Ambiguity about volatility and investor behavior

Abstract

We relate time-varying aggregate ambiguity about volatility (V-VSTOXX) to individual investor trading. We use the trading records of more than 100,000 individual investors from a large German online brokerage from March 2010 to December 2015. We find that an increase in ambiguity is associated with increased investor activity. It also leads to a reduction in risk-taking, which does not reverse over the following days. Ambiguity averse investors are more prone to ambiguity shocks. These results replicate when using the dispersion of professional forecasters as a long-term measure of ambiguity and are robust when controlling for newspaper- or market-based ambiguity measures.

Introduction

Investment decisions are decisions under uncertainty that are subject to both risk and ambiguity (Knight, 1921). According to Knight (1921), events for which the future outcome is unknown but the underlying distribution is known are referred to as “risky.” The Knightian uncertainty, or ambiguity as it is called by Ellsberg (1961) and Camerer and Weber (1992), is distinct from risk and describes events for which not only the future outcome but also the underlying distribution is unknown.

The research on ambiguity started with a thought experiment by Ellsberg (1961) showing that individuals tend to be ambiguity averse. According to Epstein and Ji (2013), ambiguity can be separated into ambiguity about volatility and ambiguity about drift. In line with this distinction, there are studies on ambiguity about (expected) returns, i.e., ambiguity about drift (e.g., Anderson et al., 2000, 2003; Chen and Epstein, 2002; Maenhout, 2004; Ju and Miao, 2012) and, more recently, studies on ambiguity about expected volatility (Anderson et al., 2009; Epstein and Ji, 2013; Baltussen et al., 2018). Epstein and Ji (2013) emphasize the need for more research on the question of whether ambiguity about volatility matters empirically. To date, research has focused on the impact of ambiguity on capital markets and asset prices, finding that ambiguity about volatility matters (Baltussen et al., 2018; Bollerslev et al., 2009; Branger et al., 2019) and that it is distinct from risk, as both affect the equity premium (Brenner and Izhakian, 2018).

There are some theoretical papers suggesting that ambiguity and individual investors’ portfolio choice are related. Among others, Bossaerts et al., (2010); Cao et al., (2005); Dow and Werlang (1992); Easley and O'Hara (2009), and Epstein and Schneider (2010) show that ambiguity aversion can cause nonparticipation. Garlappi et al., (2007) and Peijnenburg (2018) show that ambiguity aversion can reduce the fraction of financial assets allocated to equity. Empirically, the literature has researched the impact of ambiguity aversion on individuals’ financial decision making using the urn experiment suggested by Ellsberg (1961). The paper by Dimmock et al., (2016) derives ambiguity aversion of individuals in a survey using the urn experiment and shows that it matters for asset allocation decisions. The higher the ambiguity aversion is, the lower the stock market participation of individuals. Bianchi and Tallon (2018) show that ambiguity averse investors exhibit a higher home bias, rebalance their portfolios more actively, and tend to keep their risk exposure constant over time. Thus, there is only cross-sectional evidence for the impact of ambiguity aversion on the behavior of individual investors.

In this study, we contribute to the existing literature by investigating the exogenous and time-varying effect of market-based ambiguity about volatility¹ on trading activity and risk-taking using a large sample of individual investors (Antoniou et al., 2015). We show that over time ambiguity shocks lead investors to trade more and especially trade out of risky securities. This effect is stronger for investors who were surveyed and identified as ambiguity averse using the urn experiment suggested by Ellsberg (1961). Our findings provide complementary evidence to the existing literature by showing that a lower risky share results not only from initial asset allocation decisions but also from trading decisions in reaction to ambiguity shocks.

For a measure of time-varying aggregate ambiguity, the literature has not yet reached a consensus. Studies are using survey-based measures that build on the dispersion of forecasts of professional forecasters (e.g., Anderson et al., 2009; Drechsler, 2013; Andrei and Hasler, 2015; Ulrich, 2013; David and Veronesi, 2013); newspaper-based measures such as economic policy uncertainty (e.g., Baker et al., 2016); and market-based measures such as the VIX, the VVIX, or those building on high-frequency data (Brenner and Izhakian, 2018).² Among the market-based measures, the volatility of volatility (examples are the VVIX or V-VSTOXX) represents second-order beliefs, which, according to many theoretical models, are appropriate for capturing ambiguity (Klibanoff et al., 2005; Nau, 2006; Segal, 1987). Therefore, it is not surprising that the volatility of volatility is regarded as a good measure for ambiguity and used as such (Baltussen et al., 2018; Hollstein and Prokopczuk, 2018; Huang et al., 2019; Chen et al., 2014; Bali and Zhou, 2016; Bollerslev et al., 2009; Epstein and Ji, 2013; Barndorff-Nielsen and Veraart, 2012).

We follow this stream of literature and measure ambiguity using a volatility-of-volatility measure. We use the V-VSTOXX, which is the 30-day implied volatility of the VSTOXX. The V-VSTOXX is a daily measure and is the European equivalent to the VVIX and based on the Euro Stoxx index and is the regionally closest measure to our investor data. The Euro Stoxx index is a composite stock market index representing the European stock market. Thus, the ambiguity measure we use is the volatility of volatility of the Euro Stoxx. Whereas VSTOXX measures the expected volatility over the following 30 days, V-VSTOXX measures the expected uncertainty about future volatility over the following 30 days. The uncertainty in volatility is close to what Epstein and Ji (2013) label ambiguity about volatility. Using this approach provides the additional advantages of a natural, model-free, market-based, and forward-looking measure, which is computed based on liquid securities with daily availability and is thus the most suitable for our research question. Additionally, this approach allows disentangling volatility (implied volatility) and ambiguity (implied volatility of the implied volatility). We also use the interquartile range of the standard deviations of each individual professional forecaster as an alternative and more long-term measure of ambiguity. In the robustness section, we also control for and use alternative measures of ambiguity. These are newspaper-based economic policy uncertainty (EPU) and the omega measure, recently proposed by Brenner and Izhakian (2018).

We match the V-VSTOXX, which is available from March 2010 onwards, to the trading records of more than 100,000 individual investors of a large German online brokerage.³ The brokerage data cover all time-stamped security transactions for the period from January 2001 through December 2015. They mirror the well-known U.S. transaction data of Barber and Odean (2000). We exclude all individuals who obtain financial advice because we are interested in the effect of ambiguity on the trading decisions of households and not in the suggestions of financial advisers. Using these data, we conduct a within-person analysis and control for individual average trading behavior, observable time-varying variables, and observable and unobservable time-fixed characteristics of investors.

We first employ an unconditional analysis and test how aggregate ambiguity (innovations in V-VSTOXX) affects the activity of individual investors along two dimensions: logins⁴ and trades. Innovations in ambiguity are associated with higher investor activity both in terms of logins and trades. When ambiguity is high and investors have a hard time assessing risks, stock markets could receive more attention; hence, investors deal more with their portfolio as they log in more often. Additionally, investors seem to be faced with the need to adjust their portfolios as they then also tend to trade more.

The remainder of this paper analyzes the trading behavior of our investors conditional on trading. That is, given that investors trade as a response to ambiguity shocks, we investigate how they adjust their portfolios. Therefore, we are particularly interested in their risk-taking behavior. We find that ambiguity shocks cause investors to decrease their exposure to the security market by trading out of stocks and similarly risky assets. This effect does not reverse within the following ten days. This result is broadly in line with theoretical models predicting that ambiguity shocks can cause investors to reduce their risky asset share or to exit the security market (Mele and Sangiorgi, 2015; Garlappi et al., 2007; Peijnenburg, 2018). This result, as well as all others in the paper, is robust to the inclusion of time-varying aggregate volatility (innovations in VSTOXX) in the model. Additionally, we find that when we compare the effect of ambiguity (V-VSTOXX) with the effect of volatility (VSTOXX), only ambiguity yields statistically significant results in the trading behavior of individual investors. It thus seems that ambiguity matters at least as much as volatility for individual investors.

Next, we test a hypothesis that originates with Hirshleifer (2001). He argues that biases should be more severe when ambiguity is high. We test this conjecture using the FEARS index,⁵ which was originally proposed by Da et al., (2015). We thereby test whether trading reactions to changes in sentiment are different depending on the level of ambiguity. Previous studies investigating the impact of psychology on the risky choices of individual investors show that low sentiment is associated with less risk-taking (Kostopoulos et al., 2020; Schmittmann et al., 2015; Kaustia and Rantapuska, 2016; Kostopoulos and Meyer, 2018). If our conjecture is correct, we should find that in times of high ambiguity, the sentiment effect is stronger than in times of low ambiguity. We observe that sentiment effects are present in days of high and low ambiguity. However, we find evidence that the effect of sentiment looms significantly larger in high-ambiguity periods.

Dimmock et al., (2016) show that more ambiguity averse investors are less likely to participate in an ambiguous stock market. In contrast, we show that fluctuations in aggregate ambiguity matter empirically for individual investors’ decisions. Hence, it seems natural to combine the two results and conjecture that more ambiguity averse individuals are also more prone to ambiguity fluctuations. To measure the ambiguity aversion of our investors, we asked the bank to randomly choose 10,000 clients and invite them to participate in a survey. In this survey, we run an Ellsberg-type urn problem and classify the participating investors as ambiguity averse, ambiguity neutral and ambiguity-seeking individuals. The total number of investors participating in the survey is 644. Of those, 58.7% are ambiguity averse, 12% are ambiguity neutral, and 29.3% are ambiguity seeking. These figures are fully in line with previous studies such as Dimmock et al., (2016) and show that our sample is representative concerning ambiguity preferences. We find that ambiguity averse investors are four times more vulnerable to innovations in ambiguity than the average investor. Ambiguity averse investors, in contrast to ambiguity-seeking investors, decrease their exposure to risk when they experience ambiguity shocks. More technically, the sign of the estimate flips. We interpret this result as evidence that changes in V-VSTOXX indeed represent innovations in ambiguity.

Besides the V-VSTOXX, the dispersion of professional forecasters is also regarded as a good measure for ambiguity and has been used in previous studies (e.g., Anderson et al., 2009; Drechsler, 2013; Andrei and Hasler, 2015; Ulrich, 2013; David and Veronesi, 2013; Ilut and Schneider, 2014; Ilut and Saijo, 2021). While the V-VSTOXX is a high-frequency daily measure that reflects short-term variations in aggregate ambiguity at the market level, such professional forecasts can be seen and used as a distinct and rather long-term measure of ambiguity. These forecasts reflect the expectations of forecasters of economic growth over the subsequent 12 months. Therefore, we use professional forecasts of the real gross domestic product from the Survey of Professional Forecasters data provided by the European Central Bank. The survey is conducted quarterly and has the advantage of being available for a longer period of time when merged with our investor data (2001–2015). We follow this stream of literature and use professional forecasts of the real gross domestic product, complementing the short-term perspective of using the V-VSTOXX.

To combine this survey-based ambiguity measure with the investor data, we closely follow the empirical approach of Calvet et al., (2009) and calculate the total change in the investment portfolio and thereby differentiate between passive market movements and the average active change (i.e., intentional, self-directed investor rebalancing) in the portfolio. We investigate the relation between variations in the interquartile range of the standard deviations of each individual forecaster in each quarter and the active change. In line with the results for the short-term and market-based measure, we find that, as the interquartile range of the standard deviation of dispersion of professional forecasters increases, the average investor has a negative active change, i.e., actively trades out of the market.⁶ The same holds true when we condition on investors having a nonzero active change in a given month. The results replicate and substantially increase in magnitude.

Finally, in the robustness section, we rerun our V-VSTOXX analysis and control for two additional measures of ambiguity. First, we follow the approach of Brenner and Izhakian (2018) and rebuild their measure of ambiguity for the Euro Stoxx. Second, for a newspaper-based measure, we control for economic policy uncertainty using the data from Baker et al., (2016). Controlling for both alternative measures of ambiguity does not change our results qualitatively. Additionally, we show that our results are robust to replacing our ambiguity measure with these alternative measures of ambiguity.