −0.0001 −0.0002 0.0001 0.0023 (1.34)
0.0010 0.0010 0.0009 0.0011 0.0004 0.0002 0.0004 −0.0001 −0.0001 0.0012 0.0002 (0.07)
−0.0034 −0.0014 −0.0006 0.0000 −0.0001 0.0002 0.0005 0.0002 0.0008 0.0026 0.0059** (2.39)
−0.0000 0.0007 0.0006 0.0009 0.0005 0.0004 0.0004 −0.0003 −0.0000 0.0009 0.0009 (0.48)
in the decile 1 portfolio yields 5 basis points per month (25 basis points per month equal weighted). The hedge portfolio returns are not significantly different from zero. For the value weighted price hedge portfolio the time series alphas obtained from benchmark risk models are all small and statistically insignificant, with the notable exception of the Fama and French (1993) 3-factor model which yields a monthly alpha of 73 basis points per month (t-statistic 4.59). The results diverge when we consider the equal weighted hedge portfolio. Of the six benchmark models, half yield statistically significant alpha’s (CAPM, FF3 and FF5). Overall the time series evidence is too weak to reject the null hypothesis that price is not predictive of realised returns. While there is some evidence for return predictability, it is generally limited to the Fama–French 3-factor model or equal weighted returns (under some benchmark models). In particular, the value weighted time-series alphas are small, statistically insignificant and of variable sign under the more recent q-factor model of Hou et al. (2015) and the five- and six-factor models of Fama and French (2015; 2018). In Table 2 we collate the mean returns and benchmark time-series alphas (organised by rows) for the recent sample as well as the full sample, reporting value weighted and equal weighted results for price-sorted hedge portfolios. Since the factors for the q-factor model of Hou et al. (2015) and the five- and six-factor models of Fama and French (2015; 2018) are only available in the recent sample, we do not report full sample results for these more recent benchmark models. 141
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Table 2 Summary of price hedge portfolio means and time-series alphas. The table below is based on monthly CRSP stock return data starting in January 1967 and ending in December 2017 (612 months) for the recent sample and starting in July 1926 and ending in December 2017 for the full sample (1098 months). The full sample omits the Hou et al. (2015) q-factor model and the later Fama and French (2015) models since we lack factor returns for the full sample. The coefficients and t-statistics reported are for price decile hedge portfolio means and time-series alphas from benchmark models. Coefficients are reported in basis points per month. The hedge portfolios are constructed as detailed in Table 1. The t-statistics reported are based on Newey–West HAC robust standard errors with a lag of 12 months. Significance levels are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01). Recent sample
Full sample
Value weighted Coefficients (basis points/month)
Equal weighted
Value weighted
Equal weighted
Mean CAPM-α FF3-α FFC4-α HXZ4-α FF5-α FF6-α t-statistics
5 35 73*** 9 −27 35 −15
25 55*** 87*** 23 2 59*** 9
−35 16 55*** 0
−12 38** 71*** 17
Mean CAPM-α FF3-α FFC4-α HXZ4-α FF5-α FF5-α
(0.17) (1.29) (4.59) (0.49) (−0.95) (1.47) (−0.79)
(1.02) (2.44) (5.34) (1.34) (0.07) (2.39) (0.48)
(−1.10) (0.65) (3.60) (0.01)
(−0.47) (2.01) (5.57) (1.34)
Table 3 Two-way sort on size and price (full sample). The table below is based on monthly CRSP stock return data in starting in December 1926 and ending in December 2017 for the full sample. The table shows a two-way sort of all common stocks (share code 10 or 11) by size (the primary sorting variable) and then within each size quintile by the secondary sorting variable, price. The size quintiles are based on monthly sorts of all common stocks into 5 quintiles with an equal number of NYSE common stocks in each month. Within each size quintile stocks are again sorted into NYSE breakpointed price quintiles. The tables report the value weighted mean monthly return (in basis points) for intersections of size quintiles and “within” secondary sort variable (price) quintiles. Returns are delisting-adjusted total returns. The row labelled HML reports the difference between the secondary sorting variable quintile 5 and quintile 1. Standard errors for hedge portfolio returns are calculated using a weighted robust OLS regression. Standard errors are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01) respectively. Value weighted mean returns Size quintile Price quintile
1
2
3
4
5
All
1 2 3 4 5 HML All
−14 22 52 62 83 97*** 47
36 63 78 72 79 43*** 67
51 78 70 71 64 13 67
62 73 68 67 73 11 69
55 48 58 55 58 3 55
53 53 61 58 61 8 58
The Fama and French (1993) 3-factor model invariably produces economically and statistically significant time-series alphas, ranging from 55 basis points to 87 basis points per month. If we only consider equal weighted portfolios the CAPM model and the Fama and French (2015) 5-factor model also yield statistically significant alphas, albeit lower in economic terms. Cremers et al. (2012) shows that the Fama and French (1993) 3-factor model produces statistically and economically significant positive alphas even for benchmark indices such as the S&P 500 index. In contrast, the more recent benchmark models yield insignificant alphas of variable sign (with the exception of the Fama and French (2015) 5-factor equal weighted price alpha). The mean hedge portfolio return based on raw returns (the row labelled Mean in Table 2) is never statistically or economically significant and is of variable sign. Singal and Tayal (2017) argues that it is necessary to control for the effect of size in order to make the price effect apparent. In Table 3 we conduct a two-way sort by size and then, within each size quintile, by price using the full sample. We use NYSE breakpoints for both size and price quintiles. The price (high-minus-low) quintile hedge portfolio is positive and significant for the first and second size quintiles, suggesting a high price effect in the smaller stocks. However, the price hedge portfolio is not significant 142
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Table 4 Two-way sort on decade and price (full sample). The table below is based on monthly CRSP stock return data in December 1925 and ending in December 2017 for the full sample. The table shows a two-way sort of all common stocks (share code 10 or 11) by decade (the primary sorting variable) and then within each decade by price. The decade is based on the decade of the realised stock return. Within each decade stocks are again sorted into NYSE breakpointed price. The tables report the value weighted mean monthly return (in basis points) for intersections of decade and “within” price quintiles. Returns are delisting-adjusted total returns. The row labelled HML reports the difference between the secondary sorting variable quintile 5 and quintile 1. Standard errors for hedge portfolio returns are calculated using a weighted robust OLS regression. Standard errors are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01) respectively. Value weighted mean returns Decade Price
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
All
1 2 3 4 5 HML All
−81 11 54 37 123 204 *** 81
−9 −56 −22 −19 −38 −29 −33
111 100 92 89 64 −47 ** 76
112 99 96 87 113 1 105
56 25 22 17 24 −32 *** 24
33 35 29 16 0 −33 *** 10
−47 47 68 58 50 97 *** 49
52 85 77 78 139 87 *** 115
−8 19 −17 −12 −49 −41 *** −27
102 107 117 116 113 11 114
39 62 59 59 57 19 ** 58
Table 5 Price quintile hedge portfolio performance in size-decade sub-samples. The tables below are based on monthly panel data from the full sample spanning December 1925 to December 2017 (inclusive) using common stocks (share codes 10 or 11). The columns contain results pertaining to quintiles sorted by size. The size quintiles are based on NYSE breakpoints such that each quintile contains an equal number of NYSE listed common stocks in each month. The rows contain results relating to consecutive decades. Each intersection of size quintile and decade contains the price quintile hedge portfolio (P5-P1) mean return (in basis points) calculated using observations within that size quintile and decade. Price quintiles within each intersection are calculated using NYSE breakpoints in each month. Panel A tabulates value weighted (by lagged market capitalisation) price hedge portfolio returns and Panel B tabulates the count of observations. Standard errors for hedge portfolio returns are calculated using a weighted robust OLS regression. Standard errors are indicated with *(p < 0.1), **(p < 0.05) and ***(p < 0.01) respectively. Panel A: Value weighted mean returns Size quintiles (NYSE breakpoints) Decade
1
2
3
4
5
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
−170 −145* −52 −11 −56*** 10 214*** 90*** 72*** 102***
121* −54 −15 −4 47** −6 132*** 51*** 41** 14
59 −66 −46** 21 25 −31* 80*** 43** −35* 21
130** −27 −50** 27* −1 −15 28* 69*** −38* 23
133** 17 −35* 42** 14 −17 −21 83*** −45* −1
Panel B: Count of observations Size quintiles (NYSE breakpoints) Decade
1
2
3
4
5
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
4920 16,899 20,090 24,432 94,216 292,265 446,591 501,145 358,092 183,967
4953 17,002 20,226 24,586 34,875 64,966 86,318 116,792 92,391 61,439
5003 17,071 20,244 24,626 31,350 49,278 56,509 70,258 61,693 42,129
4966 17,070 20,254 24,627 29,466 39,662 40,570 53,548 49,820 36,627
5095 17,312 20,309 24,707 28,731 35,231 34,451 43,697 43,752 33,171
in the 3rd, 4th and 5th size quintiles. The evidence in favour of a high price effect is concentrated in the first two size quintiles that together account for only 7% of market capitalisation, with no significant predictability evident in the remaining 93% of market capitalisation. 143
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Next we consider the predictive power of price in sequential chronological sub-samples, each a decade in length. Table 4 presents the results of sorting by price within each decade. A very strong high price effect is evident in the 1920’s. The statistically significant price hedge portfolio returns are negative or insignificant from 1930 to 1970 inclusive. From 1980 to 2010 the significant price hedge portfolios are positive, with the notable exception of the 2000’s. To gain a better understanding of the prevalence of the price effect across time and within different size groupings, we construct a two-way tabulation of mean price hedge portfolio returns within the intersection of decade and size quintiles. This is effectively a sequential three-way sort by decade, then (within each decade) by size quintile, then (within each decade and size quintile intersection) by price quintile. The results for mean quintile hedge portfolio returns sorted on price are collated in Table 5. In Table 5 the columns contain results pertaining to quintiles sorted by size. The size quintiles are based on NYSE breakpoints. The rows contain results relating to consecutive decades. Each intersection of size quintile and decade contains the price quintile hedge portfolio mean return (in basis points) calculated using only observations within that size quintile and decade. Price quintiles within each intersection are constructed using NYSE breakpoints. Panel A tabulates value weighted (by lagged market capitalisation) price hedge portfolio returns and Panel B tabulates the count of observations. We find that the pattern of value weighted hedge portfolio returns detailed in Panel A of Table 5 are not uniform. While hedge portfolio returns are significant in some size and decade intersections, the sign varies. It appears that there was a broadly positive relationship between price quintile and realised return in the 1980’s and the 1990’s (a high price effect). In the other decades the significant hedge portfolio returns are sparser. The relationship is predominantly negative up to 1980 (a low price effect). This may explain the findings in Blume and Husic (1973) and Bachrach and Galai (1979), who both document a low price effect. From the 1980’s onwards a positive relationship between price and return is evident in most of the significant hedge portfolio returns, with the notable exception of the 2000’s, where a negative relationship is evident in the three largest size quintiles. 3. Conclusion We re-examine the price effect in US data from 1925 to 2017. Value weighted (NYSE breakpointed) and equal weighted hedge portfolios yield mean returns that are statistically and economically insignificant. We do find modest evidence of a positive relationship between price and subsequent return (a high price effect) when using the Fama and French (1993) 3-factor model. In contrast, value weighted time-series alpha’s calculated using the CAPM, the Carhart (1997) 4-factor model, the Hou et al. (2015) qfactor model and the five- and six-factor models of Fama and French (2015; 2018) are all statistically and economically insignificant. When hedge portfolio returns based on sorting by price are calculated in sub-samples within the intersection of size quintiles and decades, we find that the predictive power is mostly concentrated in the lowest size quintiles, consistent with Singal and Tayal (2017). In addition, this predictability is predominantly negative (a low price effect) in the decades up to the 1970’s or 1980’s but predominantly positive (a high price effect) thereafter. We conclude that the evidence does not support the notion of a pervasive and stable price effect in US stocks. References Asness, C., Frazzini, A., Pedersen, L.H., 2017. Quality Minus Junk. Bachrach, B., Galai, D., 1979. The risk-return relationship and stock prices. J. Financ. Quant. Anal. 14 (2), 421–441. Baker, M., Greenwood, R., Wurgler, J., 2009. Catering through nominal share prices. J. Finance 64 (6), 2559–2590. Ball, R., Gerakos, J., Linnainmaa, J.T., Nikolaev, V.V., 2015. Deflating profitability. J. Financ. Econ. 117 (2), 225–248. Bandi, F.M., Russell, J.R., Sabbaghi, O., 2009. The Price Level Puzzle. Working Paper. Blume, M.E., Husic, F., 1973. Price, beta, and exchange listing. J. Finance 28 (2), 283–299. Brown, W.D., Pfeiffer, R.J., 2007. Causes and consequences of the relation between split-adjusted share prices and subsequent stock returns. J. Bus. Finance Acc. 34 (1–2), 292–312. https://doi.org/10.1111/j.1468-5957.2006.00645.x. Carhart, M.M., 1997. On persistence in mutual fund performance. J. Finance 52 (1), 57–82. Cremers, M., Petajisto, A., Zitzewitz, E., 2012. Should benchmark indices have alpha? Revisiting performance evaluation. Technical Report. National Bureau of Economic Research. Edmister, R.O., Greene, J.B., 1980. Performance of super-low-price stocks. J. Portf. Manage. 7 (1), 36–41. Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 33 (1), 3–56. Fama, E.F., French, K.R., 2015. A five-factor asset pricing model. J. Financ. Econ. 116 (1), 1–22. https://doi.org/10.1016/j.jfineco.2014.10.010. Fama, E.F., French, K.R., 2018. Choosing factors. J. Financ. Econ. 128 (2), 234–252. Fritzemeier, L.H., 1936. Relative price fluctuations of industrial stocks in different price groups. J. Bus. Univ. Chic. 133–154. Goodman, D.A., Peavy, J.W., 1986. The low price effect: relationship with other stock market anomalies. Rev. Bus. Econ. Res. 22 (1), 18. Green, T.C., Hwang, B.-H., 2009. Price-based return comovement. J. Financ. Econ. 93 (1), 37–50. https://doi.org/10.1016/j.jfineco.2008.09.002. Hou, K., Xue, C., Zhang, L., 2015. Digesting anomalies: an investment approach. Rev. Financ. Stud. 28, 650–705. Kumar, A., 2009. Who gambles in the stock market? J. Finance 64 (4), 1889–1933. Shumway, T., 1997. The delisting bias in CRSP data. J. Finance 52 (1), pp.327–340. Shumway, T., Warther, V.A., 1999. The delisting bias in crsp’s NASDAQ data and its implications for the size effect. J. Finance 54 (6), 2361–2379. Singal, V., Tayal, J., 2017. Stock Prices Matter. SSRN. Zaremba, A., Shemer, J., 2018. Price-based Investment Strategies. Palgrave Macmillan, pp. 213–225. Chapter 7
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