The role of investor attention in idiosyncratic volatility puzzle and new results

Abstract

We find that stocks with low investor attention show a more substantial return-idiosyncratic volatility puzzle than stocks with high investor attention. We also document that high idiosyncratic volatility stocks with high investor attention at the end of the month when portfolios are formed are responsible for the puzzle, but they lose investor attention and have negative returns at the beginning of the next month. We further show that the idiosyncratic volatility puzzle exists only in the first half of the following month after portfolios are formed. It holds even for stocks with low investor attention.

Appendix: Definitions of variables

ATT: Abnormal Dollar Trading Volume (ATT) is defined as the dollar trading volume on the day/average dollar trading volume over the previous year following Barber and Odean (2008).

IVOL: During month t, we run the following regression of excess daily returns of each stock i on contemporaneous daily Fama–French factors:

$$R_{{i,d}} - R_{{f,d}} ~ = \alpha _{i} + \beta _{i} MAKTRF_{d} + s_{i} SMB_{d} + h_{i} HML_{d} + \varepsilon _{{i,d}} ~$$

R_i,d is the return of stock i on day d, R_f,d is the daily risk-free rate, and MKTRF_d, SMB_d, and HML_d are the daily Fama–French factors. The monthly idiosyncratic volatility of stock i in month t is defined as the standard deviation of the residuals from this regression times the square root of the number of trading days in the month:

$$IVOL_{{i,t}} = \sqrt {var\left( {e_{{i,d}} } \right)} ~X~\sqrt {D_{t} } ~~$$

where D_t is the number of trading days for stock i in month t.

SIZE: SIZE is the natural logarithm of the stock's month-end market capitalization (price times shares outstanding).

ISKW: Following Harvey and Siddique (2000), ISKW is the daily idiosyncratic skewness of a stock, which is the skewness of the residuals from the following regression:

$$R_{{i,d}} - R_{{f,d}} ~ = \alpha _{i} + \beta _{i} \left( {R_{{m,d}} - R_{{f,d}} } \right) + \gamma _{i} \left( {R_{{m,d}} - R_{{f,d}} } \right)^{2} + \varepsilon _{{i,d}} ~$$

Ri,d, Rf,d, and Rm,d are the return on stock i on day d, the T-Bill return on day d, and the return on CRSP value-weighted market index day d, respectively.

REV: Following Jegadeesh (1990) and Lehmann (1990), the REV variable is used to capture short-term reversals in stock returns and equals the return of stock i in month t; that is, REV_i,t = R_i,t.

Pre12Ret: Pre12Ret is the momentum variable. Following Jegadeesh and Titman (1993), each stock's momentum variable in a given month is defined as its buy and hold return over the past 12 months.

IH: We compute the individual investors' holding (IH) in stock at the end of each quarter by subtracting from 100 the ratio of shares held by large institutional investors to the total number of shares outstanding expressed as %. We further assume that it remains constant over the subsequent quarter before the next update. The quarterly holdings of institutional investors are obtained from the Thomson Reuters 13F institutional database, constructed from the 13 F filings of large institutional investors with $100 million or more in assets under management.

BTM: BTM is the firm's book-to-market ratio. Following Fama and French (1993), we compute BTM in month t of a year as the ratio of the book value of equity for the fiscal year ending in the prior calendar year and market equity at the end of December of the prior calendar year. Book value of equity, computed using Compustat data, is the stockholders' equity (DATA 216), plus balance sheet deferred taxes and investment tax credit (DATA 35), minus the book value of the preferred stock (DATA56 or DATA10 or DATA 130, in that order) at the fiscal year-end.

IllIQ: IllIQ is the measure of illiquidity for a stock in a given month. Following Amihud (2002), Illiq is measured as the ratio of stock's absolute monthly return to its dollar trading volume:

$ILLIQi,t = \left| {Ri,t} \right|$ / $VOLD{\text{ }}i,t$

R_i,t, and VOLD_i,t is the return and dollar volume, respectively, of stock i in month t.

BETA: We use the daily returns within a month to estimate stocks' beta and therefore employ the adjustment procedure of Scholes and Williams (1977) and Dimson (1979) to mitigate the impact of non-synchronous trading. Beta is estimated using the following regression model:

$$Ri,d - Rf,d = ai + \beta 1,i(Rm,d - 1 - Rf,d - 1) + \beta 2,i(Rm,d - Rf,d) + \beta 3,i(Rm,d + 1 - Rf,d + 1) + e_{{i,d}} ,$$

Ri,d, Rf,d, and Rm,d are the return on stock i on day d, the T-Bill return on day d, and the return on CRSP value-weighted market index day d, respectively. The estimate of stock's beta is given by $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } _{i} = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } 1,i + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } 2,i + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } 3,i$.

NAE: Analysts' coverage (NAE) is from IBES summary files of earnings as the monthly earnings estimates are available for each firm.

AGE: firm age (AGE) is the number of years since its founding year of incorporation if the founding year is unavailable. We follow Fink et al. (2010) to obtain original founding dates for our firms' sample between 1980 and 1998. We supplement this data for the remaining of our sample period using founding dates for IPOs compiled by Jay Ritter on his website.¹² We use the earliest available date between the founding date and incorporation date to determine the firm's age.