Idiosyncratic volatility, option-based measures of informed trading, and investor attention

Table 1 presents pooled descriptive statistics on IVol, the three measures of informed trading, MAX, short-term reversal, the logarithm of firm size, book-to-market, momentum, Amihud (2002) illiquidity, and the abnormal search volume index. Moreover, correlation coefficients are provided.⁵ Several points are noteworthy. Our sample consists of rather large, liquidly traded stocks with a median market capitalization of 3.8 bn USD and a median Amihud measure of 0.47.⁶ The distributions of \(\hbox {VS}_{\mathrm{CW}}\) and \(\hbox {VS}_{\mathrm{BH}}\) are very similar. Their negative average values show that put-implied volatilities tend to exceed call-implied volatilities. SMIRK is even more negative on average since it does not only reflect implied volatility spreads between calls and puts, but also the on average negative slope of the implied volatility curve, i.e., it also takes the skewness of the risk-neutral density into account.

Turning to the correlations, we find support for a negative relationship between IVol and the three measures of informed trading: Each of the three measures tends to be higher for low- compared to high-IVol stocks. This observation is in line with the hypothesis that sophisticated investors recognize the overvaluation of high-IVol stocks and buy corresponding put options. This demand would imply comparably high put-implied volatilities and result in low option-implied volatility spreads. Not surprisingly, as all these three volatility spreads are used to proxy informed trading, the correlation among \(\hbox {VS}_{\mathrm{CW}}\), \(\hbox {VS}_{\mathrm{BH}}\), and SMIRK is strongly positive indicating similar information content. Moreover, we find a strong positive correlation of 0.75 between IVol and MAX, which supports the positive relationship (also correlation coefficient of 0.75) reported by Bali et al. (2011) for a monthly sample. Finally, IVol and investor attention are positively correlated with a correlation coefficient of 0.13, indicating comparably high attention for stocks with high idiosyncratic volatility.

The cross-sectional return predictability of IVol and option-implied volatility spreads is well-documented in the previous literature. Referring to the former, Han and Kumar (2013), Stambaugh et al. (2015), Hou and Loh (2016), and Kumar et al. (2018) provide empirical evidence on the overvaluation of high-IVol stocks, leading to their low subsequent returns. Referring to the latter, Bali and Hovakimian (2009), Cremers and Weinbaum (2010), and Xing et al. (2010) argue that the proposed volatility spreads reflect demand effects of sophisticated investors and thus allow for the prediction of subsequent returns.

To confirm these base-line effects while simultaneously taking control variables into account, we run regressions following Fama and MacBeth (1973), with the stock return of the subsequent week as the dependent variable. The corresponding regression estimates are presented in Table 2. First, we examine the relation between IVol and subsequent returns. The IVol puzzle has been commonly investigated in larger samples that begin far before 1996 and that contain the entire cross-section of U.S. stocks (see, for example, Ang et al. 2006). On the contrary, our analyses are restricted to a comparably large and liquidly traded subset of stocks among which the magnitude of mispricing is usually assumed to be less strong. Nevertheless, regression (1) supports the significantly negative relation between IVol and subsequent returns in our sample.

In line with the original studies, each of the volatility spreads \(\hbox {VS}_{\mathrm{CW}}\), \(\hbox {VS}_{\mathrm{BH}}\), and SMIRK positively predicts subsequent returns in columns (2) to (4). Moreover, all three measures stay significant if they are jointly used as explanatory variables in regression (5). Although the coefficient magnitude sharply declines due to multicollinearity (see correlation coefficients in Table 1), each of the three measures reflects a slightly different part of the option universe and thus retains significant explanatory power. These results support the idea that sophisticated investors might trade on superior information in the option market—for example because of short-sell constraints or because they might want to express their opinion in a levered way (Black 1975; Easley et al. 1998).⁷ As a consequence of this informed option demand, cross-market return predictability emerges. This supports our analyses’ baseline prerequisite that the measures are suited to identify overvalued stocks. Finally, IVol and the three measures of informed trading remain significant when we introduce further well-known cross-sectional return determinants in regression (6).⁸

After verification of these base-line effects, the focus of our analysis lies in the interaction between the IVol puzzle and the measures of informed trading. Recall that the correlation coefficients in Table 1 depict a negative relationship between IVol and each of the three measures. This is consistent with the conjecture that sophisticated investors identify high-IVol stocks as overvalued and trade in order to exploit this anomaly.⁹ From a behavioral point of view, trading against high-IVol stocks can be attractive for sophisticated investors for the following three reasons: First, sophisticated investors can easily calculate IVol and trade in order to exploit the mispricing. Second, the corresponding literature largely favors a behavioral explanation for the IVol puzzle and does not suggest that respective trading strategies render unprofitable if systematic risk exposure is taken into account. Third, Li et al. (2016) suggest that a stock trading strategy based on IVol is unprofitable after costs such that sophisticated investors might turn to the option market in order to exploit the IVol puzzle.

Extending this line of argument, previous research shows that the IVol puzzle is driven by the overvaluation of high-IVol stocks rather than the undervaluation of low-IVol stocks (see corresponding return asymmetry in seminal portfolio sorts of Ang et al. (2006)).¹⁰ Consequently, we expect that the return effects associated with the IVol puzzle are particularly strong if sophisticated investor trading also points towards an overvaluation. Vice versa, we expect the return spreads associated with IVol to be smaller if the measures of informed trading indicate no overvaluation. For example, a correctly priced, fundamentally driven increase in idiosyncratic volatility does not imply an overvaluation and should not induce any return predictability. Thus, the measures of informed trading should be helpful in identifying those high-IVol stocks that are most likely prone to severe overvaluation.

Table 3 empirically examines this hypothesis on the relationship between measures of informed trading and IVol, presenting cross-sectional conditional double sorts. First, every stock is allocated to a portfolio based on \(\hbox {VS}_{\mathrm{CW}}\), \(\hbox {VS}_{\mathrm{BH}}\), or SMIRK. Second, each of these portfolios is divided into three IVol terciles. Table 3 presents the equally-weighted FFC-adjusted portfolio returns of the subsequent week and the return differences between the extreme terciles.¹¹ The results support a behavioral explanation for the IVol puzzle since it is especially pronounced for those stocks that are considered to be overpriced by sophisticated investors in the option market. Instead, for stocks with positive sophisticated investor opinion, the IVol puzzle is less strong since these stocks are apparently less prone to overvaluation.¹² Referring to the SMIRK-based analyses, for example, the IVol puzzle amounts to significant 0.29% per week in the low-SMIRK tercile and to insignificant 0.10% in the high-SMIRK tercile. The difference between these two figures is also statistically significant.

Moreover, Table 3 supports our hypothesis that the measures of informed trading can be used to distinguish between overvalued and fairly priced high-IVol stocks. While high-IVol stocks subsequently underperform on average, this effect does not apply to all high-IVol stocks. For example, high-IVol stocks show a substantial negative abnormal return of \(-0.34\%\) for the \(\hbox {low-CS}_{\mathrm{CW}}\) tercile but an even slightly positive abnormal return for the \(\hbox {high-CS}_{\mathrm{CW}}\) tercile (0.07%). In addition, Table 3 shows that the return spreads associated with \(\hbox {VS}_{\mathrm{CW}}\), \(\hbox {VS}_{\mathrm{BH}}\), and SMIRK are particularly strong for high-IVol stocks.¹³ This underpins our conjecture that informed option trading is presumably most successful for the most overvalued stocks, which offer the largest return opportunities.

Table A20 in the Online Appendix further supports this mispricing hypothesis. First, the return predictability associated with IVol should be strongest when new fundamental information on the stock is released (Engelberg et al. 2018). Second, informed option trading is supposed to be most successful before substantial information becomes public (Atilgan 2014). We therefore expect that the observed return patterns in Table 3 become stronger if the return measurement period contains a quarterly earnings announcement. Indeed, the return spreads on average more than double for this subsample of firm-week-observations.

To sum up, the IVol puzzle is most pronounced for those stocks that sophisticated investors perceive as overvalued. Thus, our findings are in line with those of Stambaugh et al. (2015) who also find a strong dependence of the IVol puzzle on the direction of a stock’s mispricing. However, they proxy overvaluation through a combination of eleven market anomalies. Thus, their measure of mispricing does not allow for a link to the opinion of sophisticated investors and their trading on overvaluation. Moreover, Table A21 in the Online Appendix shows that the return patterns in Table 3 are not subsumed by the measure proposed by Stambaugh et al. (2015). If we only use the parts of \(\hbox {VS}_{\mathrm{CW}}\), \(\hbox {VS}_{\mathrm{BH}}\), and SMIRK that are orthogonal to their mispricing score, the findings from Table 3 remain qualitatively unchanged.

The correlation figures in Table 1 and the double sorts in Table 3 suggest that sophisticated investors trade against overvalued high-IVol stocks in the option market. This raises the question why stock prices do not correctly reflect fundamental values in the first place given the existence of a seemingly well-informed investor group that could arbitrage away the mispricing. In this context, the theoretical models of De Long et al. (1990) and Shleifer and Vishny (1997) imply that noise traders can cause stock mispricing even in the presence of rational market participants (see also an empirical application in Aabo et al. (2017)). In reality, these noise traders are often considered to be unsophisticated private investors. In this context, Han and Kumar (2013) show that the IVol puzzle only exists among stocks that are strongly traded by private investors. Similarly, Stambaugh et al. (2015) show that the IVol puzzle’s magnitude is substantially higher following periods of high market-wide investor sentiment.

Beyond sentiment, Kumar et al. (2018) consider investor attention a key driver of the IVol puzzle as it only appears among stocks that show up on daily winner and loser rankings in newspapers. This finding is related to the following line of argument. Given the enormous amount of stock market information, paying attention to every piece would exceed individuals’ cognitive abilities (Kahneman 1973) such that only a few stocks end up in the choice set of unsophisticated private investors. Barber and Odean (2008) formalize the idea of attention-induced trading. Only if investors pay attention to a stock, they can exert buying pressure and trigger the stock’s overvaluation. In conclusion, these studies suggest that private sentiment-driven investors are responsible for the overvaluation of attention-grabbing stocks like high-IVol stocks. Therefore, our second hypothesis implies a positive relationship between the IVol puzzle’s magnitude and private investor attention.

We test this hypothesis by using Google Trends data as a direct stock-specific measure for sentiment-related private investor attention. Supporting our methodological approach, Da et al. (2011, 2014) show that Google Search volume can be used to proxy for private investor attention and sentiment.¹⁴ Table 1 has already provided initial indication that IVol and investor attention are related as the respective correlation coefficient is 0.13.

Table 4 reports conditional double sorts where we first sort on private investor attention (a stock’s abnormal search volume) and then on IVol. The corresponding weekly return effect associated with IVol increases from insignificant 0.09% in the low-ASVI tercile to significant 0.16% in the high-ASVI tercile.¹⁵ This finding supports our hypothesis that links the origin of the IVol puzzle to the trading behavior of sentiment-driven private investors.¹⁶

The natural follow-up question is how the IVol puzzle interacts with both the sophisticated and the private investor group. Hence, our final central hypothesis is that the IVol puzzle is most pronounced for stocks that are considered overvalued by sophisticated investors and that receive high private investor attention at the same time.

We test this relation in conditional triple sorts. At the end of each week, we first allocate stocks into three portfolios based on their abnormal search volume. Then within each tercile, we form portfolios based on each of the three measures of informed trading. Finally, the stocks in each sub-portfolio are allocated to one of three IVol terciles. Table 5 shows the FFC-adjusted subsequent portfolio returns for the high-ASVI tercile in Panel A and the low-ASVI tercile in Panel B. The results show that the IVol puzzle is indeed strongest if both attention is high and sophisticated trader opinion is low. Referring to the \(\hbox {VS}_{\mathrm{BH}}\)-based analyses in the high-ASVI tercile, the corresponding weekly return effect associated with IVol decreases from significant 0.23% for negative sophisticated trader opinion to 0.12% for positive sophisticated trader opinion. Comparing these figures with the low-ASVI tercile, the IVol puzzle becomes smaller and insignificant. Moreover, we find additional evidence that the overvaluation and low subsequent returns of high-IVol stocks are no overarching phenomenon, but most pronounced for high-attention stocks with low measures of informed trading. These results strongly support a behavioral explanation of the return patterns associated with idiosyncratic volatility: private investors can cause an overvaluation of high-IVol stocks if the market power of sophisticated investors does not suffice to compensate demand effects of these investors. In this case, sophisticated investors trade on the mispricing in the option market. This interpretation directly implies that we should observe stronger return effects for stocks with high illiquidity and severe short-sell constraints. We explore this line of argument in the following subsection.

Fundamental price risk and market frictions such as trading costs and short-sell constraints can render arbitrage strategies unattractive (see, for example, Lam and Wei 2011). As a consequence, the magnitude of potential mispricing can be higher if limits to arbitrage are more severe. Since we consider IVol as a potential mispricing indicator, spreads associated with IVol should be more pronounced for constrained stocks. Indeed, several articles including Boehme et al. (2009), Duan et al. (2010), and Stambaugh et al. (2015) document that short-sell impediments result in larger return spreads associated with IVol. In addition, stock market constraints should also imply that sophisticated investors trade on their superior information in the option market rather than in the stock market. Thus, we hypothesize that the measures of informed trading are particularly able to identify overvalued high-IVol stocks if short-selling is restricted. Hence, these constrained high-IVol stocks with negative sophisticated investor opinion should earn the lowest subsequent returns. Similarly, illiquidity and short-sell constraints can prevent sophisticated investors from immediately correcting the mispricing stemming from private investor activity. We therefore expect that high-IVol stocks with potential sentiment-driven price pressure from private investors and restricted short-selling earn very low subsequent returns as well.

Tables 6 and 7 examine this line of argument using conditional cross-sectional triple sorts. We include four proxies for market frictions and limits to arbitrage. First, we use the Amihud (2002) illiquidity measure, as defined in Sect. 2. Second, we use residual institutional ownership following Nagel (2005) to account for the level of professional institutional investors. These investors might reduce the amount of mispricing per se or provide a sufficient number of lendable shares to enable short-selling.¹⁷ The calculation of residual institutional ownership follows Nagel (2005): the fraction of shares held by institutional investors is winsorized at 0.01% and 99.99%; then the logit transformation of this fraction is regressed on log-size and squared log-size. Each week’s cross-sectional residuals constitute the residual institutional ownership measure.¹⁸ As a third measure, we apply the stock’s average closing bid-ask-spread over the previous year (Goyenko et al. 2009). Fourth, we use the stock’s model-free option-implied volatility (MFIV). MFIV corresponds to the standardized second moment of the risk-neutral density and is calculated from option prices following the methodology of Bakshi et al. (2003). Similar to the VIX on the market level, MFIV represents a forward-looking measure of volatility on the individual stock level. According to Pontiff (2006), volatility is one of the major factors limiting arbitrage activity.

In the first analyses of Table 6, we assign stocks to Amihud (2002) illiquidity terciles and sort on the option-implied volatility spreads and IVol afterwards. The empirical results support our line of argument: the most negative subsequent FFC-adjusted portfolio returns are obtained for those high-IVol stocks that are illiquid and overvalued based on the sophisticated investors’ opinion. On the contrary, for the most liquid stocks with positive sophisticated investor opinion, the IVol puzzle largely disappears. Overall, the strength of the IVol puzzle seems to depend on both the opinion of sophisticated investors about the stock’s overpricing and the stock’s exposure to market frictions. We repeat this analysis for the other three limits to arbitrage proxies. The picture remains broadly the same and supports the suggested mechanisms. Merely the results with respect to residual institutional ownership are slightly weaker; this might indicate that—within our sample of comparably large firms—short-sell constraints play a less strong role as arbitrage impediments compared to general illiquidity proxies.

Next, we assess the origin of the IVol puzzle by relating it to attention-driven investors (see Table 7). Again, we first assign stocks to one of the limits to arbitrage portfolios and sort on investor attention and IVol afterwards. For all limits to arbitrage proxies, the IVol puzzle is strongest for those stocks that are illiquid/short-sell constrained and exposed to high investor attention. These findings are in line with our conjecture that the IVol puzzle particularly emerges if private investors are active and if sophisticated investors cannot eliminate the mispricing due to market frictions.