The role of reference-dependent preferences in the idiosyncratic volatility puzzle: Evidence from Korea

Figures & data

Table 1. Idiosyncratic Volatility and Stock Returns

	Realized idiosyncratic volatility (RIVOL)			Expected idiosyncratic volatility (EIVOL)
	VW	EW		VW	EW
1 (Low)	−0.0013	0.0035		−0.0017	−0.0008
2	−0.0010	0.0036		0.0000	−0.0002
3	−0.0030	0.0026		−0.0023	−0.0026
4	−0.0043	−0.0021		−0.0006	−0.0033
5 (High)	−0.0237	−0.0254		−0.0094	−0.0177
H-L	−0.0224*** (−4.11)	−0.0289*** (−6.62)		−0.0078** (−2.34)	−0.0169*** (−7.02)
FF3 alpha	−0.0190*** (−3.97)	−0.0252*** (−6.68)		−0.0059* (−1.85)	−0.0148*** (−6.82)

For each month, value-weighted and equal-weighted quintile portfolios are formed from July 1990 to June 2018 by sorting the stocks based on the Realized Idiosyncratic Risk (RIVOL), as used by Ang et al. (2006), and Expected Idiosyncratic Risk (EIVOL), as used by Fu (2009). Portfolio 1 (Low) is the lowest idiosyncratic volatility stock, and Portfolio 5 (High) is the highest idiosyncratic volatility stock. The last row H-L is the difference in monthly return between the high and low IVOL portfolios. The t-statistics, using Newey and West (1987) method, are reported in parentheses.

* Significant at the 10% level; ** Significant at the 5% level; ** Significant at the 1% level.

Table 2. Capital gains overhang in the relation between IVOL and future returns

Panel A: Realized Idiosyncratic Risk (RIVOL)
	VW portfolios returns					EW portfolios returns
	UCL		UCG		UCL1-UCG2	UCL		UCG		UCL1-UCG2
	UCL1	UCL2	UCG1	UCG2		UCL1	UCL2	CG1	CG2
1 (Low)	−0.0676	−0.0102	0.0310	0.0799		−0.0587	0.0015	0.0426	0.1094
2	−0.0766	−0.0184	0.0270	0.0848		−0.0683	−0.0033	0.0453	0.1111
3	−0.0844	−0.0207	0.0272	0.0976		−0.0803	−0.0052	0.0447	0.1234
4	−0.1072	−0.0301	0.0186	0.1082		−0.0978	−0.0178	0.0400	0.1336
5 (High)	−0.1412	−0.0328	0.0319	0.1141		−0.1408	−0.0234	0.0522	0.1623
H-L	−0.0742*** (−6.36)	−0.0227*** (−3.84)	0.0009 (0.12)	0.0378*** (4.46)	−0.1120*** (−7.67)	−0.0825*** (−8.54)	−0.0249*** (−6.11)	0.0096* (1.72)	0.0561*** (6.13)	−0.1386*** (−10.57)
FF3 alpha	−0.0740*** (−6.49)	−0.0202*** (−3.28)	0.0016 (0.21)	0.0399*** (4.41)	−0.1140*** (−7.26)	−0.0808*** (−8.77)	−0.0230*** (−5.23)	0.0097 (1.53)	0.0575*** (6.07)	−0.1383*** (−10.06)
Panel B: Expected Idiosyncratic Risk (EIVOL)
	VW portfolios returns					EW portfolios returns
	UCL		UCG		UCL1-UCG2	UCL		UCG		UCL1- UCG2
	UCL1	UCL2	UCG1	UCG2		UCL1	UCL2	UCG1	UCG2
1 (Low)	−0.0936	−0.0213	0.0282	0.0910		−0.0886	−0.0145	0.0425	0.1142
2	−0.0820	−0.0174	0.0211	0.0893		−0.0812	−0.0109	0.0373	0.1202
3	−0.0783	−0.0158	0.0294	0.0942		−0.0833	−0.0099	0.0440	0.1286
4	−0.0855	−0.0146	0.0292	0.1065		−0.0899	−0.0064	0.0503	0.1406
5 (High)	−0.0962	−0.0180	0.0329	0.0967		−0.1053	−0.0054	0.0513	0.1432
H-L	−0.0028 (−0.33)	0.0033 (0.68)	0.0053 (1.14)	0.0060 (0.65)	−0.0088 (−1.19)	−0.0166*** (−2.65)	0.0090** (2.27)	0.0094 (1.60)	0.0285*** (4.10)	−0.0451*** (−5.03)
FF3 alpha	−0.0022 (−0.25)	0.0024 (0.49)	0.0047 (0.94)	0.0050 (0.50)	−0.0072 (−1.41)	−0.0175*** (−2.85)	0.0087** (2.14)	0.0105* (1.70)	0.0290*** (3.94)	−0.0465*** (−5.02)

For each month, the Capital Gains Overhang of stock i is computed as CGO_i,t = (P_i,t − RP_i,t)/P_i,t, where P_i,t is the price of stock i at the end of month t and RP_i,t is the reference price for each stock i at the end of month t (Grinblatt & Han, 2005; Hur et al., 2010). Based on the CGO value relative to 0, the sample data were divided into two sub-groups, namely unrealized capital gain (UCG) sub-group (CGO ≥ 0) and unrealized capital loss (UCL) sub-group (CGO < 0). In the next, the UCG and UCL values were classified into two sub-groups based on their median values. Particularly, UCL1 and UCL2 are below and above the median of unrealized capital loss (UCL), respectively. Similarly, UCG1 and UCG2 are below and above the median of unrealized capital gains (UCG), respectively. Within the UCL1, UCL2, UCG1, and UCG2, the value-weighted (VW) and equal-weighted (EW) returns of the quintile portfolios were shaped in each month from July 1990 to June 2018 by sorting the stocks based on the Realized Idiosyncratic Risk (RIVOL), as used by Ang et al. (2006), and Expected Idiosyncratic Risk (EIVOL), as used by Fu (2009). Portfolio 1 (Low) is the lowest idiosyncratic volatility stock and Portfolio 5 (High) is the highest idiosyncratic volatility stock. The t-statistics using Newey and West (1987) method are reported in parentheses.

* Significant at the 10% level; ** Significant at the 5% level; *** Significant at the 1% level.

Table 3. Cross-sectional test within Idiosyncratic Risk

		Realized Idiosyncratic Risk (RIVOL)			Expected Idiosyncratic Risk (EIVOL)
	MODEL1	MODEL2	MODEL3	MODEL4	MODEL5	MODEL6	MODEL7
IVOL		−0.1683*** (−6.30)	0.0274 (1.24)	0.0821*** (2.83)	−0.0418*** (−4.97)	0.0356*** (5.04)	0.0312*** (2.94)
CGO	0.5583*** (31.96)		0.5602*** (31.32)	0.4420*** (19.21)		0.5596*** (31.94)	0.5455*** (30.49)
IVOL*CGO				1.0850*** (5.54)			0.1059* (1.75)
Beta	0.0251*** (5.16)	−0.0017 (−0.26)	0.0249*** (5.18)	0.0199*** (4.22)	−0.0003 (−0.04)	0.0227*** (4.77)	0.0222*** (4.68)
Logme	−0.0096*** (−10.15)	−0.0040*** (−2.83)	−0.0093*** (−9.58)	−0.0092*** (−9.44)	−0.0022 (−1.65)	−0.0094*** (−9.98)	−0.0094*** (−9.95)
Logbm	0.0038*** (3.15)	0.0041*** (2.94)	0.0038*** (3.34)	0.0033*** (2.82)	0.0053*** (3.66)	0.0041*** (3.47)	0.0040*** (3.36)
Ret1	−0.3276*** (−26.71)	−0.0349*** (−3.69)	−0.3333*** (−27.61)	−0.3434*** (−28.43)	−0.0482*** (−5.19)	−0.3283*** (−26.88)	−0.3305*** (−27.27)
Ret27	−0.1318*** (−12.12)	−0.0022 (−0.42)	−0.1332*** (−12.31)	−0.1345*** (−12.19)	−0.0042 (−0.78)	−0.1323*** (−12.18)	−0.1329*** (−12.21)
Lturn	0.0031 (1.47)	−0.0045*** (−3.11)	0.0033 (1.61)	0.0028 (1.36)	−0.0051*** (−3.77)	0.0028 (1.33)	0.0028 (1.37)

This table shows the Fama and MacBeth (1973) cross-sectional regression test results between the stock returns and several explanatory variables. That includes the Realized Idiosyncratic Risk (RIVOL) as used by Ang et al. (2006), the Expected Idiosyncratic Risk (EIVOL) as used by Fu (2009), the Capital Gains Overhang (CGO), the interaction term between RIVOL or EIVOL and CGO as IVOL_CGO, the market beta of stock as (Beta), the log of the market capitalization (Logme), the book-to-market ratio (Logbm), the momentum (Ret27), the past previous returns (Ret1), and the liquidity measure (Lturn). The t-statistics using Newey and West (1987) method are reported in parentheses. The sample covers the period from July 1990 to June 2018.

* Significant at the 10% level; ** Significant at the 5% level; *** Significant at the 1% level.

Figure 1. Relationship between IVOL and likelihood of positive for various levels of CGO

Table 4. Time series regressions within Idiosyncratic Risk

	UCL1		UCL2		UCG1		UCG2
MODEL	1	2	1	2	1	2	1	2
Panel A: Realized Idiosyncratic Risk (RIVOL)
VW	−0.0763*** (−6.54)	−0.0162* (−1.94)	−0.019*** (−2.82)	0.0068 (0.41)	0.0101* (1.66)	−0.0207 (−1.01)	0.0404*** (4.60)	−0.0075 (−0.29)
EW	−0.081*** (−8.96)	−0.055** (−2.40)	−0.0232*** (−5.26)	−0.0177 (−1.31)	0.0019 (0.25)	−0.0203 (−1.18)	0.0578*** (6.04)	−0.0267 (−1.13)
Panel B: Expected Idiosyncratic Risk (EIVOL)
VW	−0.0006 (−0.06)	−0.0186 (−0.94)	0.0034 (0.68)	−0.0287 (−1.53)	0.006 (1.19)	0.0106 (0.68)	0.0069 (0.73)	−0.0131 (−0.39)
EW	−0.0166*** (−2.62)	−0.0456*** (−4.06)	0.0093** (2.30)	−0.0178 (−0.99)	0.0121** (2.05)	0.0058 (0.20)	0.0307*** (4.14)	−0.0099 (−0.39)

Equation (1)(1) ${\left(\mathrm{H}---\mathrm{L}\right)}_{\mathrm{t}}=\alpha +{\beta }_{\mathrm{M}\mathrm{K}\mathrm{T}}\mathrm{M}\mathrm{K}\mathrm{T}\mathrm{R}{\mathrm{F}}_{\mathrm{t}}+{\beta }_{\mathrm{S}\mathrm{M}\mathrm{B}}\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_{\mathrm{H}\mathrm{M}\mathrm{L}}\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_{\mathrm{U}\mathrm{M}\mathrm{D}}\mathrm{U}\mathrm{M}{\mathrm{D}}_{\mathrm{t}}+{\mathrm{e}}_{\mathrm{t}}$(1) shows the estimated alphas from time-series regressions of the returns of zero-investment portfolios, (H–L), using the Carhart four-factor model and Equation (2)(2) ${\left(\mathrm{H}---\mathrm{L}\right)}_{\mathrm{t}}=\alpha +{\beta }_{\mathrm{M}\mathrm{K}\mathrm{T}}\mathrm{M}\mathrm{K}\mathrm{T}\mathrm{R}{\mathrm{F}}_{\mathrm{t}}+{\beta }_{\mathrm{S}\mathrm{M}\mathrm{B}}\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_{\mathrm{H}\mathrm{M}\mathrm{L}}\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_{\mathrm{U}\mathrm{M}\mathrm{D}}\mathrm{U}\mathrm{M}{\mathrm{D}}_{\mathrm{t}}+{\beta }_{\mathrm{W}\mathrm{M}\mathrm{L}}\mathrm{W}\mathrm{M}{\mathrm{L}}_{\mathrm{t}-1}+{\mathrm{e}}_{\mathrm{t}}$(2) shows Carhart four-factor model and WML factor. The H-L portfolio returns are constructed as in Table 2 for the RIVOL and EIVOL. UCL1 and UCL2 are below and above median capital losses portfolios of unrealized capital loss (UCL) stocks, respectively. Similarly, UCG1 and UCG2 are below and above the median capital gains portfolios of the unrealized capital gains (UCG) stocks, respectively. Within the UCL1, UCL2, UCG1, and UCG2, the value-weighted (VW) and equal-weighted (EW) returns of the quintile portfolios were shaped in each month from July 1990 to June 2018 by sorting the stocks based on the RIVOL and EIVOL. The dependent variable is the difference between the highest and lowest idiosyncratic volatility portfolios (H–L portfolios). The independent variables include the excess market return (MKTRF), Size (SMB), book to market (HML) following Fama and French (1993), and the momentum factor (UMD) following Carhart (1997). The WML factor, estimated based on the return on a value-weighted portfolio that is long losers from the previous month and short winners from the previous month. The Newey and West (1987) adjust t-statistic is reported in the parentheses.

(1) ${\left(\mathrm{H}---\mathrm{L}\right)}_{\mathrm{t}}=\alpha +{\beta }_{\mathrm{M}\mathrm{K}\mathrm{T}}\mathrm{M}\mathrm{K}\mathrm{T}\mathrm{R}{\mathrm{F}}_{\mathrm{t}}+{\beta }_{\mathrm{S}\mathrm{M}\mathrm{B}}\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_{\mathrm{H}\mathrm{M}\mathrm{L}}\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_{\mathrm{U}\mathrm{M}\mathrm{D}}\mathrm{U}\mathrm{M}{\mathrm{D}}_{\mathrm{t}}+{\mathrm{e}}_{\mathrm{t}}$(1)

(2) ${\left(\mathrm{H}---\mathrm{L}\right)}_{\mathrm{t}}=\alpha +{\beta }_{\mathrm{M}\mathrm{K}\mathrm{T}}\mathrm{M}\mathrm{K}\mathrm{T}\mathrm{R}{\mathrm{F}}_{\mathrm{t}}+{\beta }_{\mathrm{S}\mathrm{M}\mathrm{B}}\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_{\mathrm{H}\mathrm{M}\mathrm{L}}\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_{\mathrm{U}\mathrm{M}\mathrm{D}}\mathrm{U}\mathrm{M}{\mathrm{D}}_{\mathrm{t}}+{\beta }_{\mathrm{W}\mathrm{M}\mathrm{L}}\mathrm{W}\mathrm{M}{\mathrm{L}}_{\mathrm{t}-1}+{\mathrm{e}}_{\mathrm{t}}$(2)

* Significant at the 10% level; ** Significant at the 5% level; *** Significant at the 1% level.

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