Dispersion Of Beliefs Research Articles

Disagreement in Option Market and Cross Section Stock Returns

In the paper, we find out that there is a significant relation between option trading volume and open interest distributions across various strike levels and expected stock returns. Specifically, we construct volume and open interest weighted option strike dispersions. Portfolio level analysis and firm-level cross-sectional regression both indicate a negative and significant relation between expected returns and option strike dispersion. The results are consistent with Miller (1977) theory. The option strike dispersion can be regarded as a proxy for investors’ belief dispersion. Long-short strategy purchasing stocks with low option strike dispersion and shorting those with high option strike dispersion earns annualized abnormal return 14.05% with sharp ratio 0.79.

Dispersion in Beliefs among Active Mutual Funds and the Cross-Section of Stock Returns

Dispersion in Beliefs among Active Mutual Funds and the Cross-Section of Stock Returns

Analogy Based Valuation of Currency Options

The two most intriguing anomalies in currency markets are: 1) the implied volatility smile in currency options, and 2) the forward discount bias in currency exchange rates. I show that if currency options are valued in analogy with the underlying currency and beliefs are heterogeneous, then the forward discount bias causes the smile. The analogy based currency option pricing formula is put forward, which converges to Garman-Kohlhagen formula if there is no forward discount bias. In the presence of the forward discount bias, an increase in belief dispersion increases the slope as well as the curvature of the smile.

The importance of belief dispersion in the response of gold futures to macroeconomic announcements

We investigate the behaviour of gold futures around the release of macroeconomic announcements. Market activity, in terms of traded volume, returns, and volatility, responds to new information quickly, with the majority of the reaction complete within 90-s. Surprises on the announcement of unemployment rate and GDP have the largest impact. Contrary to prior results for the equity market, gold futures exhibit greater reactions to ‘good’ economic news (which is negative for gold prices) and the magnitude of the response does not appear to increase during recession. Importantly, we employ a novel measure of belief dispersion, and we are able to demonstrate that the market response to macroeconomic news is significantly larger when belief dispersion is wider.

Monetary Policy with Diverse Private Expectations

We study the impact of diverse beliefs on conduct of monetary policy. Individual belief is modeled by a state variable that defines an individual’s perceived laws of motion. We use a New Keynesian Model that is solved with a quadratic approximation hence individual decisions are quadratic functions. Aggregation renders the belief distribution an aggregate state variable. Although the model has standard technology and policy shocks, diverse expectations change materially standard results about a smooth trade-off between inflation volatility and output volatility. Our main results are summed up as follows: (i) The policy space contains a curve of singularity which is a collection of policy parameters that divides the space into two sub-regions. Some trade-off between output and inflation volatilities exists within each region and some across regions. (ii) The singularity causes volatility of variables to be non monotone in policy parameters. Policymakers cannot assume a more aggressive policy will change outcomes in a predictable manner. (iii) When beliefs are diverse a central bank must also consider the volatility of individual consumption and the related volatility of financial markets. We show aggressive anti-inflation policy increases consumption volatility and aggressive output stabilization policy entails rising inflation volatility. Efficient central bank policy must therefore be moderate. (iv) High optimism about the future typically lowers aggregate output and increases inflation. This “stagflation” effect is stronger the stickier prices are. Policy response is muted since the effects of higher inflation and lower output on interest rates partially cancel each other. Effective policy requires targeting exuberance directly or its effects in asset markets. Central banks already do so with short term interventions. (v) The observed high serial correlation of 0.80 in policy shocks contributes greatly to market volatility and we show that a reduction in persistence of central bank’s deviations from a fixed rule will contribute to stability. (vi) Belief dispersion is measured by cross sectional standard deviation of individual beliefs. An increased belief diversity is found to make policy coordination harder and results in lower aggregate output and lower rate of inflation. Bank policy can lower belief dispersion by being more transparent.

The Role of Dispersed Information in Pricing Default: Evidence from the Great Recession

The recent Global Games literature makes important predictions on how financial crises unfold. We test the empirical relevance of these theories by analyzing how dispersed information affects banks' default risk. We find evidence that precise information acts as a coordination device which reduces creditors' willingness to roll over debt to a bank, thus increasing both its default risk and its vulnerability to changes in expectations. We establish two new results. First, given an unfavorable median forecast, less dispersed beliefs greatly increase default risk; this is consistent with incomplete information models that rely on coordination risk while in contrast with a wide range of models that neglect this component. Second, less dispersion of beliefs amplifies the reaction of default risk to changes in market expectations; importantly, precise information raises banks' vulnerability by more than standard measures of banks' fragility. Taken together, our results suggest that enhanced transparency, by providing agents with more precise information, increases banks' vulnerability to changes in sentiment and raises the default risk of weaker banks. Finally, we address concerns of endogeneity of market expectations by introducing a novel set of instruments.

Does Belief Heterogeneity Explain Asset Prices: The Case of the Longshot Bias

This article studies belief heterogeneity in a benchmark competitive asset market: a market for Arrow–Debreu securities. We show that differences in agents' beliefs lead to a systematic pricing pattern, the favourite–longshot bias (FLB): securities with a low-pay-out probability are overpriced, whereas securities with high probability pay-out are underpriced. We apply demand estimation techniques to betting market data, and find that the observed FLB is explained by a two-type population consisting of canonical traders, who hold virtually correct beliefs and are the majority type in the population (70%); and noise traders exhibiting significant belief dispersion. Furthermore, exploiting variation in public information across markets in our data set, we show that our belief heterogeneity model empirically outperforms existing preference-based explanations of the FLB.

Belief Dispersion in the Stock Market

We develop a dynamic model of belief dispersion which simultaneously explains the empirical regularities in a stock price, its mean return, volatility, and trading volume. Our model with a continuum of (possibly Bayesian) investors differing in beliefs is tractable and delivers exact closed-form solutions. Our model has the following implications. We find that the stock price is convex in cash-flow news, and it increases in belief dispersion while its mean return decreases when the view on the stock is optimistic, and vice versa when pessimistic. We also show that the presence of belief dispersion leads to a higher stock volatility, trading volume, and a positive relation between these two quantities. Furthermore, we demonstrate that the more familiar, otherwise identical, two-investor economies with heterogeneous beliefs do not necessarily generate our main results. Our quantitative analysis reveals that the effects of belief dispersion are economically significant and support the empirical evidence.

Information and the dispersion of posterior expectations

We explore the intuitive idea that more information leads to greater dispersion of posterior beliefs about the expected state of the world. First, we show that two dispersion orders that have been widely used as informativeness criteria do not satisfy the desirable property of ordinality of states (OS), i.e., invariance to increasing monotone state transformations. Then, for the class of monotone information systems, we characterize the weakest information criteria that respect OS and imply the dispersion orders. Our characterizations consist of intuitive conditions on the joint distributions of signals and states. Because of OS, the information criteria induce the dispersion orders not only on the posterior expectations of states, but also of state utilities, under any strictly increasing vNM utility function.

A Hidden Markov Model Approach to Information-Based Trading: Theory and Applications

Summary This paper develops a novel approach to information-based securities trading by characterizing the hidden state of the market, which varies following a Markov process. Extensive simulation demonstrates that the approach can successfully identify market states and generate dynamic measures of information-based trading that outperform prevailing models. A sample of 120 NYSE stocks further verifies that it can better depict trading dynamics. With this sample, we characterize the features of information asymmetry and belief dispersion around earnings announcements. The sample is also applied to the study of the co-movements of trading activities due to private information or disputable public information. Copyright © 2014 John Wiley & Sons, Ltd.

Belief Dispersion and Investment Allocation

I analyze the effect of belief differences among investors in equity markets on corporate investment composition. When some investors have highly optimistic beliefs about risky projects relative to the average beliefs, firms rationally respond by allocating investment to riskier projects to exploit the belief dispersion: firms increase relative shares of investment in Research & Development (R&D) and Mergers & Acquisitions (M&A), and decrease the investment share of physical capital expenditure (CAPX). A one standard deviation increase in belief dispersion raises investment shares of R&D and M&A by 4.37% and 1.31%, respectively, and reduces the share in CAPX by 5.67%. This effect remains and even becomes amplified when firms experience positive return shock to CAPX -- a case in which more investment in CAPX would be expected. To establish a causal relationship, I use mergers of brokerage houses as an exogenous shock to analyst coverage, a change that affects belief dispersion. My results show that belief dispersion in the financial sector can lead to risk-taking behaviour in corporate investment. To explain my results, I build a simple model based on Bolton et al. (2006), in which investors agree to disagree and stock prices reflect the beliefs of the most optimistic investors. In this model, the manager-owners of firms have the option to resell their shares to more optimistic investors, and as a result, shift investment composition towards riskier projects to scale up their resale option.

Dispersion in beliefs among active mutual funds and the cross-section of stock returns

We propose a measure of dispersion in fund managers׳ beliefs about future stock returns based on their active holdings, i.e., deviations from benchmarks. We find that both the level of and the change in dispersion positively predict subsequent stock returns on a risk-adjusted basis. This effect is particularly pronounced among stocks with high information asymmetry and binding short-sale constraints. These results suggest that a subgroup of informed managers drives up the dispersion in active holdings when they place large bets after receiving positive private information. Binding short-sale constraints, however, prevent them from fully using their negative private information, leading to low dispersion in active holdings.

The Role of Dispersed Information in Pricing Default: Evidence from the CDS Market

Starting in September 2007 the banking system worldwide was turned upside down; both level and volatility of banks' CDS spreads experienced an eightfold increase that can hardly be motivated by changes in fundamentals. The recent Global Games literature proposes a theory that explains banks' default without resorting to panics. We assess the empirical relevance of this literature and find that dispersion of beliefs plays a key role in affecting default risk. More precise information greatly amplifies the reaction of CDS spreads to market expectations; for highly leveraged banks, this sensitivity is four times larger if the market receives precise signals instead of imprecise ones. These findings suggest that dispersed information and higher order beliefs are essential to understand what may look like an overreaction of market participants to news. Moreover, we document a strong direct impact of dispersion of beliefs on default risk: when news is bad enough, a one standard deviation decrease in dispersion of beliefs leads to an increase in CDS spreads of 120 basis points, which is half of its standard deviation in times of crisis. Finally, we address concerns of endogeneity of market expectations by introducing a novel set of instruments whose validity requires very mild assumptions on the agents' learning process.

Are Household Investors Noise Traders: Evidence from Belief Dispersion and Stock Trading Volume

We document a robust positive relationship between the belief dispersion about macroeconomic conditions among household investors and the stock market trading volume, using more than 30 years of household survey data and a novel approach to measuring belief dispersions. Notably, such a relationship prevails even after various series of professional analysts' belief dispersions are controlled for. Consistent with a causal effect, such a relationship is most pronounced for belief dispersion among individuals who are most likely to own stocks and for trading volume of stocks that are most visible to household investors. Finally, we present suggestive evidence that the dispersion of changes in belief is also positively associated with the stock trading volume. Our analysis implies that household investors, traditionally viewed as tending to trader randomly, likely possess and trade on information that is not available to professional investors.

The Equity Risk Premium in 2014

We analyze the history of the equity risk premium from surveys of U.S. Chief Financial Officers (CFOs) conducted every quarter from June 2000 to March 2014. The risk premium is the expected 10-year S&P 500 return relative to a 10-year U.S. Treasury bond yield. While the risk premium sharply increased during the financial crisis peaking in February 2009, the premium has decreased to a level of 3.73% which is only slightly higher than the long-term average. However, the total market return forecast is a modest 6.43%. The survey also provides measures of cross-sectional disagreement about the risk premium, skewness, and a measure of individual uncertainty. Consistent with the last four quarters of surveys, CFOs see more downside risks than upside risks. In addition, we find that dispersion of beliefs is above the long-term average as well as individual uncertainty. We also present evidence on the determinants of the long-run risk premium. Our analysis suggests the level of the risk premium closely tracks both market volatility (reflected in the VIX index) as well as credit spreads. However, the most recent data show a divergence between VIX and the risk premium.

Are Household Investors Noise Traders: Evidence from Belief Dispersion and Stock Trading Volume

We document a robust positive relationship between the belief dispersion about macroeconomic conditions among household investors and the stock market trading volume, using more than 30 years of household survey data and a novel approach to measuring belief dispersions. Notably, such a relationship prevails even after various series of professional analysts' belief dispersions are controlled for. Consistent with a causal effect, such a relationship is most pronounced for belief dispersion among individuals who are most likely to own stocks and for trading volume of stocks that are most visible to household investors. Finally, we present suggestive evidence that the dispersion of changes in belief is also positively associated with the stock trading volume. On balance, our analysis implies that household investors, frequently believed to trade randomly as noise traders, appear to trade on their beliefs.

Differences in Opinion and Equilibrium Asset Returns in a Multi-Asset Market

This paper analyzes the impact of disagreement on equilibrium stock returns in a multi-asset market. Most dynamic models of disagreement focus on a market with a single stock which is a claim on the aggregate consumption. In reality, investors can speculate on the future cashflows of multiple stocks. In a continuous-time pure exchange economy, we assume investors have logarithmic preferences and disagree about future dividends. We show that the effect of disagreement can be very different in a multi-asset market compare to a single-asset market. In a single-asset market, although disagreement affects equilibrium returns, the effect is negligible if the dispersion in beliefs is small. In comparison, when there are multiple assets in the market, investors may have small disagreement about each asset, however, when the number of assets is relatively large (as in the real financial market), the overall level of belief dispersion could be much higher compared to the single-asset market. Consequently, we find that effect of disagreement can lead to a much higher excess volatility and larger time-variation in expected returns in a multi-asset market than in a single-asset market. We also study the effect of correlation in optimism/pessimism between assets. We find that correlation in optimism/pessimsm can lead to excess correlation in asset returns even though assets have independent future dividends. Furthermore, we show that when optimism/pessimism are negatively correlated, assets with the same level of belief dispersion can have different excess volatilities and also different expected returns. Lastly, we find that in a multi-asset market, initial run-up in asset prices may not lead any fluctuations in the distribution of consumption shares, thus have no effect of expected asset returns, which is in contrast of Yan (2010)’s finding of price-overshooting and mean-reversion in asset returns.

The Equity Risk Premium in 2013

We analyze the history of the equity risk premium from surveys of U.S. Chief Financial Officers (CFOs) conducted every quarter from June 2000 to December 2012. The risk premium is the expected 10-year S&P 500 return relative to a 10-year U.S. Treasury bond yield. While the risk premium sharply increased during the financial crisis peaking in February 2009, the premium has decreased to a level of 3.83% which is only slightly higher than the long-term average. However, the total market return forecast is at a historical low of 5.46%. The survey also provides measures of crosssectional disagreement about the risk premium, skewness, and a measure of individual uncertainty. Consistent with the last four quarters of surveys, CFOs see more downside risks than upside risks. In addition, w e find that dispersion of beliefs is above the long-term average as well as individual uncertainty. We also present evidence on the determinants of the long-run risk premium. Our analysis suggests the level of the risk premium closely tracks both market volatility (reflected in the VIX index) as well as credit spreads. However, the most recent data show a divergence between VIX and the risk premium.

Cross-Checking the Media

A characteristic of the news market is that consumers often cross-check information, i.e. observe several news outlets. At the same time, data on political media suggest that more partisan consumers are more likely to cross-check. We explore these phenomena by building a model of horizontal competition in newspaper endorsements. Without cross-checking, outlets are unbiased and minimally differentiated. When cross-checking is allowed, we show that cross-checkers are indeed more partisan than those who only acquire one report. Furthermore, cross-checking induces outlets to differentiate, and the degree of differentiation is increasing in the dispersion of consumer beliefs. Differentiation is detrimental to consumer welfare, and a single monopoly outlet may provide higher consumer welfare than a competitive duopoly.

Connecting two markets: An equilibrium framework for shorts, longs, and stock loans

We analyze a reduced-form framework for understanding the equity loan market's impact on share prices. We show that hard-to-borrow stocks will have distinct return patterns, responding more to shocks in the supply of shares available, and to changes in the heterogeneity of investor beliefs, than other stocks. We conduct two empirical tests in which we find strong support for these equilibrium predictions. In our first test, we take advantage of a tax-driven exogenous shock to share loan supply and find that when supply is reduced around dividend record dates, prices of hard-to-borrow stocks increase 1.1% while prices of easy-to-borrow stocks are unaffected. In our second test, we find that hard-to-borrow stocks have 4.8% lower three-month returns than other stocks, with negative returns concentrated in stocks with high heterogeneity in investor beliefs. Thus, we extend the Diether, Malloy, and Scherbina (2002) result that stocks with a greater dispersion of investor beliefs have lower returns.