Literature review and research question

In his seminal work, Knight (1921) introduced the dichotomy between risk and ambiguity. The principal difference between these two concepts is that risk can be quantified according to a probability model, while no unique model exists for determining ambiguity. As a consequence, economic actors do not have a clear understanding of the possible outcomes of their decisions (Agliardi et al., 2016). Ellsberg (1961), in his famous experiment, demonstrated that people exhibit ambiguity aversion. Since then, the impact of ambiguity has become a major focus in many areas of economic research; several papers have confirmed not only the existence of ambiguity aversion but also that people are even willing to incur costs to avoid ambiguity (e.g., Charness and Gneezy, 2010; Trautmann and Van De Kuilen, 2015).

In a finance context, ambiguity has largely been the focus of capital market and asset pricing research.⁴ More recently, a large number of studies have incorporated the concept into corporate finance settings. In a theoretical model, Garlappi et al. (2017), for example, reveal the negative outcomes of ambiguity within the board of directors on corporate investment decisions. Agliardi et al. (2016) investigate the effect of ambiguity in a contingent claims context and find that well-diversified shareholders make suboptimal decisions, such as exercising the bankruptcy option prematurely and overvaluing debt. Empirical work also shows that risk and ambiguity separately affect corporate finance decisions, often in opposite directions (e.g., Izhakian and Yermack, 2017;

Coiculescu et al., 2019; Herron and Izhakian, 2020; Izhakian et al., 2021). A crucial insight from both strands of literature is that ambiguity leads investors to overvalue negative outcomes and undervalue positive outcomes (e.g., Epstein and Schneider, 2008; Agliardi et al., 2016; Herron and Izhakian, 2018). That is, shareholders cannot correctly assess the actions of managers based on what they observe in the market. Moreover, ambiguity implies market incompleteness, which limits the extent to which (agency) problems can be solved contractually (Mukerji and Tallon, 2001).

We build on these insights by analyzing if shareholders strive to reduce ambiguity through their influence on the board of directors. The theoretical literature suggests that predictable policy decisions will reduce the amount of ambiguity and make it easier for shareholders to evaluate the actions taken by management (Packard and Clark, 2020). Decisions that are unique, unfamiliar, and exhibit strong fluctuations, on the other hand, can increase ambiguity, as they are more

4See, for example, Chen and Epstein (2002), Pflug and Wozabal (2007), Epstein and Schneider (2008), Easley and O’Hara (2009), Boyarchenko (2012), Ju and Miao (2012), Epstein and Ji (2013), Brenner and Izhakian (2018), and Augustin and Izhakian (2020).

difficult for shareholders, and even professional analysts, to understand and evaluate (Litov et al., 2012; Benner and Zenger, 2016).⁵ The empirical literature also shows that shareholders dislike fluctuations in corporate policy decisions (e.g., Kor and Mahoney, 2005; Xiang et al., 2020) and that stable strategies, defined as policy decisions that do not deviate significantly from a long-term mean or exhibit greater variances, provide superior performance as measured by the return on investment (Bowman, 1963; Kunreuther, 1969; Remus, 1978).

To have an impact on these decisions, shareholders can use their influence on the board of directors, the primary means for controlling shareholders (John and Senbet, 1998). In classical agency models, independent directors or outsiders are representatives of the shareholders and are typically tasked with monitoring management and ensuring that the decisions are made in the interest of the principal (Jensen, 1993; Denis and McConnell, 2003; Hermalin and Weisbach, 2003). Despite some concerns in the literature that independent directors are not necessarily ideal monitors in some specific situations (e.g., Coles et al., 2008), extensive empirical research supports the notion that outsiders do carry out a monitoring function and add value to the firm (e.g., Byrd and Hickman, 1992; Nguyen and Nielsen, 2010). More specifically, independent directors have been shown to positively affect, among other things, CEO appointments and dismissals (e.g., Knyazeva et al., 2013), market reactions to the adoption of anti-takeover measures (e.g.,

Brickley et al., 1994), and takeover premiums (e.g., Cotter et al., 1997). No study so far has analyzed the effect of independent directors on either the stability of corporate policy decisions or ambiguity in general. We expect that majority independent boards will reduce the level of ambiguity.

In prior studies, the type of ambiguity that investors face has often been operationalized as uncertainty about risk, or the volatility of volatility, which fits the theoretical concept well.

Time-varying or stochastic volatility implies that there exists not just a probability distribution for stock returns, but also a variation in the assessment of that distribution (e.g., Klibanoff et al., 2005; Baltussen et al., 2018). A large amount of evidence suggests that volatility is indeed time-varying in financial markets and thus relevant both in a theoretical and empirical sense.⁶ Further, these studies suggest that the dynamics of the volatility are so complex that it is unlikely that even a sophisticated economic agent would be able to learn about the underlying process

5Reasons why managers choose unfamiliar and complex strategies include, inter alia, a desire to make them harder for competitors to copy, but also overconfidence and attempts to make strategies appear to be of high quality (Rivkin, 2000; Wu and Knott, 2006).

6See, for example, Eraker and Shaliastovich (2008), Bollerslev et al. (2012), Drechsler (2013), Bansal et al. (2014), Agarwal et al. (2017), Baltussen et al. (2018), Campbell et al. (2018), and Huang et al. (2019).

and develop any reasonable level of confidence about future volatility behavior (Carr and Lee, 2009; Epstein and Ji, 2013).

VOV is also useful for capturing ambiguity faced by shareholders in a corporate finance context, because it is a direct empirical consequence of managerial decisions in risk-related corporate finance and investment policies that, as we describe above, cause ambiguity in the first place.⁷ We will illustrate this using the example of R&D expenditures. While increases in R&D investment are generally associated with increased firm value (Hall et al., 2005) and improved operating performance (Hou et al., 2021), they are also often long-term investments with highly uncertain outcomes (Baysinger et al., 1991; Kothari et al., 2002), which makes them risky. This inherent riskiness of R&D expenditures is reflected in the volatility of stock returns, meaning that increases (decreases) in R&D investments increase (decrease) volatility (Chan et al., 2001; Hou et al., 2021). Frequent changes in expenditures then lead to higher VOV. As each individual policy is a potential source of ambiguity, the VOV represents an aggregate measure of the individual ambiguities. Thus, there is a direct link between corporate policy decisions and the VOV and thus the ambiguity perceived by the shareholder.

To empirically test whether independent directors on the board do indeed address this problem, we use the listing rule changes made by the NYSE and NASDAQ exchanges in the early 2000s that required firms to have majority independent boards. Studies that have also used this setting have concluded that the exogenous shock to board independence provides a sharp tool for making causal inferences and that it increased board oversight. Armstrong et al. (2014) find that firms with majority independent boards reduce the information asymmetry between informed and uninformed investors. Guo and Masulis (2015) report that previously noncompliant firms have increased CEO turnover following poor performance, which the authors attribute to enhanced monitoring. Increasing board independence has also led to more effective control of overconfident and powerful CEOs. Banerjee et al. (2015) show that in firms with overconfident CEOs, risk and investment exposure have fallen, while post-acquisition returns have grown. This is seen as an indication of how stronger board oversight has improved CEO decision-making.

Humphery-Jenner et al. (2019) provide evidence that greater board independence can serve to rein in powerful CEOs and align their interests more closely with those of the shareholders. In firms that were noncompliant with the listing rules and had powerful CEOs, there was a marked increase in R&D expenditures with subsequently higher numbers of patents that turned out to

7Agliardi et al. (2016) also include time-varying volatility in their model to capture the ambiguity for the shareholder.

be more valuable. Finally, Balsmeier et al. (2017) analyze the effect of board independence on innovation and find that affected firms increase patent output and citations. With respect to the body of research on the effect of independent directors, they conclude that these studies paint a picture of independent directors indeed carrying out an oversight function as predicted by standard agency models, alleviating concerns that the role of monitors cannot be filled by outsiders.

It is important to note that none of these studies address the issue of ambiguity or VOV. Bargeron et al. (2010) show that independence reduces stock return volatility, yet VOV is distinctly different from volatility and the two are only weakly correlated (Huang et al., 2019). Armstrong et al.

(2014) provide evidence that more independent directors lead to greater transparency, which could potentially influence ambiguity, yet they do not test for it. Even if we assumed that increased transparency reduces ambiguity, Armstrong et al. (2014) provide no evidence of the channel that could lead to this result. In our study, we investigate possible sources of ambiguity by analyzing effects of board independence on different firm policies. In a way, our results complement the evidence in Armstrong et al. (2014), as we show that board independence leads to less variation in investment decisions, which could result in reduced information asymmetry, increased analyst following, and lower forecast errors. We formulate our expectation accordingly:

Majority independent boards will exercise greater monitoring and reduce the level of ambiguity as measured by the VOV. They will accomplish this by effecting lower fluctuations in risk-related policies.