مشاوران و قیمت دارایی ها: یک مدل از ریشه های حباب

We develop a model of asset price bubbles based on the communication process between advisors and investors. Advisors are well-intentioned and want to maximize the welfare of their advisees (like a parent treats a child). But only some advisors understand the new technology (the tech-savvies); others do not and can only make a downward-biased recommendation (the old-fogies). While smart investors recognize the heterogeneity in advisors, naive ones mistakenly take whatever is said at face value. Tech-savvies inflate their forecasts to signal that they are not old-fogies, since more accurate information about their type improves the welfare of investors in the future. A bubble arises for a wide range of parameters, and its size is maximized when there is a mix of smart and naive investors in the economy. Our model suggests an alternative source for stock over-valuation in addition to investor overreaction to news and sell-side bias.

What are the origins of speculative asset price bubbles? This question remains unanswered despite a large and growing literature on speculative trading and asset price bubbles in economics. Motivated in part by the behavior of Internet stocks during the late 1990s, a surge in new research has arrived at two conclusions. The first is that differences of opinion among investors and short sales constraints are sufficient to generate a price bubble.1 The second is that once a bubble begins, it is difficult for smart money to eliminate the mispricing (i.e., there are limits of arbitrage).2 All these studies take as given that investors disagree about asset values. But where does this divergence of opinion come from? In this paper, we develop a model of the origins of bubbles. Two sets of stylized facts motivate our analysis. The first is that asset price bubbles tend to occur during periods of excitement about new technologies.3 In the U.S., speculative episodes have coincided with the following major technological breakthroughs: (1) railroads, (2) electricity, (3) automobiles, (4) radio, (5) micro-electronics, (6) personal computers, (7) biotechnology, and most recently (8) the Internet.4 The second is that in the aftermath of the Internet bubble, the media and regulators placed much of the blame on biased advisors for manipulating the expectations of naive investors. While not directly related to the Internet experience, indirect evidence from academic research in support of this view held by the media and regulators include: (1) analyst incentives to generate biased, optimistic forecasts; (2) naive individual investors who do not recognize that these biased recommendations are motivated by incentives to sell stocks; and (3) analysts’ optimistic forecasts have an impact on prices.5 We focus on the role of advisors and their communication process with investors in generating divergence of opinion and asset price bubbles. Building on the existing literature, we assume that there are two types of investors, smart and naive, who are short sales constrained. While smart investors recognize the heterogeneity in advisors, naive ones take whatever recommendations they receive at face value. Importantly, all advisors are well-intentioned in that they care about the welfare of their advisees and want to honestly disclose their signals to investors. We also assume that at times of technological innovation, only some advisors understand the new technology (the tech-savvies); others do not and can only make a downward-biased recommendation (the old-fogies). We also consider an alternative assumption in which the old-fogies are replaced by dreamers who only issue upward-biased recommendations. The divergence of opinion and price bias results do not depend on this assumption but the old-fogey assumption is more theoretically interesting and there is evidence that it is relevant at a minimum for the recent Internet experience.6 A key contribution of our model is that it serves as a warning that even if a stock appears overvalued, it may not be due to investors overreacting to news nor to sell-side bias. We are not disclaiming the role of sell-side bias in the dot-com bubble—only that such bias is not needed to generate asset price bubbles. Indeed, it is not clear that such bias can explain bubbles that have occurred during earlier periods. We observe that during the dot-com period, even so-called objective research firms with no investment banking business, such as Sanford and Bernstein, issued recommendations every bit as optimistic as investment banks (see, e.g., Cowen, Groysberg, and Healy, 2003).7 This suggests that there must exist other causes of upward biased forecasts by advisors aside from the sell-side incentives of analysts. Moreover, we think of our model as applying more broadly to other advisors such as buy-side analysts who are likely to be a more important part of the market. In short, our paper is an exploration of an alternative and potentially more theoretically interesting mechanism for generating divergence of opinion as opposed to simply assuming investors overreact to news or are overly exuberant. More specifically, we consider an economy with a single asset, which we call the new technology stock. There are three dates, 0, 1, and 2. At date 0, advisors are randomly matched with investors (the advisees). Advisors also observe the terminal payoff (which is realized at date 2) and can send signals about this payoff to their advisees at date 0. A tech-savvy can send whatever signal he wants, while an old-fogey, who does not understand the new technology, is limited to a downward-biased signal. The investor type is unknown to the advisor, and the advisor type is unknown to the investor. The advisor–investor relationship is similar to that of a parent and teenaged child, in which the smart teenager is not sure whether dad is cool, and the cool dad tries to impress his teenaged child because he wants his child to heed his advice in the future. At date 1, these advisors are randomly matched with a new set of investors. These investors can invest in a separate risky project requiring an initial fixed cost. Advisors again receive information about this risky project, which pays off at date 2. Once again, a tech-savvy can send whatever signal he wants, while an old-fogey is restricted to a downward-biased signal. Each investor has access to the track record of his advisor, namely the signal (or recommendation) that was sent by the latter at date 0. A smart investor can use this information to update his belief about his advisor's type. To put this simple model into some context, think of the advisor at date 0 as a sell-side analyst covering technology stocks, but (counterfactually) with only good intentions. Date 1 represents the future career opportunities of this analyst; for example, sell-side analysts typically become advisors to hedge funds or corporations later in their careers. Importantly, what the advisor says at date 0 can be used for or against him at date 1. The updating of a smart investor's belief about his advisor's type is a key driver of our model. We first consider the equilibrium at date 1. Because of uncertainty about advisor type, smart investors may end up making investments when they should not, since they are not sure whether a negative signal (i.e., a signal value less than the fixed cost of investing) is truly negative or if it just came from an old-fogey. We solve for a Bayesian-Nash equilibrium in the reporting strategies of the advisors and the investment policies of the advisees. In this equilibrium, tech-savvy advisors bias their signals downward over the set of states in which it is not efficient for the advisee to invest. By downwardly biasing their signals over these states, the tech-savvy advisors lead the smart advisees to conclude that a certain set of negative signals cannot be generated by tech-savvy advisors. This signaling enables smart investors to avoid at least some inefficient investments. However, it also imposes a dishonesty cost upon the tech-savvy advisor, and this dishonesty cost is incurred per advisee. As a result, the tech-savvy advisor has an incentive to establish a better reputation at date 0 through his recommendation about the technology stock, since smart investors subsequently will use his date 0 recommendation to update their beliefs on his type. The stronger his reputation among smart investors becomes at date 1, the more easily he can avoid dishonesty costs in inducing his advisees to make efficient investments in that period. This reputational incentive leads the tech-savvy advisor to inflate his forecasts to signal his type to smart investors. We show that such a Bayesian-Nash equilibrium exists at date 0. While smart advisees properly deflate this upward bias, naive investors unfortunately take what the advisor says at face value. We show that a price bubble can arise as a result of this signaling equilibrium. It is important to note that the assumption about heterogeneity in advisor types (tech-savvies versus old-fogies) does not bias the results in our favor. To the contrary, this assumption, in combination with our assumption of investor heterogeneity, would tend to produce a downward bias in prices since naive investors take whatever old-fogies say at face value. In other words, the effect of optimistic signaling by well-intentioned tech-savvies has to be strong enough to overcome this baseline downward bias. It is not clear ex ante that this need be the case. However, we show that such a technology price bubble does exist when there is a sufficient number of naive investors guided by tech-savvy advisors. To develop intuition for the price bias, let us consider two polar cases. First, suppose that there are only smart investors in the economy. In equilibrium, tech-savvy advisors will tend to bias their forecasts upward so as to distinguish themselves from old-fogies. However, smart investors understand this and in equilibrium will adjust their beliefs accordingly. In this case, price will be an unbiased signal of fundamentals. Next, suppose that there are only naive investors in the economy. In equilibrium, tech-savvy advisors will honestly disclose their signals since they do not worry about the ability of naive investors to infer their type. In this case, however, price will typically contain a downward bias due to the pessimistic recommendations of old-fogies, which the naive investors take at face value. When both types of investors are present in the economy, the price could be upwardly biased. Tech-savvy advisors will bias their messages upward, and the extent of this bias increases with the fraction of smart investors. While smart investors can de-bias these messages, naive investors are unable to do so. Due to short sales constraints, the price is determined by the marginal buyer and is not affected by investors with a lower valuation. If the marginal investor is a naive advisee of a tech-savvy, then price will be upwardly biased. Our theory yields testable implications. For instance, unlike models such as DeLong, Shleifer, Summers, and Waldmann (1990), the degree of mispricing in our model is largest when there are both sets of investors in the economy. Furthermore, we consider a number of robustness issues. We show that our main results survive when we loosen two assumptions: (1) allow old-fogies to send biased messages at a cost just like tech-savvies and (2) allow an investor at date 0 to observe the recommendations of other advisors as well. We also consider a number of extensions. In our model, smart investors are worried about unduly pessimistic advisors. However, due to short sales constraints, our pricing results would survive even when smart investors are worried about unduly optimistic advisors (dreamers). Importantly, our results are robust to allowing for both dreamers and old-fogies to simultaneously be in the economy (see Section 3.3). Our model is technically about a price bias and not about bubbles. We intentionally neglect the key element of speculative trading (i.e., buying in anticipation of capital gain) modeled elsewhere to keep things simple. But it is similar in spirit to models of speculative trading driven by heterogeneous beliefs and offers an important new rationale for investor divergence of opinion. Our theory is related to the literature on costly signaling (see, e.g., Kreps, 1990 and Fudenberg and Tirole, 1991). A key theme that this paper shares with earlier work is that concerns about reputation can affect the actions of agents who try to shape their reputations (Holmstrom and Ricart i Costa, 1986; Holmstrom, 1999). Previous studies have shown that reputational incentives can lead agents to take perverse actions, such as saying the expected thing which may lead to information loss (Scharfstein and Stein, 1990; Ottaviani and Sorensen, 2006), adopting a standard of conformist behavior (Bernheim, 1994), or making politically correct statements so as not to appear racist (Morris, 2001). More specifically, our model, similar to Morris (2001) but unlike the others, emphasizes the perverse reputational incentives of a well-intentioned advisor: in our model, the well-intentioned tech-savvy advisor engages in costly signaling at date 0 so as to better help future investors. This contrasts with career-concerns-based models, such as Scharfstein and Stein (1990), in which the advisor does not know his own type and engages in signal jamming to achieve a better reputation for his own personal gain. Our work departs from the existing literature on reputational signaling by focusing on the interaction of sophisticated agents (tech-savvies and smart investors) and naive agents (old-fogies and naive investors), in a model that is geared toward examining implications for asset pricing. Finally, our paper complements interesting recent work by Hirshleifer and Teoh (2003) on the disclosure strategies of firms when some of their investors have limited attention. Like us, they emphasize the importance of introducing boundedly rational agents in understanding the effect of disclosures on asset prices. Unlike us, they focus on how the presentation of information may lead to different results with inattentive investors and the resulting incentives of managers to potentially manipulate earnings to fool inattentive investors. Our paper is organized as follows. We present the model and discuss related empirical implications in Section 2. We consider robustness and extensions in Section 3. In Section 4, we conclude with a reinterpretation of the events of the Internet period in light of our findings. Proofs are presented in the Appendix.

We conclude by re-interpreting the events of the Internet period in light of our model. In the aftermath of the Internet bubble, many have cited the role of biased advisors in manipulating the expectations of naive investors. We agree with the focus on the role of advisors but observe that there is something deeper in the communication process between advisors and investors that can lead to an upward bias in prices during times of excitement about new technologies, even absent any explicit incentives on the part of analysts to sell stocks. Our model suggests that the Internet period was a time when investors were naturally concerned about whether their advisors understood the new technology, i.e., were their advisors old-fogies or tech-savvies? Investors do not want to listen to old-fogies. As a result, well-intentioned advisors have an incentive to signal that they are tech-savvy by issuing optimistic forecasts, and this incentive is based on their desire to be listened to by future advisees. Unfortunately, naive investors do not understand the incentives of advisors to inflate their forecasts, and consequently asset prices are biased upward. This view is not totally without empirical support. In addition to the evidence cited in the introduction, it is well known that the reports issued by sell-side analysts are typically read only by institutional investors, who for the most part do a good job of de-biasing analyst recommendations. Unfortunately, during the Internet period, many retail investors took the positive, upbeat recommendations of analysts a bit too literally. Again, this is not to say that analysts during this period were solely well-intentioned, but simply that when there are naive investors, there can be a bubble during times of technological excitement even if all analysts are well-intentioned.