Is individual trading priced in the preferred stock discount?

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Is individual trading priced in the preferred stock discount? Cheol Parka, Paul Moon Sub Choib, Joung Hwa Choic,

⁎,1

a

Business School, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea College of Business Administration, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Republic of Korea c Division of Global Business Administration, Kangnam University, 40 Gangnam-ro, Giheung-gu, Yongin-si, Gyeonggi-do 16979, Republic of Korea b

A R T IC LE I N F O

ABS TRA CT

JEL classification: G12 G15 G32

Individuals have long been blamed for noise trader risk. Moreover, the literature suggests that the discount of preferred shares against comparable common equities is due to dual-class differences in dividend yield, voting rights, management control, and turnover. In this paper, we argue and present evidence that noise trader risk, as proxied by the individual trading weight, explains the preferred stock discount observed in the Korean stock market after controlling for the conventional determinants. This main result and additional considerations empirically support the presence of noise trader risk.

Keywords: Preferred stock discount Noise trader risk Individual trading weight

1. Introduction The overall discount of preferred shares against their comparable common stocks is a persistent phenomenon found ubiquitously and globally. The cross-country difference in the discount corresponds to the premium of voting rights for common shareholders that varies across the borders. In this study, we look at the time-variation of the preferred stock discount (PSD) in an advanced emerging market, controlling for the conventional determinants known in the literature. The literature theoretically predicts that noise trader risk (NTR) diverges asset prices from their fundamental values. In the light of this, we specifically use the individual trading weights (ITWs) of pairs of common and preferred stocks as a proxy for NTR associated with PSD.2 Our proxy well explains PSD and shows that NTR is present in the stock market. Individual investors have long been suspected as noise traders in the stock market because of their limited access to firms' inside and fundamental information. Jensen (1968) and Lease et al. (1974) show that individuals often tend to trade single stocks on erroneous noise or invest in mutual funds at high fees rather than construct or hold a market portfolio. Kyle (1985) and Black (1986) also labeled uninformed individuals noise traders for their suboptimal trading behavior in the market. Although many studies have shown evidence of noise trading by uninformed individuals, an extensive discussion of the effect of noise trading seems to have begun after the theoretical predictions of De Long et al. (1990). In their study, they show that when the proportion of uninformed individual

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Corresponding author. E-mail addresses: [email protected] (C. Park), [email protected] (P.M.S. Choi), [email protected] (J.H. Choi). 1 Special thanks are due to Jonathan Batten (the Editor), Mark Seasholes (Associate Editor), an anonymous referee, Warren Bailey, and Andrew Karolyi. We also appreciate Jae Man Chung, Seth H. Huang, Sung Wook Joh, Bong-Chan Kho, Woojin Kim, Kuan-Hui Lee, Rae Soo Park and seminar participants at Seoul National University and the Korea Securities Association (2017). This research is based on a chapter of the Ph.D. dissertation of J.H. Choi at Seoul National University (Choi, 2015). Part of this research was conducted while P.M.S. Choi and J.H. Choi were visiting scholars at the Samuel Curtis Johnson Graduate School of Management, Cornell University, and were funded by the grants provided by the Fulbright Scholarship Program, Ewha Womans University, and the Korea Securities Association. Hyeik Kim, Ye Jun Kim and Francis Joonsung Won provided excellent research assistance. Standard disclaimer rules apply and all errors are our own. 2 As the relative price deviation of a preferred stock issue from its comparable common stock listing, PSD is measured by the excess of the common share price over the preferred stock price and divided by the common share price. https://doi.org/10.1016/j.ememar.2018.03.006 Received 13 July 2017; Received in revised form 27 February 2018; Accepted 25 March 2018 1566-0141/ © 2018 Elsevier B.V. All rights reserved.

Please cite this article as: Park, C., Emerging Markets Review (2018), https://doi.org/10.1016/j.ememar.2018.03.006

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traders in stocks increases, the transaction risk generated by the uninformed traders can limit the entrance of short-term, risk averse and rational arbitrageurs. In this case, arbitrageurs are deterred from exploiting price deviations, which causes stocks to be traded at persistent discounts, even when there is no fundamental risk in the stock market. Choi and Choi (2018) argue that ITW—defined as the proportion of individual traders-initiated buys and sells out of the total trading volume of a given stock listing—can proxy for NTR and explain the returns of common stocks. They further construct an excess return factor of sorted portfolios that are dense (high in ITW) and scarce (low in ITW) in terms of individual traders (dense-minus-scarce, DMS). The NTR factor (DMS) is then shown to significantly account for the returns of sorted portfolios in the stock markets of Korea and Taiwan, which cogently shows that NTR is priced in common stock returns in Asia. In the corporate finance literature, in addition to the dual-class differences in dividend payout, the cause of PSD has been largely explained by the absence of voting rights following Zingales' (1994, 1995) seminal works. First, private benefits with management control accompanied by voting rights can make common stocks with voting rights more valuable than preferred stock (Zingales, 1994). Second, the price deviations between common and preferred shares are not substantial in countries with well-separated corporate ownership and management and a highly diversified composition of shareholders, such as the U.S. (Zingales, 1995). Various country cases for Israel (Levy, 1983), the U.K. (Megginson, 1990), Switzerland (Horner, 1988), Korea (Chung and Kim, 1999; Kim et al., 1996) and 18 countries (Nenova, 2003) also show the cross-sectional variation of PSD along with deviations in the premium of voting rights due to the cross-border stratification of corporate governance.3 Generally speaking, a country under the civil law system with inferior shareholder protection (La Porta et al., 1998, 2002) in the emerging markets is likely to show a large premium of voting rights. However, even after accounting for largely non-volatile voting rights, PSD has shown large time variations. Further, Muravyev (2004) suggested turnover in addition to voting rights as an additional factor of the common stock premium (PSD) in Russia. The turnover factor complements the time-varying characteristic of PSD, which cannot be explained by non-volatile voting rights. In Korea, institutional changes that affect the private benefits of large shareholders in tandem with their ownership (Chung and Kim, 1999; Kim et al., 1996) and that occur in the market for corporate control (Kook and Jung, 1996), and the turnover of preferred shares (Chay and Moon, 2005; Han, 2010) appear to matter in evaluating voting rights and determining PSD. However, considering largely static dual-class differences in dividends, voting rights and time-varying turnover still leave much room for the unexplained dynamics of the discount of Korean preferred shares. In the Korean stock market, preferred stocks, on average, exhibit heavier individual trades than their comparable common listings do. Because the creation of NTR depends on the volume of uninformed individual traders (De Long et al., 1990), following Choi and Choi's (2018) suggestion of ITW as a proxy for NTR, we expect that the discount of a preferred stock will enlarge corresponding to an increase of ITW relative to that of the comparable common share. A given pair of common and preferred equities, which share the identical firm-level characteristics, can be contrasted by ITW after controlling for fundamental and systematic risks and dual-class differences in dividend yield, voting rights and turnover. Given 185 pairs of “old-type” preferred4 and common shares listed on the Korea Stock Exchange (KSE, 169) and the Kosdaq (16) from January 2000 until October 2014,5 we find that the excess of ITW of preferred shares over that of comparable common listings (relative ITW) economically and statistically significantly explains the time variation of PSD after controlling for firm-level characteristics and the aforementioned dual-class factors. Individuals in the Korean stock market turn out to deter the parity-convergence of common-preferred equity pairs, which is evidence of NTR that impedes the enforcement of price discovery. While existing studies in the literature since De Long et al. (1990) have focused on the systematic patterns of individual traders and on the dynamic relationship between investor sentiment and stock returns, this study sheds light on how a subset of investment strategies, i.e., “longpreferred, short-common”, can be priced by a parsimonious measure of NTR–ITW in our case. Our approach is made feasible due to a peculiar feature of the database (DataGuide) of our sample that identifies the ratios of investor types for every stock listing. Moreover, our choice of Korean data is motivated by several aspects. The Korea Exchange is the holding company of KSE (main board), the Kosdaq (dominantly listed with growth stocks) and the Options and Futures Exchange. These are considered some of the most active and liquid securities trading venues in the emerging (MSCI) and developed (FTSI) markets. This is a valid reflection of the Korean economy given its size and influence on global commercial transactions. The representativeness of our data implies that the implications of this empirical research can be emulated in other markets. We additionally consider several aspects surrounding the findings herein. First, we show that the source of the risk that mutually diverges the prices of common-preferred share pairs tends to systematically affect the relative pricing of preferred stocks. Specifically, statistically significantly positive correlations among factor-orthogonal relative ITWs and residual PSDs, respectively, and their substantial principal components attest that. Second, the discount of preferred shares at issuance is noticeably less than the timeaverage discount, reflecting the market-timing incentive of issuers based on the cost of capital. Third, our main finding continues to hold for relatively invariant PSDs and for the premiums of preferred shares, and under various market conditions. Lastly, while this study is primarily regarding an advanced emerging market, we find a preliminary, corresponding corroboration of NTR-priced PSD in another emerging market economy, Taiwan. The rest of this research is organized as follows. Section 2 describes data sources, defines key variables, and presents the preliminary results. Section 3 investigates the main thesis of this paper—the pricing of NTR on the discount of preferred shares. Section 4

3 PSDs in various economies are as follows: 81.5% in Italy, 45.5% in Israel, 20% in Switzerland, 13.3% in the U.K., 3% (Zingales, 1994) or 5.4% (Lease et al., 1983) in the U.S., and 10% (Chung and Kim, 1999) or 48% (Nenova, 2003) in Korea. 4 The “new type” preferred shares are introduced and tested for the robustness of our main finding in Section 4.3. 5 In the Korean stock market, trade-level investor group identification was made available since 2000.

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Table 1 Summary statistics for daily observations of common and preferred stock pairs This table is based on the pairs of “old type” preferred and common shares listed on the KSE and the Kosdaq from January 2000 until October 2014. Those listings with trading days under the January effect, i.e. the first 5 trading days in any year, listings with less than 10 trading days or of lowest 10% in trading volume, and common-preferred share pairs with higher than 10% in the preferred stock discount (PSD) are excluded from this sample. The final sample consists of 185 pairs of common and preferred stocks traded on the KSE (169) and the Kosdaq (16) with a total of 385,706 firm-day observations. Turnover is the ratio of the trading amount over the number of outstanding shares. The investor trading weight is the ratio of the trading volume of shares of a specific—individual, institutional, and foreign—investor group over the total trading volume of shares. Panel A. Return, market capitalization, trading volume, and trading amount Return (inc. div. yield)

Mean Median Std. Dev. Min Max

Preferred

Common

0.09% 0.00% 4.41% -95.2% 133.3%

0.04% 0.00% 3.98% -94.9% 70.4%

Market cap. (KRW billion)

Trading volume ('000s)

Preferred (A)

Common (B)

(B/A)

Preferred (A)

Common (B)

(B/A)

158 6 1,211 0.009 26,601

2,694 231 12,174 0.137 229,787

(17.1) (39.8) (10.1) (15.2) (8.6)

34 4 143 0.060 10,786

702 170 2,644 0.001 205,995

(20.5) (38.2) (18.5) (0.0) (19.1)

Trading amount (KRW million) Preferred (A) 514 27 3,385 0.010 484,385

Common (B)

(B/A)

14,585 1,498 41,973 0.008 1,582,893

(28.4) (54.9) (12.4) (0.9) (3.3)

Panel B. Turnover and investor trading weight Turnover (%)

Mean Median Std. Dev. Min Max

Preferred

Common

(A)

(B)

1.94% 0.36% 6.35% 0.00% 483.23%

1.61% 0.57% 4.87% 0.00% 445.47%

Investor trading weight (%) (B/A)

(0.8) (1.6) (0.8) (0.0) (0.9)

Preferred stock

Common stock

Individual

Institution

Foreign

Individual

Institution

Foreign

90.9% 100.0% 19.2% 0% 100%

4.4% 0.0% 11.3% 0% 100%

4.8% 0.0% 13.3% 0% 100%

76.3% 86.0% 25.1% 0% 100%

13.1% 7.2% 15.0% 0% 100%

10.5% 3.5% 15.0% 0% 99.9%

considers additional circumstances: tests of systematic co-movement of individual traders, the discount of preferred shares at issuance, robustness checks for the empirical results contingent upon market conditions and various subsamples of PSD, and a Taiwan example of NTR in the discount of preferred stocks. Finally, Section 5 concludes this research. 2. Data, variables, and preliminary results 2.1. Databases The daily prices of 185 pairs of common and preferred stocks listed on KSE and Kosdaq from January 2000 until October 2014 were procured from DataGuide. Other information on dividends, voting rights, trading volume and amount, and transaction information were also obtained from DataGuide based on the pairs of “old type” preferred and common shares. “New type” preferred shares are excluded in the main analysis because they have fewer disadvantages for preferred equity holders, such as minimum dividend yield, cumulative dividend options, and common convertibility.6 We filtered out the first 5 trading days in any year due to the January effect, listings with fewer than 10 trading days or the lowest 10% in trading volume, and common-preferred pairs with higher than 10% in PSD. Over the sample period, for the indexation of private benefits from voting rights, the status information of sample firms' affiliation with conglomerates (chaebols) was procured from the Korea Fair Trade Committee (KFTC). The final sample consists of 185 pairs of common and preferred shares traded on KSE (169) and Kosdaq (16) with a total of 347,235 firm-day observations. Table 1 provides the descriptive statistics of key variables for the sample pairs of common and preferred shares on a daily basis. The total market capitalization, trading amount, and trading volume of common stocks are approximately 17, 20, and 28 times those of their preferred counterparts, respectively. However, preferred shares appear to be relatively more liquid by 33%p based on turnover, defined as trading volume normalized by the total outstanding preferred stock issues. In terms of ITW, preferred stocks (91%) are more densely traded by individual traders than common shares. In contrast, allegedly informed institutional and foreign investors occupy 4.4% and 4.8% (0% in median) of average trades in preferred shares versus 13.1% and 10.5% on common stocks, respectively. This finding indirectly corroborates the limited opportunities for arbitrageurs to exploit PSD, which later turns out to be 6 In Korea, “new type” preferred shares were first issued in 1996 to alleviate the pricing anomalies of less liquid, “old type” preferred stocks whose additional floatation is outlawed. Not only do the number of old type preferred shares (185) outnumber that of new type alternatives (56), but also including the latter in a robust test leaves the inferences herein largely intact (Section 4.3).

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Table 2 Time-series trends of preferred stock discount rate and main explanatory variables As the dependent variable, the preferred stock discount (PSD) is the price difference of common over preferred shares divided by the common stock price (Zingales, 1994; Kim et al., 1996). For the dividend-related variables, the dividend dummy variable (Dividend) of a given period equals one if payout took place in the previous period, for dividend payment is deemed a credible and consistent signal, or zero otherwise. 5 trading days prior to a given dividend day (Dividend Drop) are controlled for with a dummy variable which will be interacted with the dividend dummy in the egression model because PSD may contract until the announced dividend day due to a higher demand for the preferred share issue. For the voting rights-related variables, absolute control is gained by a shareholder with more than a 50% stake (Absolute Control). The value of voting rights is non-linearly affected by large shareholders’ stake (Largest Stake). As the ownership of large shareholders gradually increases far from the absolute control stake, the value of voting rights will rise upon more likely proxy fights (Proxy Fight). However, as the probability of proxy fights lowers after the gain of absolute control (over 50% stake), voting rights will be valued less by then upon stabilization of management. The sample firms are whether affiliated with conglomerates (Korea Fair Trade Committee-designated) or not (Chaebol). The measures of liquidity are turnover (trading volume normalized by total number of outstanding shares), and dollar volume and the Amihud's (2002) ratio. Amihud's (2002) suggests the ratio of the absolute value of return over contemporaneous dollar volume as a gauge of illiquidity. The individual trading weight (ITW) is the ratio of the individual trading volume of shares over the total trading volume of shares. All relative measures in this study are the excesses of preferred over common shares. All estimates other than the autocorrelation coefficient and Durbin-Watson statistics are at an annual frequency. The autocorrelation coefficient and Durbin-Watson statistics for the relative ITW (RITW) and PSD are at based on firm-month observations. Dep. variable Preferred Stock Discount

Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Mean Std.Dev. Autocorrelation Durbin-Watson

0.160 0.043 0.068 0.136 0.227 0.215 0.237 0.314 0.276 0.366 0.353 0.331 0.387 0.351 0.268 0.249 0.108 #REF! #REF!

Relative Individual Trading Weight

0.090 0.111 0.103 0.106 0.109 0.105 0.155 0.173 0.178 0.170 0.163 0.160 0.211 0.218 0.213 0.151 0.044 #REF! #REF!

Dividend group

Voting rights group

Liquidity group

Dividend

Dividend Drop

Largest Stake

Absolute Control

Proxy Fight

Chaebol

Relative Dollar Volume

Relative Amihud Ratio

Relative Turnover

0.097 0.922 0.962 0.973 0.977 0.977 0.991 0.988 0.996 0.993 0.990 0.999 1.000 1.000 1.000 0.924 0.230

0.022 0.021 0.022 0.022 0.022 0.021 0.023 0.022 0.022 0.021 0.022 0.022 0.022 0.024 0.003 0.021 0.005

15.96 18.74 19.01 33.34 35.39 36.64 35.95 37.44 38.50 39.22 39.94 41.23 41.50 40.58 40.80 34.28 8.813

0.000 0.008 0.015 0.180 0.192 0.218 0.183 0.192 0.212 0.228 0.250 0.266 0.277 0.242 0.239 0.180 0.094

0.000 0.000 0.000 0.004 0.006 0.004 0.000 0.002 0.001 0.000 0.000 0.000 0.004 0.012 0.012 0.003 0.004

0.349 0.387 0.387 0.411 0.453 0.448 0.480 0.491 0.529 0.538 0.548 0.555 0.573 0.578 0.572 0.487 0.077

0.338 0.262 0.179 0.190 0.196 0.097 0.284 0.371 0.332 0.187 0.487 0.624 0.575 0.316 0.266 0.313 0.150

0.060 0.018 0.025 0.096 0.207 0.081 0.077 0.046 0.070 0.062 0.029 0.018 0.037 0.024 0.020 0.058 0.049

0.015 0.014 0.006 -0.009 -0.010 -0.007 -0.006 0.004 0.000 -0.004 0.019 0.008 -0.001 0.009 0.006 0.003 0.009

substantial (Table 2). 2.2. Variables For the regression of PSD onto ITW and other variables known to affect PSD—e.g., dividends, the voting right proxy, turnover, etc.—a host of variables to implement our analysis are defined, characterized and provided in the following subsections. 2.2.1. Preferred stock discount There are three known measures of PSD in the literature. First, Zingales (1994) and Kim et al. (1996) define PSD as the price difference of common over preferred divided by the common share price for their respective Italian and Korean studies: Common share price − Preferred share price . Second, various country cases studying the U.S. (Cox and Roden, 2002), Russia (Muravyev, 2004), Common share price and Korea (Chay and Moon, 2005; Han, 2010) all adopt the ratio of the prices of preferred over common listings as such: Preferred share price . Lastly, in their analysis of institutional changes in voting rights, Kook and Jung (1996) use the relative premium of a Common share price

Preferred share price − Common share price

given common stock to quantify the value of legal entitlement as follows: , which may be overly Preferred share price unstable as a dependent variable, due to the more volatile nature of preferred stock prices. Although the first and second gauges of PSD are equivalent, because the purpose of this research is to identify NTR that affects the relative pricing of preferred shares, we adhere to Zingales (1994) and Kim et al.’s (1996) convention as the dependent variable, which is also the return of common-preferred arbitrage or pairs trading. The PSD of a given common-preferred stock pair of firm i on trading day t is defined as follows:

PSDi, t ≡

Common share pricei, t − Preferred share pricei, t Common share pricei, t

.

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2.2.2. Explanatory variables The discount of preferred shares, or the premium of common shares, have been largely explained by dual-class differences in dividends, voting rights and turnover in the literature. In this research, we introduce the density of individual traders as a proxy for NTR that contributes to determining PSD. 2.2.2.1. Individual trading weight. Choi and Choi (2018)7 suggest ITW as a proxy for NTR explaining stock returns, and they define the ITW of stock i in trading interval t as: Individual trading volume of sharesi, t ITWi, t ≡ . Total trading volume of sharesi, t 2.2.2.2. Relative individual trading weight. De Long et al. (1990) show that those stocks with high proportions of individual traders can carry price discounts due to NTR. Assuming ITW is a proxy for NTR, this research tests whether the excess ITW of preferred over common shares can serve as a statistically and economically meaningful determinant of PSD. We define the relative ITW (RITW) of a given common-preferred pair (i) on a given day (t) as follows:

RITWi, t ≡ ITW of preferred stock i, t − ITW of common stocki, t

Indiv.trading volume of preferred stock i, t

Indiv.trading volume of common stocki, t − . Total trading volume of preferred stock i, t Total trading volume of common stocki, t Accordingly, extending the reasoning of De Long et al. (1990), preferred shares whose ITW is higher than their common counterpart will trade at discounted prices relative to the respective associated common listings. As a result, PSD is expected to be steeper the higher the difference of ITWs of preferred over common shares (RITW). =

2.2.2.3. Dividend. As Korean old-type preferred shares tend to yield an additional 1% dividend (against KRW 5000 face value, thus KRW 50 more) relative to common shares, the announcement of a dividend payout rather than the amount of dividend will affect the relative discount of preferred stocks. The dividend dummy variable in a given year (y) equals one if a payout occurred in the previous year (y − 1) of a common stock (i), or zero otherwise. The lag is used because dividend payment is deemed a consistently credible signal.

1 if divided was paid in period y − 1 Dividendi, y = ⎧ ⎨ ⎩ 0 o. w. PSD may contract until the announced dividend day due to a higher demand for the preferred share issue. Thus, 5 trading days prior to a given dividend day are controlled for with a dummy variable which will be interacted with the dividend dummy in the regression model.

1 from − 5 days until day prior to dividend day t Dividend Dropi, t = ⎧ ⎨ ⎩ 0 o. w. Should an additional 1% dividend of a preferred stock listing be accepted as likewise in the subsequent period, there will be a relative rise in the preferred share price and the increment will be more pronounced closer to the dividend day. The interacted term of the dividend drop and payout dummies is expected to negatively affect PSD. 2.2.2.4. Value of voting rights. Zingales (1994, 1995) agues the value of voting rights is influenced by the extent of private benefits via entitled management control and the probability of proxy fights. Large shareholders' voting rights will be deemed more valuable corresponding to larger privileges ex post. Additionally, proxy fights will occur as the large shareholders attempt to increase their stakes to absolute control ownership (exceeding 50%). However, the probability of further proxy fights will diminish afterwards. Although many studies do not discuss the magnitude of private benefits due to the unavailability of direct measurement, we follow the conglomerate dummy variable of Kim et al. (1996).8 The percentage ownership of large shareholders is used to predict the probability of control transfer by Kim et al. (1996), Kook and Jung (1996) and Chay and Moon (2005).9 However, the value of voting rights is non-linearly affected by large shareholders' stake. As the ownership of large shareholders gradually increases far from an 7 In Choi and Choi (2018), six “ITW (3) by size (2)” portfolios are rebalanced on a quarterly basis; the monthly returns of these portfolios are estimated using the value weights of market capitalizations, as at the end of previous months. As a result, the excess return of portfolios that are “dense” and “scarce” (the highest and lowest 30% in ITW, respectively) in individual traders controlling for size (dense-minus-scarce, DMS) is estimated as follows:

Dense ∩ Smallt + Dense ∩ Bigt ⎞ Scarce ∩ Smallt + Scarce ∩ Bigt ⎞ DMSt = Denset ⎛ − Scarcet ⎛ . 2 2 ⎝ ⎠ ⎝ ⎠ ⎜

⎟

⎜

⎟

When the DMS factor is augmented to Fama and French's (1993) and Carhart's (1997) factors of market, size and value premiums and momentum effect, the extended model better explains the cross-section of common stock returns on the Korean and Taiwan stock exchanges in terms of R-squared and Gibbons et al.'s (1989) F-test. 8 Kim et al. (1996) find that PSD of a conglomerate affiliate is higher than otherwise. This is in line with Zingales's (1994) argument of the private benefits created by transferring wealth among the firms within a conglomerate. 9 Zingales (1994) reports that the dummy variable of absolute control ownership is empirically equivalent to the Shapely value of proxy fights with presence of two large shareholders.

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absolute control stake, the value of voting rights will rise upon looming proxy fights. As proxy fights are unlikely after the gain of absolute control (over 50% stake), voting rights will be less valued after the stabilization of management. Since PSD is expected to be larger the higher the value of voting rights, the relative discount of an average preferred stock listing is steeper (1) for a KFTC-designated conglomerate affiliate whose private benefits are deemed larger than that of a non-conglomerate firm; or (2) for a more probable proxy fight; or (3) the higher the largest stake for a likelier proxy fight; or (4) the lower the interacted term of the largest stake and the absolute control stake for a less likely proxy fight. The variables discussed thus far pertain to the value of voting rights of firm i in time interval t, and their expected signs are as follows: 1 for a conglomerate affiliate Cheaboli (+ ) = ⎧ , ⎨ 0 o. w. ⎩ Largest Stakei, t (+) = Largest common share percentage ownership,

1 for largest comm. ownership > 50% Absolute Controli, t ( −) = ⎧ ⎨ ⎩ 0 o. w. ⟹Largest Stake × Absolute Control ( −). 2.2.2.5. Liquidity. Muravyev (2004), Chay and Moon (2005), and Han (2010) find the relative turnover of preferred over common shares can be a significant explanatory variable of PSD in their respective Russian and Korean studies. The measures of turnover are trading volume, relative turnover (trading volume normalized by the total number of outstanding shares), and dollar volume. In comparison, Amihud (2002) suggests the ratio of the absolute value of return over the contemporaneous dollar volume as a gauge of illiquidity. PSD is expected to be larger the lower the relative turnover or dollar volume or the higher the relative Amihud ratio of preferred over common shares. The definitions of these relative measures of turnover of a given common-preferred pair (i) on a given day (t) and their predicted signs with respect to PSD are as follows:

Relative Turnoveri, t ( −) =

Pref. stock trading volumei, t Total no. of outstanding pref. sharesi, t

−

Comm. stock trading volumei, t Total no. of outstanding comm. sharesi, t

Relative Dollar Volumei, t (− ) =

Preferred stock dollar volumei, t , Common stock dollar volumei, t

Relative Amihud Ratioi, t ( +) =

Preferred stock returni, t Common stock returni, t . − Pref. stock dollar volumei, t Comm.stock dollar volumei, t

,

2.2.2.6. Fama and French's (1993) three factors. The market factor is the monthly excess returns of the value-weighted average of the KOSPI and Kosdaq indices over the monthly adjusted rate of 1 year MSB (Rm, t − Rf, t). The breakpoints of portfolio formation of the size (small-minus-big, SMB) and valuation (high-minus-low, HML) factors are entirely based on KSE-listed common shares to prevent the estimates from being biased towards KOSDAQ-listed small capitalization stocks. The size (SMB) and valuation (HML) buy-andhold portfolios are annually rebalanced at the end of every June based on the last year-end market capitalizations and book-to-market ratio (B/M): small (below median) versus big; and valuations: low (lowest 30%), high (highest 30%), and medium (the rest). As a result, the respective factors are the excess returns based on the monthly value (market capitalization)-weighted average returns of 6 implied portfolios. Given this, the SMB and HML factors in month t are estimated as follows:

SMBt = Smallt ⎛ ⎝

HMLt = Hight

(

SHt + SMt + SLt ⎞ BH + BMt + BLt ⎞, − Bigt ⎛ t 3 3 ⎝ ⎠ ⎠

SHt + BHt 2

) − Low ( t

SLt + BLt 2

).

2.3. Preliminary results Table 2 lists the annual estimates, means, and standard deviations of PSD and the key explanatory variables of regressions to be implemented later. Through the sample period, an average preferred stock listing trades at a substantial discount of 24.9% against its benchmark common share, and the discount rate varies over time with a trend. Because the important covariates also show timeseries variation, they appear to be possible explanatory variables of PSD.10 In Table 3, which tabulates the pairwise correlation coefficients of PSD and other variables, we note the highest and statistically significant correlation (20.9) between PSD and ITW, suggesting that ITW is likely to be a strong determinant of PSD: PSD and RITW co-move towards the same direction one out of five cases. The dummy variable of previous year's dividend payout and the interaction term of large common share ownership and absolute control stake dummies show unexpected, significantly possible correlations. The relative Amihud's measure also reveals a negative association with PSD. Although other explanatory variables have their expected 10 Table 2 additionally provides the first-order autocorrelation coefficient and Durbin-Watson statistics for PSD and RITW based on firm-month observations. On average, both variables are positively autocorrelated with their Durbin-Watson statistics falling strictly below 2 implying these variables show evidence of autocorrelation. This concern will be addressed by double-clustering for time and firms in the panel regression analysis.

6

7

Preferred Stock Discount Dividend (-) Dividend × Dividend drop (-) Largest Stake (+) Largest Stake × Absolute Control (-) Proxy Fight (+) Chaebol (+) Relative Dollar Volume (-) Relative Amihud Ratio (+) Relative Turnover (-) Relative ITW (+)

Variable (Expected sign associated with PSD)

1 -0.005** 0.069*** 0.015*** 0.017*** 0.073*** -0.001 -0.002 -0.044*** 0.085***

0.062*** 0.014***

0.023*** 0.188*** -0.007*** -0.048*** -0.133*** 0.209***

Dividend

1

-0.003 -0.004**

0.000 0.001 -0.002 -0.001

-0.001 0.003

Dividend Drop

Dividend group

1 0.034*** -0.003*

Preferred Stock Discount

Dep. variable

0.028*** -0.134*** 0.026*** 0.019*** 0.049*** -0.035***

1 0.796***

Largest Stake

1 -0.029*** -0.178*** 0.026*** 0.026*** 0.031*** -0.074***

Largest Stake × Absolute Control

1 -0.049*** 0.000 -0.003 0.019*** 0.034***

Proxy Fight

Voting rights group

1 -0.022*** -0.058*** -0.038*** 0.265***

Chaebol

1 -0.030*** 0.052*** -0.022***

Relative Dollar Volume

1 -0.025*** -0.042***

Relative Amihud Ratio

Liquidity group

1 -0.028***

Relative Turnover

1

Relative ITW

Table 3 Correlation coefficients This table of correlation coefficients is based on the 185 pairs of “old type” preferred and common shares listed on the KSE and the Kosdaq from January 2000 until October 2014. The preferred stock discount (PSD) is the price difference of common over preferred shares divided by the common stock price (Zingales, 1994; Kim et al., 1996). For the dividend-related variables, the dividend dummy variable (Dividend) of a given period equals one if payout took place in the previous period, for dividend payment is deemed a credible and consistent signal, or zero otherwise. 5 trading days prior to a given dividend day (Dividend Drop) are controlled for with a dummy variable which will be interacted with the dividend dummy in the egression model because PSD may contract until the announced dividend day due to a higher demand for the preferred share issue. For the voting rights-related variables, absolute control is gained by a shareholder with more than a 50% stake (Absolute Control). The value of voting rights is non-linearly affected by large shareholders’ stake (Largest Stake). As the ownership of large shareholders gradually increases far from the absolute control stake, the value of voting rights will rise upon more likely proxy fights (Proxy Fight). However, as the probability of proxy fights lowers after the gain of absolute control (over 50% stake), voting rights will be valued less by then upon stabilization of management. The sample firms are whether affiliated with conglomerates (Korea Fair Trade Committee-designated) or not (Chaebol). The measures of liquidity are turnover (trading volume normalized by total number of outstanding shares), and dollar volume and the Amihud's (2002) ratio. Amihud's (2002) suggests the ratio of the absolute value of return over contemporaneous dollar volume as a gauge of illiquidity. The individual trading weight (ITW) is the ratio of the individual trading volume of shares over the total trading volume of shares. All relative measures in this study are the excesses of preferred over common shares.

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PSD

RITW

0.4

0.25

1

0.20

0.9

0.15

0.8

0.10

0.7

0.05

0.6

0.00

0.5

0.3

ITW

0.2 0.1 0.0 -0.1 -0.2

PSD (LHS)

ITW of Common Shares ITW of Preferred Shares

Rel. ITW (RHS)

Fig. 1. Comparative dynamics of preferred stock discount and relative individual trading weight. These figures show the trends of the preferred stock discount (PSD) and the relative individual trading weight (RITW) from the 185 pairs of “old type” preferred and common shares listed on the KSE and the Kosdaq from January 2000 until October 2014. Panel A shows PSD (left Y-axis) and RITW (right Y-axis). Panel B exhibits the ITWs of common and preferred shares. The daily PSDs and RITWs of each pair are weight-averaged using preferred share market capitalizations on a quarterly basis.

signs with PSD, as these allegedly exogenous variables appear also correlated, judging their impacts on PSD awaits further analyses. Fig. 1 shows the trends of PSD and relative ITW from the 185 pairs of “old type” preferred and common shares listed on KSE and the Kosdaq from January 2000 until October 2014. Panel A shows PSD and relative ITW, whose vertical axis on the left is for PSD, while the vertical axis on the right for the relative ITW. Panel B exhibits the ITWs of common and preferred shares. Daily PSDs and

Fig. 2. De-trended preferred stock discount and de-trended relative individual trading weight. This figure shows the quarterly trends of the de-trended preferred stock discount (PSD) and de-trended relative individual trading weight (RITW) based on the 185 pairs of “old type” preferred and common shares listed on the KSE and the Kosdaq from January 2000 until October 2014. Detrended PSD is the residual from regressing PSD onto the time trend term and conventional explanatory variables (Section 2.2.2) including the payout dummy and its interaction with the dividend drop dummy, the largest stake and its interaction with the absolute control stake, the dummy for affiliation with a conglomerate, relative measures in the amount, trading volume, and illiquidity (Amihud, 2002). The time-series residuals from the regression are value-weighted using the market capitalizations of comparable common stocks. Superimposed is the de-trended relative ITW which is the residuals from regressing RITW onto the time trend term. 8

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ITWs of each pair are averaged on a quarterly basis. In Fig. 2, on a quarterly basis, de-trended PSD is the residual from regressing PSD onto the time trend term and conventional explanatory variables (Section 2.2.2) including the payout dummy and its interaction with the dividend drop dummy, the largest stake and its interaction with the absolute control stake, the dummy for affiliation with a conglomerate, relative measures in the amount, trading volume, and illiquidity (Amihud, 2002). The time-series residuals from the regression are value-weighted using the market capitalizations of comparable common stocks. Superimposed is de-trended RITW which is the residuals from regressing RITW onto the time trend term. There is a noticeable co-movement between de-trended PSD and de-trended RITW with a 69.3% correlation, suggesting NTR is associated with the discount of preferred shares even after sieving out the time trend and the existing determinants known in the literature. 3. Main results NTR in stock trades stems from short-term price uncertainty due to erroneous perceptions of uninformed traders. In general, mispriced stocks will be identified by informed traders or arbitrageurs who will force their trades towards the fair values. However, the presence of noise traders will prevent arbitrageurs from entering the market under disequilibria because of the short-term nature of their portfolios. As a result, displaced stock prices will persist for a prolonged period (De Long et al., 1990). This section provides the empirical test results of our research question pertaining to NTR. First, this research focuses whether the excess ITW of a given preferred stock listing over its comparable common equity determines PSD controlling for identical firm-level characteristics and dual-class differences of dividends, voting rights, and turnover. Preferred shares neither place a burden on firm leverage nor dilute existing ownership, while they cater the need of investors who favor higher cash flows over voting rights and are entitled with seniority in asset claims and cumulatively unpaid dividends. Therefore, the price deviations between common and preferred shares of identical fundamental values are known in the literature to be due to dual-class differences in dividends and voting rights. However, because the additional cash flows to the preferred shareholders in Korea are marginal (an additional 1% dividend against KRW 5000 face value relative to common shares), the voting rights premiums of common stocks have been considered as the dominant source of persistent PSD in Korea.11 Ubiquitously observed in numerous capital markets around the world, PSD not only structurally varies across the borders due to differences in the sovereign extent of corporate governance, but also fluctuates over time. Korean-listed preferred shares had traded at an average 10% discount against common equities in the 1990's, but the disparity has broadened up to the range of 20% to 40% since 2000.12 As seen in Table 2, the moderate trend in the value of voting rights implies hidden elements of the time-varying discount rate of preferred equities. Accordingly, Muravyev (2004) and Chay and Moon (2005) argue that the relative turnover differential between common and preferred shares can be a significant explanatory factor. Before we designate NTR as a determinant of the time variation of PSD, we are reminded of the fact that preferred stock listings are more heavily traded by individual investors than comparable common equities are (Table 1). Therefore, the relative pricing of preferred shares against common stocks with the identical fundamentals and aggregate risk can be expounded by dual-class differences including the relative deviation in the density of individual traders. This section affirms the NTR-pricing argument with specific evidence from PSD. In Table 4, PSD is regressed onto RITW controlling for the variables pertaining to dividends, voting rights, and turnover (defined in Section 2.2.2) based on the 185 pairs of common and “old-type” preferred equities traded from January 2000 until October 2014. As the density of individual traders is conspicuously inversely correlated with firm size, the simple association between PSD and RITW may be noisy without controlling for the size effect. Accordingly, as a inversely relative size measure of a given preferred stock versus its comparable common share, the relative smallness is defined as Relative Smallnessi, t = 1 −

(

market cap . of preferred stocki, t market cap . of common stocki, t

),

for firm i on trading day t. As common risk factors that can affect PSD, the market, firm-size (SMB), and valuation (HML) factors are also sequentially controlled for. Other than the yearly dummies of dividend information and conglomerate affiliation, every variable is estimated on a firm-day basis. The panel is, then, constructed on a fund-month basis for the regression analysis. The finding in Model 1 shows that an additional proportion of individual traders (RITW) on a preferred share by 1%p relative to its comparable common stock tilts the discount of the preferred issue by 20.3% on a monthly basis. In other words, the risk premium of individual trading in the relative pricing of preferred shares is economically and statistically stark. The discount steepens the lower the relative market value of preferred shares (1.412), with higher estimates of relative smallness (Model 2). This association remains robust to controlling for the known determinants of PSD such as dividends (Model 3), voting rights (Models 4) and turnover (Model 5), with economically valuable and statistically significant coefficient estimates in the range of 0.116 up to 0.184. Model 6 additionally controls for Fama-French 3 factors. As seen by comparing Model 5 with Model 6, controlling for the 3 factors of market, firm size (SMB) and valuation (HML) does not affect the economic extent and statistical significance of RITW at all. 11 Some preferred shares trade with premiums relative to their comparable common equities are largely due to speculation sought after the illiquidity of preferred stocks. At first, we exclude these outliers by filtering out pairs with preferred premiums and PSDs in the lowest 10% (below PSD of 3.4%). These preferred shares with premiums will be considered in a robustness test in Section 4.3. 12 In the 1990's not only preferred shares were actively traded in their early phase since introduction (Chay and Moon, 2005), but the overall widening of PSD is deemed due to the following events that affected the value of voting rights such as the restriction of cross-preferred shareholding among firms in 1994, exclusion of preferred stocks from index futures contracts in 1994, enactment of coerced open stock purchase in 1996, relaxation of foreign ownership restriction in 1997 (Kook and Jung, 1996).

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Table 4 Preferred stock discount explained by relative individual trading weight. These regressions are performed on the full pairs of “old type” preferred and common shares listed on the KSE and the Kosdaq from January 2000 until October 2014. As the dependent variable, the preferred stock discount (PSD) is the price difference of common over preferred shares divided by the common stock price (Zingales, 1994; Kim et al., 1996). For the explanatory variables, the individual trading weight (ITW) is the ratio of the individual trading volume of shares over the total trading volume of shares, and the relative ITW (RITW) is the ITW of a preferred stock minus the ITW of the comparable common share. The relative smallness of a given preferred stock is 1 minus the ratio of the market capitalizations of preferred over common shares (Relative Smallness). For dividend-related variables, the dividend dummy variable (Dividend) of a given period equals one if payout took place in the previous period or zero otherwise. 5 trading days prior to a given dividend day (Dividend Drop) are controlled for with a dummy variable which is interacted with the dividend dummy. For the voting rights-related variables, absolute control is gained by a shareholder with more than a 50% stake. The value of voting rights is non-linearly affected by large shareholders' stakes. As the ownership of large shareholders gradually increases far from absolute control stake, the value of voting rights will rise upon more likely proxy fights (Proxy Fight). However, as the probability of proxy fights lowers after the gain of absolute control (over 50% stake), voting rights will be valued less by then upon stabilization of management. The sample firms are whether affiliated with conglomerates (Korea Fair Trade Committee-designated) or not (Chaegol). The measures of liquidity are turnover (trading volume normalized by total number of outstanding shares), and dollar volume and the Amihud's (2002) ratio. Amihud (2002) suggests the ratio of the absolute value of return over contemporaneous dollar volume (KRW 100 million in this study) as a gauge of illiquidity. All relative measures are the excesses of preferred over common shares. The market factor (Market) is the monthly excess returns of the value-weighted average of the KOSPI and the Kosdaq indices over the monthly adjusted rate of 1 year monetary stability bond (MSB). The size (SMB) and valuation (HML) buy-and-hold portfolios are annually rebalanced at the end of every June based on the last year-end market capitalizations for the SMB factor: small (below median) versus big; and based on the book-to-market ratio (B/M) for the HML factor: low (lowest 30%), high (highest 30%), and medium (the rest). The log of common share market capitalization (KRW billion) is controlled for. Standard errors are adjusted for clustering at the firm level and across time (Petersen, 2009), and the corresponding t-statistics are presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels, respectively.

RITW

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.203*** (5.965)

0.184*** (4.985) 1.412** (2.378)

0.182*** (4.922) 1.459** (2.425) −0.114** (−2.120) −0.002 (−0.674)

0.124*** (3.806) 2.863*** (3.388) −0.123 (−1.155) 0.000 (−0.099) −0.001 (−0.372) 0.0000 (0.003)

0.116*** (3.595) 2.776*** (3.585) −0.129 (−1.319) −0.001 (−0.412) −0.001 (−0.291) −0.0001 (−0.050)

0.116*** (3.594) 2.776*** (3.585) −0.130 (−1.319) −0.001 (−0.259) −0.001 (−0.292) −0.0001 (−0.050)

0.001 (0.707) 0.001 (1.409) −1.280*** (−9.714)

0.001 (0.706) 0.001 (1.410) −1.280*** (−9.714) 0.132*** (4.782) 0.145*** (3.554) 0.124* (1.970) −2.131*** (−2.904) Yes Yes 0.118 279,500

Relative smallness Dividend Dividend × dividend drop (t-5 to t-1) Largest stake Largest stake × absolute control Chaebol dummy Relative dollar volume Relative Amihud ratio Relative turnover Market SMB HML Constant Firm-fixed effect Time-fixed effect Adj. R2 N

0.441*** (8.422) Yes Yes 0.062 347,235

−0.868 (−1.539) Yes Yes 0.077 347,235

−0.902 (−1.579) Yes Yes 0.079 347,235

−2.223*** (−2.781) Yes Yes 0.081 279,525

−2.132*** (−2.906) Yes Yes 0.118 279,525

Model 7

Model 8

−0.116 (−1.608) −0.003 (−0.368) 0.004 (1.156) −0.0012 (−0.710) 0.188** (2.606) 0.001 (0.482) −0.005** (−2.587) −1.722*** (−7.501)

−0.086 (−0.931) −0.004 (−1.115) −0.001 (−0.391) 0.0002 (0.150)

0.000 (−0.069) 0.001 (1.090) −1.328*** (−10.376)

0.279** (2.342) No Yes 0.078 279,525

0.478** (2.484) Yes Yes 0.081 279,525

Models 7 identifies the conventional model for PSD without our NTR proxy, RITW, and not considering the firm-fixed effect. PSD is statistically significantly less for those firms that paid dividends in previous fiscal years (−0.116). The price deviations are additionally eroded for the pairs before their dividend drops (−0.003), albeit numerically and statistically weakly. For the variables of voting rights, PSD is steeper the higher the large shareholder ownership is (0.004) as the value of voting rights for common equity holders rises. However, PSD wanes once an absolute controlling stake has been secured (−0.0012), which depreciates voting rights: neither coefficient estimate is statistically significant. The common shareholders of a chaebol-affiliated firm are deemed more privileged than their non-conglomerate peers, because the voting rights of the former are evaluated to be more valuable due to heightened private benefits (0.188). The coefficient estimates of relative dollar volume and illiquidity (Amihud) measures either are statistically insignificant or have signs opposite to earlier predictions. The relative turnover variable has all economically and 10

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statistically meaningful implications (−1.722): The price difference is lower the more relatively liquid the preferred shares are. When the firm-fixed effect is considered in Model 8, the significance disappears for the chaebol dummy (due to the firm fixed effect), and the Amihud ratio. The signs of the coefficient changes in the opposite direction for the largest stake and the interaction term with absolute control, albeit statistically insignificantly. Overall, the conventional models (Models 7 and 8) appear relatively incompetent to the newer models (Models 1 through 6) that recognizes NTR, proxied for by RITW, as a determinant of PSD. The empirical exercises with various combinations of models and controls delivered in Table 4 tentatively conclude that the discount of preferred shares is economically valuably and statistically meaningfully affected by the relative proportion of individual trading on preferred stocks over common equities. This “individuals as noise traders” argument provides an important clue to decomposing the sources of PSD by controlling for dual-class characteristics while canceling out the perfectly shared fundamentals of the issuing firms. This treatise also makes a contribution to the lineage of studies on PSD since Zingales (1994, 1995) by identifying the population density of individual traders as a new factor in the relative pricing of dual-class shares. However, the sizable portion of the discount has yet to be explained by the models formulated thus far, e.g., 1 − R2 = 0.882 for Model 5 or 6 in Table 4, which calls for further scholastic attention on the matter. 4. Additional considerations 4.1. Individuals as the source of systematic noise Our research question is based on the assumption that individuals' movements are systematic. Numerous studies have reported the systematic movements of individual investors. For example, Kang et al. (2013) show this by using market sentiment as a proxy for the correlations of buy-sell imbalances (BSIs) of individuals extracted from their transactions in KSE-listed stocks. Choi and Choi (2018) find that NTR, proxied for by ITW, determines common stock returns in the Korean stock market, and that NTR is created by the co-movement of individual traders. Besides, they suggest a risk factor (dense-minus-low, DMS) based on the excess returns of portfolios of high over low in ITW. Turning to the very focus of this research, we empirically test the NTR of individuals by associating the relative densities of individual investors (RITW) with the implied return of common-preferred pairs trading (PSD). To demonstrate that our analyses are in line with and contribute to the relevant literature, we perform two tests based on Kaniel et al. (2008) and Kumar and Lee (2006). First, we simulate 1000 pair-wise correlation coefficients of the changes of RITWs and residual PSDs, orthogonal to the known determinants other than NTR, based on the 185 pairs of preferred shares and their comparable common stocks. Second, we conduct the principal component analyses of the changes of RITWs and PSDs and review the percentage of variance explained by the first 5 principal components. Lastly, we further briefly explorer whether those who create NTR contributing to PSD are small stock traders. Panel A of Table 5 displays the summary statistics of the value-weighted measures of 185 common-preferred pairs over 179 sample months. The change of RITW (ΔRITW) for each firm is defined as the average of the daily RITW of common-preferred pairs of firm i during month t minus that of the previous month, t − 1. The PSD of firm i in month t is the price difference of common over preferred stocks divided by the common share price. In the spirit of Kumar and Lee (2006), the factor-orthogonal change in RITW (ΔRITW (ortho.); εit) and residual PSD (PSD (ortho.); ηit) are obtained from the following regressions, respectively:

ΔRITWit = γ0 + γm Markett + γs SMBt + γh HMLt + εit ,

PSDit = β0 + βc Conventionali, t + βm Markett + βs SMBt + βh HMLt + ηit , where Markett is the market excess return as the difference of monthly KOSPI return over the monthly risk-free rate, which is the 1year monetary stability bond (MSB) annual rate divided by 12; SMBt is the excess return of the portfolios of small stocks over large listings (SMB factor); HMLt is the excess return of the portfolios of value stocks (high in book-to-market ratio) over growth firms (low); and Conventionali, t is the basket of conventional, firm-level determinants of PSD (Section 2.2.2). The purpose of these regressions is to remove the components caused by known explanatory co-variates other than NTR. Panel B of Table 5 exhibits the distributions and significances of the correlation coefficients of 1000 randomly selected pairs of changes in factor-orthogonal RITW (ΔRITW (ortho.)) and residual PSD, following Kumar and Lee (2006). The upper two graphs in Fig. 3 show the plots of the probability density functions (p.d.f.'s) of randomly drawn correlations. First, the randomly drawn pairwise correlations of the changes of factor-orthogonal RITW (ΔRITW) are, on average, statistically significantly positive (0.017). Second, the simulated correlations of the residual PSDs of sample common-preferred pairs are also, on average, statistically significantly positive (10.5%). Panel C of Table 5 presents the results of the principal component analysis on the change of factororthogonal RITW (ΔRITW (ortho.)), showing that the first 5 factors explain 15.5% of the total variance of the additional proportion of individual traders of preferred shares relative to comparable common stocks (RITW).13 When the known factors of PSD is controlled for (PSD (ortho.), the variance explained by the first five factors is nearly half of the total variation (43%). Overall, Panels B and C suggest that the common-preferred pairs in the Korean stock market tend to be affected by the systematic movements of individual investors. Lastly, Panel D of Table 5 shows the summary statistics of the simulated correlations of the residual PSD of all common-preferred pairs and small stock measures, the SMB factor and the Small Stock Index of KOSPI, obtained from DataGuide. The distributions of 13

The panel data for the principal component analyses was multiply imputed (Dempster et al., 1977; van Dyk and Meng, 2001) for missing observations.

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Table 5 Systematic co-movements of individual traders. Panel A displays the summary statistics of the value-weighted indices of relative ITW (RITW) and preferred stock discount (PSD) of 185 pairs of “old type” preferred and common shares listed on the KSE and the Kosdaq from January 2000 until October 2014. The change of RITW (ΔRITW) of a common-preferred shares pair is defined as the average daily RITW of the pair during a given month minus that of the previous month. The PSD of a given pair in a given month is the price difference of common over preferred stocks divided by the common share price. “ΔRITW (ortho.)” and “PSD (ortho.)” refer to market-orthogonal ΔRITW and PSD obtained from the following regressions: ΔRITWit = γ0 + γmMarkett + γsSMBt + γhHMLt + εit PSDit = β0 + βcConventionali, t + βmMarkett + βsSMBt + βhHMLt + ηit Panel B exhibits the distributions and significances of the correlation coefficients of 1000 random pairs of 300 stocks in terms of changes in ITW (ΔRITW) and PSDs. Panel C implements the principal component analysis. Panel D shows the summary statistics of the simulated correlations of the residual PSD (ortho.) of each common-preferred share pair respectively with the SMB factor and the Small Stock Index of KSE-listed stocks, obtained from DataGuide. Panel A. Summary statistics for value-weighted measures

Value-weighted ΔRITW (ortho.) Value-weighted PSD (ortho.)

No. of obs.

Mean

Std. dev.

Minimum

Maximum

179 179

−0.10% 8.40%

9.40% 7.50%

−25.80% −7.50%

25.80% 30.90%

Panel B. Correlation distributions of random pairs

ΔRITW (ortho.) PSD (ortho.)

No. of obs.

Mean

Std. dev.

t-Value

p-Value

1000 1000

0.017 0.105

0.096 0.297

5.287 10.789

0.000 0.000

Panel C. Variance contribution (%)

ΔRITW (ortho.) PSD (ortho.)

Factor 1

Factor 2

Factor 3

Factor 4

Factor 5

Factors 1–5

3.7 11.3

3.3 10.6

3.0 8.7

2.8 6.5

2.7 6.0

15.5 43.0

Panel D. Correlation distributions of residual PSD and small stock measures

SMB and PSD (ortho.) Small Stock Index and PSD (ortho.)

No. of obs.

Mean

Std. dev.

t-Value

p-Value

1000 1000

0.038 0.070

0.149 0.186

7.156 10.438

0.000 0.000

randomly drawn correlations are plotted in the lower half in Fig. 3. Even though the residual PSDs of common-preferred share pairs are supposed to be orthogonal to the SMB factor they are, on average, positively correlated with the SMB factor to some degree (3.8%). Alternatively, the Small Stock Index is somewhat more positively correlated (7%) with residual PSDs, on average. As a result, there appears to be some evidence of small traders' contribution to creating NTR that affects the determination of PSD. In other words, the noise traders of preferred shares might as well frequently trade small stocks or the two investor groups co-move to some extent. 4.2. Discount at the issuance of preferred shares A puzzle that might intrigue some readers is why firms would issue preferred stock at a discount, if they had an option to issue common stock at a lower cost of capital? One consistency result we can add is to check whether preferred stock issuances are concentrated in times when PSD is either negligible, or when preferred stocks are trading at premiums. Alternatively, at the individual firm-level, do we observe that in the life-cycle of a preferred issue, preferred shares are issued at a premium, and then gradually PSD starts to emerge?14 Fig. 4 is based on the 59 pairs of KSE and Kosdag-listed old type preferred and common shares, newly issued from January 2000 until October 2014. Panel A shows the preferred stock discounts (PSDs, Y-axis) of new listings versus the contemporaneous PSD index (X-axis), which is constructed by using preferred share market capitalizations as value weights. We note a tendency of co-movement of the discount of new preferred share issues and the overall discount of existing preferred stock listings with a 11.7% statistically significantly positive correlation. By counting the coordinates, 51 cases out of 59 listing decisions (86.4%) of preferred shares during the sample period had occurred when the existing preferred stocks were trading at a premium, on average, or when the preferred 14

We thank the anonymous referee for raising these issues.

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Fig. 3. Distributions of simulated correlations. These plots show the distributions of correlations. Following Kumar and Lee (2006), the upper two probability density functions (p.d.f.’s) of correlations are based on 1000 randomly drawn pairs of the changes in relative ITW (ΔRITW, Panel A) and residual PSD (Panel B), respectively, whose sample statistics are summarized in Panel B of Table 5. The lower two p.d.f.’s show the distributions of 1000 simulated correlations of residual PSDs and small stock measures, the SMB factor (Panel C) and the Small Stock Index (Panel D), respectively, whose summary statistics are presented in Panel D of Table 5.

share cost of capital was significantly low. In addition, 27 listings (45.8%) were issued at a premium when the PSD index negative (premium). This inflation of preferred share listing prices is contrast with the globally ubiquitous underpricing of the initial public offerings (IPOs) of common stocks (Loughran et al., 1994). Overall, these accounts hint at the market timing of corporate listing decisions of preferred shares to opportune the low cost of capital. Panel B plots the first-day PSDs of new listings against their listing prices and we find that the preferred shares issued at premiums are highly concentrated in the low listing price range less than KRW20,000 or USD20.15 These anomalies are, however, diluted away when the daily trends of the indices of PSD and RITW, value-weighted using preferred share market capitalizations, are superimposed in Panel C. PSD (left Y-axis), on average, begins from mid-30% and rises up to mid-50% in the first 250 trading days since issuance. Time-series wise, preferred shares are issued when their overall cost of capital is relatively low. On the supply side, firms want to raise capital without diluting managerial control at their expense of more obliged and stable payouts in exchange for the inflated proceeds from issuance. On the demand side, prospective preferred shareholders bid for new issues to capture predictable dividends. As these issued preferred shares become mature, their discount appears to be very closely correlated with RITW (right Y-axis) in line with our thesis. PSD is roughly 50% in time mean which corresponds to Nenova's (2003) finding of Korea's value of voting rights. However, it is unlikely that the value of voting rights is as volatile as the time-series path of PSD, which is explained by RITW in the long run. 4.3. Robustness tests This section executes various robustness tests on the main empirical results in Section 3 identifying NTR, proxied for by RITW, as a determinant of PSD controlling for conventional explanatory variables. To begin with, the first robustness test is targeted at new-type 15

Footnotes 6 and 12 can be helpful in understanding the historical backgrounds of these anomalies and market timing of corporate listing decisions.

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A

B

1.0

0.5

0.5

0.0

0.0

Preferred Stock Discount at Issuance

Preferred Stock Discount at Issuance

1.0

-0.5

-1.0

-1.5

-2.0

-0.5

-1.0

-1.5

-2.0

-2.5

-2.5

-3.0

-3.0

45˚ -3.5

-3.5 -3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

0

50,000

100,000

150,000

Preferred Stock Discount Index

C

200,000

250,000

300,000

350,000

Axis Title

Axis Title

Listing Price of Preferred Share

PSD 1

Rel. ITW 0.5

0.8

0.3

0.6

0.1

0.4

-0.1

0.2

-0.3 PSD (left Y-axis)

ITW, rel. (right Y-axis)

0

-0.5 0

250

500

750

1,000

1,250

1,500

1,750

2,000

2,250

2,500

2,750

3,000

3,250

3,500

3,750

Number of trading days since issuance

Fig. 4. Preferred stock discount at issuance. This figure is based on the 59 pairs of the KSE and Kosdag-listed “old type” preferred and common shares, newly issued from January 2000 until October 2014. Panel A shows the preferred stock discounts (PSDs, Y-axis) of new listings versus the contemporaneous PSD index, which is a preferred share market capitalization-value weighted index. Panel B plots the first-day PSDs of new listings against their listing prices. Panel C shows the daily trends of the PSD Index and the index of relative individual trading weight (RITW), which is also a preferred share market capitalizationvalue weighted index.

preferred stocks, whose conditions of dividends and voting rights are distinct from the old types.16 Table 6 summarizes the sample statistics of new-type preferred stock listings. Although these issues were introduced to alleviate the conspicuous anomalies of existing preferred shares partly due to illiquidity, the daily trading volume is, on average, still far behind that of existing old-type preferred stocks. However, as these new types are embedded with cumulative dividend and commonshare convertibility options, their disparity is noticeably less than the old ones. Table 7 is a replication of Table 4 based on the augmented sample with new-type preferred shares. The primary (new type I dummy) and secondary (new type II dummy) issues of new-type preferred shares following existing old-type preferred stocks are indexed as dummy variables. In Model 5 or 6, having included the size variables and controlled for the time- and firm-fixed effects, individual traders continue to play a role in discounting preferred shares, and the magnitudes of the coefficient estimates of RITW and size variables have remained the same or slightly increased. Concerns that the signs and significances of the variables pertaining to dividends, voting rights, and turnover may have reverted or weaken, respectively, after adding new-type preferred stock listings to the sample appear overdone. Especially, the chaebol dummy and relative turnover, which is independent of the corporate article, still retain their big impacts (high coefficient estimates). Overall, 1%p more trading in preferred shares by individuals, compared to

16

See Footnote 6.

14

15

Old type New type I New type II

Preferred stock type

185 46 10

No. of issuers

97.0 14.3 4.2

Traded listings per day 2,694 2,536 6,857

(B)

(A) 158 176 36

Common

Preferred

(17.1) (14.4) (189.1)

(B/A)

Market cap. (KRW billion)

34.3 30.2 11.2

(A)

Preferred

701.7 851.7 795.1

(B)

Common

(20.5) (28.2) (70.9)

(B/A)

Trading volume (KRW '000s)

90.9% 91.6% 92.0%

Indiv.

4.4% 3.8% 4.1%

Inst.

4.8% 3.8% 4.0%

Foreign

Preferred stock

76.3% 78.0% 64.5%

Indiv.

13.1% 12.3% 18.7%

Inst.

10.5% 9.8% 16.8%

Foreign

Common stock

Investor trading weight (%)

0.252 -0.110 0.204

Equal- weighted

0.427 0.392 0.554

Value- weighted

PSD

Table 6 Comparison of new-type and old-type preferred shares, and common stocks This table is based on the pairs of old-type and new-type preferred shares and common stocks listed on the KSE and the Kosdaq from January 2000 until October 2014. Those listings with trading days under the January effect, i.e. the first 5 trading days in any year, listings with less than 10 trading days or of lowest 10% in trading volume, and common-preferred share pairs with higher than 10% in the preferred stock disctount (PSD) are excluded from this sample. The final sample consists of 185, 46, and 10 pairs of old-type, new-type I, and new-type II preferred shares, respectively, and their comparable common stocks traded on the KSE and the Kosdaq. The investor trading weight is the ratio of the trading volume of shares of a specific—individual, institutional, and foreign—investor group over the total trading volume of shares. PSD is the price difference of common over preferred shares divided by the common stock price (Zingales, 1994).

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Table 7 Inclusion of new-type preferred shares. This table replicates Table 4 based on the full pairs of “old type” preferred and common shares listed on the KSE and the Kosdaq from January 2000 until October 2014. As the dependent variable, the preferred stock discount (PSD) is the price difference of common over preferred shares divided by the common stock price (Zingales, 1994; Kim et al., 1996). For the explanatory variables, the individual trading weight (ITW) is the ratio of the individual trading volume of shares over the total trading volume of shares, and the relative ITW (RITW) is the ITW of a preferred stock minus the ITW of the comparable common share. The relative smallness of a given preferred stock is 1 minus the ratio of the market capitalizations of preferred over common shares (Relative Smallness). For dividend-related variables, the dividend dummy variable (Dividend) of a given period equals one if payout took place in the previous period or zero otherwise. 5 trading days prior to a given dividend day (Dividend Drop) are controlled for with a dummy variable which is interacted with the dividend dummy. For the voting rights-related variables, absolute control is gained by a shareholder with more than a 50% stake. The value of voting rights is non-linearly affected by large shareholders' stakes. As the ownership of large shareholders gradually increases far from absolute control stake, the value of voting rights will rise upon more likely proxy fights (Proxy Fight). However, as the probability of proxy fights lowers after the gain of absolute control (over 50% stake), voting rights will be valued less by then upon stabilization of management. The sample firms are whether affiliated with conglomerates (Korea Fair Trade Committee-designated) or not (Chaegol). The measures of liquidity are turnover (trading volume normalized by total number of outstanding shares), and dollar volume and the Amihud's (2002) ratio. Amihud (2002) suggests the ratio of the absolute value of return over contemporaneous dollar volume (KRW 100 million in this study) as a gauge of illiquidity. All relative measures are the excesses of preferred over common shares. The market factor (Market) is the monthly excess returns of the value-weighted average of the KOSPI and the Kosdaq indices over the monthly adjusted rate of 1 year monetary stability bond (MSB). The size (SMB) and valuation (HML) buy-and-hold portfolios are annually rebalanced at the end of every June based on the last year-end market capitalizations for the SMB factor: small (below median) versus big; and based on the book-to-market ratio (B/M) for the HML factor: low (lowest 30%), high (highest 30%), and medium (the rest). The primary (New Type I) and secondary (New Type II) issues of new-type preferred shares following existing old-type preferred stocks are indexed as dummy variables. The log of common share market capitalization (KRW billion) is controlled for. Standard errors are adjusted for clustering at the firm level and across time (Petersen, 2009), and the corresponding tstatistics are presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels, respectively.

RITW

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.215*** (6.386)

0.195*** (5.428) 1.597*** (2.692)

0.193*** (5.375) 1.639*** (2.731) −0.105** (−2.298) 0.002 (0.450)

0.132*** (4.265) 3.101*** (3.748) −0.099 (−1.127) 0.004 (0.998) −0.001 (−0.297) 0.000 (−0.374)

0.123*** (4.062) 3.018*** (3.946) −0.103 (−1.269) 0.002 (0.716) 0.000 (−0.171) 0.000 (−0.449)

0.123*** (4.063) 3.018*** (3.945) −0.103 (−1.269) 0.003 (0.909) 0.000 (−0.172) 0.000 (−0.448)

−0.001 (−0.744) 0.000 (0.541) −1.224*** (−10.714)

−0.001 (−0.744) 0.000 (0.543) −1.224*** (−10.713) 0.156*** (5.735) 0.173*** (4.363) 0.137** (2.451)

Relative smallness Dividend Dividend × dividend drop (t-5 to t-1) Largest stake Largest stake × absolute control Chaebol dummy Relative dollar volume Relative Amihud ratio Relative turnover Market SMB HML New type I New type II Constant Firm-fixed effect Time-fixed effect Adj. R2 N

0.394*** (8.422) Yes Yes 0.053 413,514

−1.097* (−1.935) Yes Yes 0.071 413,514

−1.126* (−1.967) Yes Yes 0.072 413,514

−2.516*** (−3.201) Yes Yes 0.076 331,768

−2.425*** (−3.332) Yes Yes 0.111 331,768

−2.424*** (−3.330) Yes Yes 0.111 331,738

Model 7

Model 8

−0.061 (−0.773) 0.002 (0.223) 0.001 (0.264) 0.000 (−0.032) 0.166** (2.538) −0.002 (−0.673) −0.005*** (−3.065) −1.661*** (−8.435)

−0.066 (−0.856) 0.000 (−0.044) 0.000 (−0.177) 0.000 (−0.233)

−0.001 (−0.955) 0.000 (0.211) −1.271*** (−11.434)

−0.315*** (−2.955) −0.070 (−0.517) 0.271** (2.295) No Yes 0.087 331,768

0.427** (2.452) Yes Yes 0.07 331,768

comparable common stocks, gives rise to a steepening in the discount by, around, 10 to 20 cents per month for every dollar invested in the “preferred-long, common-short” portfolio. The economic value of individual trading in the pairs of common and preferred shares is substantial. In Model 7, without having controlled for the firm-fixed effect, the primary issues (new type Ι dummy) of newtype preferred shares are deemed to alleviate the overall discount of preferred stock listings due to its reinforced dual-class benefits such as cumulative dividend and convertibility entitlements. Due to scarcity in observations, the secondary (new type II dummy) 16

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issues turn out statistically insignificant in reducing the price gap of common-preferred equity pairs. For additional robustness tests, Table 8 compiles the abbreviated regression results of replicating Models 1 through 6 in Table 4 under various circumstances. The explanatory variables other than the key variable, RITW, are suppressed to conserve space. We find that NTR proxied for by the excess of the proportion of individual trading (RITW) of preferred shares over their comparable common equities is an influential determinant of PSD unanimously under, firstly, bull (Panel A) versus bear markets (Panel B) to separately account for market conditions (Fig. A.1); secondly, high (Panel C) versus low ITW (Panel D) to reflect the two distinct regimes of “high and low” versus “low and volatile” ITWs (Fig. 5); and lastly, PSD being near-parity within a narrow range (−30 % < PSD < 30%, Panel E) and the discount being negative (premium, Panel F) to account for possible endogeneity (Fig. A.2).17 4.4. Evidence of noise trader risk in Taiwan Although we have evidenced the relative pricing of preferred shares via NTR, proxied for by ITW, in the Korean stock market, it would be conducive to witness in another emerging market to bolster our inference. Luckily, Taiwan is another emerging market trading venue where the trading volume information of investor groups in every stock trade is recorded. The purchase and sales volume data of individual, institutional, and foreign investors were procured from a Taiwan-based database, CMoney, which is compiled from the data originally provided by the Taiwan Stock Exchange (TWSE).18 The sample period for the Taiwan data is from January 2002 to December 2004. Although this does not fully coincide with the Korean data, we believe that this is sufficiently purposeful. Through the sample period, we identified 8 pairs of both common and preferred shares dual-listed with 2960 firm-day observations. Having filtered out the trading days of excessive outliers with more than 50% in PSD, an average dual-listed company is worth NT$15.48 (about US¢46 in the 2004 average rate) and NT$13.49 (about US¢40) in common and preferred stocks per share, respectively, with its preferred share discounted at 12.72% against its comparable common stock. The total market values of common and preferred shares are, on average, NT$32.3 billion (about $1 billion) and NT$0.9 billion (about $28 million), respectively, for each dual-listed company. The ITW of an average preferred stock is about 16%p (RITW) higher than that of a comparable common share. In Fig. 6 we plot the average trends of both PSD (left Y-axis) and RITW (right Y-axis), using the preferred stock market capitalizations as the value weights. In Taiwan stocks are heavily traded by individual investors (Barber et al., 2007, 2009) and we find that preferred shares more densely occupied by individuals than common stocks, which is evidenced by overall positive RITW. Besides, the co-movement of PSD and RITW is evident in Taiwan as well, whose correlation is strongly positive at 54.9% on a daily basis. The apparently highly volatile PSD suggests the presence of NTR fueled by individual traders. These preliminary results are largely compatible with the findings we documented regarding the Korean stock market. 5. Conclusion This paper finds empirical evidence that individuals are a source of NTR. From the analyses herein, the proportion of individual traders is an important risk factor for determining the persistent discount of stocks. The empirical inferences are drawn from identifying the determinants of PSD. First, ITW explains the arbitrage return of common-preferred equity pairs (PSD) with identical fundamentals. An increase in the excess ITW of preferred over common shares (RITW) steepens the discount of preferred equities. Further, the statistical significance of this finding remains binding even after controlling for conventional explanatory variables such as dual-class differences in dividend yield, voting rights and turnover, or size variables. This shows that NTR created by the misperception of individuals is priced in the Korean stock market. Similar to Choi and Choi's (2018) finding that ITW explains common stock returns in Korea and Taiwan, we show that the RITW determines the return of “long-preferred, short-common” arbitrage. Individuals in the Korean stock market turn out to deter the parity-convergence of common-preferred equity pairs. We identify at least a few topics for future research. Just as this study exploits a specific feature of the main database (DataGuide) that records the trading volume of each trader group, our choice of Korean data is not free from the restriction of its availability. To our best knowledge, other than this study and Choi and Choi (2018), only studies that exploit proprietary retail trading data identified the trades of individual investors and analyze their properties, characteristics, and roles: see Barber et al. (2007, 2009) for Taiwan studies, and Barber and Odean (2000, 2001, 2002) and Kumar and Lee (2006) for U.S. findings. Our preliminary results from the Taiwan case poses a further cross-country comparison in another study. There is a dearth in the literature pertaining to, or even mentioning of, trading preferred shares by individual investors in the developed markets: See Evans (1929) for the historical background, Stickel (1991) for nonconvertible preferred shares, and Karpoff and Walkling (1990) for dividend capture in Nasdaq stocks. Further, for example, the tax code in the U.S. might encourage institutions and corporations to hold preferred shares, rather than individuals.19 These may vindicate our analysis of an advanced emerging market rather a developed economy, like the U.S., in addition to the hurdle to the procurement of a proprietary data. However, as the time variation of PSD can be substantial in a country with a large premium of voting rights due to inferior shareholder protection (La Porta et al., 2002; Nenova, 2003), upon procurement of extensive data (again) we can contrast this test for the emerging markets, mostly under the civil law system, versus the developed economies, whose majority is governed by the common 17 18 19

Fig. A.1 and A.2 are appendicized online. We thank Seth Huang for his arrangements. We thank Warren Bailey for this comment.

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Table 8 Additional robustness tests. This table replicates Table 4 for Models 1 through 6 for the subsamples under bull versus bear markets (Panels A and B, resp.), high versus low ITWs (Panel C and D, resp.), a narrow range of PSD (Panel E), and the premiums of preferred shares (Panel F). These regressions are performed on the 185 pairs of old-type preferred and common shares listed on the KSE and the Kosdaq from January 2000 until October 2014. As the dependent variable, the preferred stock discount (PSD) is the price difference of common over preferred divided by the common share price (Zingales, 1994; Kim et al., 1996). As the key explanatory variable, the relative individual trading weight (RITW) is the individual trading weight (ITW) of a preferred stock minus the ITW of the comparable common share. ITW is the ratio of the individual trading volume of shares over the total trading volume of shares. The following control variables, whose specifications follow those of Table 4, are subdued for the lack of space: The relative smallness of a given preferred stock is 1 minus the ratio of the market capitalizations of preferred over common shares (Relative Smallness). For dividend-related variables, the dividend dummy variable (Dividend) of a given period equals one if payout took place in the previous period or zero otherwise. 5 trading days prior to a given dividend day (Dividend Drop) are controlled for with a dummy variable which is interacted with the dividend dummy. For the voting rights-related variables, absolute control is gained by a shareholder with more than a 50% stake. The value of voting rights is non-linearly affected by large shareholders' stakes. As the ownership of large shareholders gradually increases far from absolute control stake, the value of voting rights will rise upon more likely proxy fights (Proxy Fight). However, as the probability of proxy fights lowers after the gain of absolute control (over 50% stake), voting rights will be valued less by then upon stabilization of management. The sample firms are whether affiliated with conglomerates (Korea Fair Trade Committee-designated) or not (Chaegol). The measures of liquidity are turnover (trading volume normalized by total number of outstanding shares), and dollar volume and the Amihud's (2002) ratio. Amihud (2002) suggests the ratio of the absolute value of return over contemporaneous dollar volume (KRW 100 million in this study) as a gauge of illiquidity. All relative measures are the excesses of preferred over common shares. The market factor (Market) is the monthly excess returns of the value-weighted average of the KOSPI and the Kosdaq indices over the monthly adjusted rate of 1 year monetary stability bond (MSB). The size (SMB) and valuation (HML) buy-and-hold portfolios are annually rebalanced at the end of every June based on the last year-end market capitalizations for the SMB factor: small (below median) versus big; and based on the book-to-market ratio (B/M) for the HML factor: low (lowest 30%), high (highest 30%), and medium (the rest). The log of common share market capitalization (KRW billion) is controlled for. Standard errors are adjusted for clustering at the firm level and across time (Petersen, 2009), and the corresponding t-statistics are presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. Panel A. Bull markets

Relative ITW Adj. R2 N

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.197*** (5.891) 0.061 185,434

0.177*** (4.847) 0.077 185,434

0.175*** (4.799) 0.079 185,434

0.120*** (3.716) 0.081 151,246

0.111*** (3.493) 0.114 151,246

0.111*** (3.494) 0.114 151,246

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.209*** (6.020) 0.064 161,801

0.192*** (5.117) 0.078 161,801

0.190*** (5.036) 0.080 161,801

0.130*** (3.877) 0.081 128,279

0.122*** (3.678) 0.124 128,279

0.122*** (3.677) 0.124 128,254

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.378*** (2.966) 0.125 120,955

0.368*** (2.907) 0.137 120,955

0.360*** (2.872) 0.140 120,955

0.359*** (3.387) 0.173 88,145

0.340*** (3.244) 0.196 88,145

0.340*** (3.244) 0.196 88,140

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.166*** (5.422) 0.140 226,280

0.140*** (4.175) 0.168 226,280

0.140*** (4.173) 0.168 226,280

0.094*** (3.402) 0.204 191,380

0.087*** (3.102) 0.237 191,380

0.087*** (3.102) 0.237 191,360

Model 2

Model 3

Model 5

Model 6

Panel B. Bear markets

Relative ITW Adj. R N

2

Panel C. High ITW

Relative ITW Adj. R2 N

Panel D. Low ITW

Relative ITW Adj. R2 N

Panel E. PSD within the range of 30% and − 30% Model 1

Model 4

(continued on next page) 18

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Table 8 (continued) Panel E. PSD within the range of 30% and − 30%

Relative ITW Adj. R N

2

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.056*** (3.393) 0.079 82,039

0.049*** (2.910) 0.129 82,039

0.049*** (2.883) 0.129 82,039

0.042** (2.297) 0.157 59,121

0.041** (2.188) 0.168 59,121

0.041** (2.191) 0.168 59,116

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

0.773** (2.595) 0.124 55,507

0.774** (2.562) 0.128 55,507

0.771** (2.552) 0.129 55,507

0.604** (2.282) 0.238 37,674

0.571** (2.223) 0.249 37,674

0.571** (2.224) 0.249 37,671

Panel F. Preferred stock premium

Relative ITW Adj. R N

2

PSD

RITW

0.2

0.12

PSD 1

0.1 0.10 0.0 0.08

-0.1

0.95

-0.2 0.06 -0.3 -0.4

0.04

0.9

-0.5 0.02 -0.6 -0.7

0.00

PSD (LHS)

0.85

Rel. ITW (RHS)

ITW of Common Shares ITW of Preferred Shares

PSD

RITW

PSD

0.6

0.35

1

0.5

0.30 0.9 0.25

0.4

0.20

0.8

0.15

0.7

0.3 0.2

0.10 0.6

0.1

0.05

0.0

0.00

PSD (LHS)

0.5

Rel. ITW (RHS)

ITW of Common Shares ITW of Preferred Shares

Fig. 5. Comparative dynamics of preferred stock discount per individual trading weight (ITW) and relative ITW. These figures show the trends of the preferred stock discount (PSD) and relative individual trading weight (RITW) from the 185 pairs of “old type” preferred and common shares listed on the KSE and the Kosdaq from January 2000 until October 2014. Panels A and C show the PSDs (left Y-axis) and RITWs (right Y-axis) for the subsamples with high and low ITWs, respectively. Panels B and D show the ITWs of common and preferred for subsamples with high and low ITWs, respectively. The daily PSDs and RITWs of each pair are weight-averaged using preferred share market capitalizations on a quarterly basis.

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RITW 1

PSD 0.5 PSD (left Y-axis) RITW (right Y-axis)

0.4

0.8

0.3

0.6

0.2

0.4

0.1

0.2

0 Jan-2002

Jan-2003

Jan-2004

0 Jan-2005

Fig. 6. Preferred stock discount and relative individual trading weight in Taiwan. This figure shows the daily trends of the average preferred stock discount (PSD) of and relative individual trading weight (ITW) based on the pairs of preferred and common shares listed on the Taiwan Stock Exchange (TWSE) from January 2002 until December 2004. The market capitalizations preferred stocks are used as the value weights.

legal statutes (La Porta et al., 1998). Likewise, we leave this undone task for future studies of our own and readers'. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ememar.2018.03.006. References Amihud, Y., 2002. Illiquidity and stock returns: cross-section and time-series effects. J. Financ. Mark. 5, 31–56. Barber, B.M., Lee, Y.T., Liu, Y.J., Odean, T., 2007. Is the aggregate investor reluctant to realise losses? Evidence from Taiwan. European Financial Management 13, 423–447. Barber, B.M., Lee, Y.T., Liu, Y.J., Odean, T., 2009. Just how much do individual investors lose by trading? Rev. Financ. Stud. 22, 609–632. Barber, B.M., Odean, T., 2000. Trading is hazardous to your wealth: the common stock investment performance of individual investors. J. Financ. 55, 773–806. Barber, B.M., Odean, T., 2001. Boys will be boys: gender, overconfidence, and common stock investment. Q. J. Econ. 116, 261–292. Barber, B.M., Odean, T., 2002. Online investors: do the slow die first? Rev. Financ. Stud. 15, 455–489. Black, F., 1986. Noise. J. Financ. 41, 529–543. Carhart, M.M., 1997. On persistence in mutual fund performance. J. Financ. 52, 57–82. Chay, J.-B., Moon, P.-S., 2005. Discount pricing of preferred stocks to common stocks: the role of liquidity premiums (in Korean). The Korean J. Financ. 18, 263–287. Choi, J.H., 2015. Individuals as Noise Traders: Evidence from Korean Stock Listings. Ph.D. dissertation. Seoul National University. Choi, P.M.S., Choi, J.H., 2018. Is individual trading priced in stocks? J. Int. Money Financ (Forthcoming). Chung, K.H., Kim, J.-K., 1999. Corporate ownership and the value of a vote in an emerging market. J. Corp. Finan. 5, 35–54. Cox, S.R., Roden, D.M., 2002. The source of value of voting rights and related dividend promises. J. Corp. Finan. 8, 337–351. De Long, J.B., Shleifer, A., Summers, L.H., Waldmann, R.J., 1990. Noise trader risk in financial markets. J. Polit. Econ. 98, 703–738. Dempster, A.P., Laird, N.M., Rubin, D.B., 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B Methodol. 39, 1–38. Evans, G.H., 1929. The early history of preferred stock in the United States. Am. Econ. Rev. 19, 43–58. Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 33, 3–56. Gibbons, M.R., Ross, S.A., Shanken, J., 1989. A test of the efficiency of a given portfolio. Econometrica 57, 1121–1152. Han, B.H., 2010. Preferred stock price and trade liquidity (in Korean). Korean Journal of Business Administration 23, 1–22. Horner, M.R., 1988. The value of the corporate voting right: evidence from Switzerland. J. Bank. Financ. 12, 69–83. Jensen, M.C., 1968. The performance of mutual funds in the period 1945–1964. J. Financ. 23, 389–416. Kang, J., Kwon, K.Y., Sim, M.H., 2013. Retail investor sentiment and stock returns (in Korean). The Korean Journal of Financial Management 30, 35–68. Kaniel, R., Saar, G., Titman, S., 2008. Individual investor trading and stock returns. J. Financ. 63, 273–310. Karpoff, J.M., Walkling, R.A., 1990. Dividend capture in NASDAQ stocks. J. Financ. Econ. 28, 39–65. Kim, J.K., Park, S.S., Choi, D.S., 1996. Empirical analysis on preferred stock discount (in Korean). The Korean Journal of Finance Association 9, 65–96. Kook, C.P., Jung, G.H., 1996. The determinants of ownership structure in Korea: using linear structural relationships (in Korean). The Korean Journal of Finance Association 9, 249–285. Kumar, A., Lee, C., 2006. Retail investor sentiment and return comovements. J. Financ. 61, 2451–2486. Kyle, A.S., 1985. Continuous auctions and insider trading. Econometrica 53, 1315–1335. La Porta, R., Lopez-de-Silanes, F., Shleifer, A., Vishny, R., 1998. Law and finance. J. Polit. Econ. 106, 1113–1155. La Porta, R., Lopez-de-Silanes, F., Shleifer, A., Vishny, R., 2002. Investor protection and corporate valuation. J. Financ. 57, 1147–1170. Lease, R.C., Lewellen, W.G., Schlarbaum, G.G., 1974. The individual investor: attributes and attitudes. J. Financ. 29, 413–433.

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