Specifically, I focus on one prevailing pattern of investor beliefs in the finance literature, return extrapolation. The return extrapolation concept also poses challenges for the asset pricing models under the rational expectations frameworks.
TIME-VARYING IMPACT OF INVESTOR SENTIMENT
Introduction
Conversely, when wealth levels are low, high investor sentiment predicts high future returns because the market is subject to a price correction. Like the top-down literature, my analysis shows that investor sentiment has a major impact on the overall stock market.
Motivating Facts
This qualitative time series helps us understand the dynamics of investor sentiment in the market. Survey measures of investor sentiment are positively associated with past returns on the overall stock market.
The Behavioral Model
In general, l(St,xt) is a monotonic function both in the transformed relationship between wealth and yield zt and the latent state variable yt. As a result, both investor sentiment and asset prices will fall in the future, producing negative returns.
Model Implications
With the extrapolation model in my behavioral model, I now investigate the time-varying impact of investor sentiment. Furthermore, when the wealth level of extrapolators is low, investor sentiment has a strong positive predictive power.
The Role of Extrapolation: A Rational Benchmark Model
In the top panel, I report the price-dividend ratio ¯l(xt) as a function of the asset-dividend ratio. I also report the equilibrium volatility ¯σP,t(xt) as a function of the asset-to-dividend ratio.
Concluding Remarks
Moreover, it helps shed light on the leverage behavior of households and the associated real consequences for the economy. All these facts point to the importance of belief-based investor sentiment in understanding both asset price facts and real economic activity.
ASSET PRICING WITH RETURN EXTRAPOLATION
Introduction
In the model, the agent separately forms beliefs about the stock market's dividend growth and about aggregate consumption growth. The agent's approximately correct beliefs about consumption growth allow the model to generate low interest rate volatility.
The Model
In this way, the agent's expectation of price growth affects her expectation of dividend growth. As a result, (2.15) implies that the bias in the agent's expectation of consumption growth—the difference between gCe(St) and gC—is small.
Model Implications
The agent's expectation of future price increases then increases, pushing up the stock market price relative to dividends. When the stock market has experienced high price growth in the past, the agent's expectation of future price growth increases, increasing the current price-dividend ratio. Over longer horizons, no additional mean change in agent beliefs contributes to the predictability of stock market returns.
In the model, the persistence of the price-dividend ratio is determined by the persistence of the agent's beliefs.
Comparative Statics
Belief parameters. – Figure B.6a shows the long-term average of the equity premium, the volatility of stock returns, the price-dividend ratio, and the interest rate, each as a function of θ, a parameter that measures the extent to which the agent is behavioral. In other words, with higher θ, the agent relies more on recent past returns to form beliefs about future returns. In our model, higher values of θ, χ, and λ lead to higher φ, so the agent's expectations of future returns depend more on recent past returns.
In general, the model implies that, when the agent forms beliefs based on a short history of past returns, the predictability of returns is strong.
Comparison with Rational Expectations Models
That is, the agent in Bansal and Yaron (2004) has extrapolative beliefs about future raw returns. In our model, the agent extrapolates past returns on the stock market, but extrapolates past consumption growth much less. The correspondence between the agent's beliefs about returns and her beliefs about consumption growth is low.
On the contrary, in Bansal and Yaron (2004) the similarity between the agent's beliefs about stock market returns—which rationally determine returns—and her beliefs about consumption growth—which determine equilibrium interest rates—is high.
Fundamental Extrapolation
Our model does not give rise to excessive predictability: return extrapolation in the model generates only perceived but not true long-term risks, and therefore the true consumption growth and yield growth remain unpredictable. Instead, she calculates its expected value given the history of past dividend growth: St ≡ E[˜µS,t|FtD]. In other words, the agent's expectation of dividend growth geD(St) is a linear combination of a rational component gD and a sentiment component St constructed from past dividend growth.
On the other hand, fundamental extrapolation leads the agent to expect high dividend growth in the future, but not high returns: after high dividend growth in the past, the stock market price rises to such an extent that the agent's expectation of future returns does not change significantly.
Conclusion
Equation (2.32) shows that in a fundamental extrapolation model, sentiment S, the state variable that drives asset price dynamics, can be specified exogenously without solving the equilibrium; this greatly simplifies the model. On the other hand, with return extrapolation, sentiment determines—and is endogenously determined by—asset prices. Consequently, such a model requires solving for beliefs and asset prices at the same time, and thus imposes a greater modeling challenge.
Finally, our representative-agent model neglects an important channel that affects asset prices: the time-varying fraction of wealth held by behavioral agents.
DARK MATTER” OF FINANCE IN THE SURVEY
- Introduction
- Data
- Consistency between Two Types of Surveys
- Connections between Return Extrapolation and Perceived Left-tail Prob- abilitiesabilities
- Concluding Remarks
Therefore, based on the expectation information in the investor expectations surveys, I can effectively derive a sequence of left tail probabilities and compare it to the reported probability of the tail event in the Shiller tail risks survey. With the reliability of investor expectations surveys, I continue to investigate the links between investor expectations surveys and the Shiller tail risks survey. To provide a robust test, I report all possible correlations between each survey of investor expectations and the Shiller left-tail risk survey.
The reported results strengthen the links between return extrapolation and perceived left probabilities.
BIBLIOGRAPHY
Substitution, risk aversion and the temporal behavior of asset consumption and returns: An empirical analysis.
APPENDIX TO CHAPTER ONE
Micro-foundations for Fundamental Investors
Pt + 1 . l −t−r), (A.2) where γh represents the risk aversion coefficient of fundamental investors and αtf is the total demand for risky assets of fundamental investors. Therefore, the total per capita demand for dollars from fundamental investors is Qt ≡ αtfWtf = PF,t−Pt.
Rational Benchmark Model
Behavioral Model
The linear demand function of fundamental investors and the geometric Brownian form of the dividend process and the logarithmic form of the extrapolators' utility function together imply a linear relationship between the equilibrium price Pt and the dividend process Dt. For the boundary conditions when xt → 0, fundamental investors dominate and the price of the risky asset is mainly driven by demand from fundamental investors; according to market clearing conditions (1.20) I have. In the case when xt → ∞, extrapolators dominate and to clear the market, α goes to 0; otherwise asset prices go to infinity.
Figures and Tables
All standard errors in parentheses are based on the Newey-West correction (Newey and West (1986)). Ret+N =a+bSentt+cWt/Dt+dSentt×Wt/Dt+t, (A.61) where Ret+N represents the excess return of the CRSP value-weighted index over the next N-month, Sentt represents the sentiment of investors variable, Wt represents the total value of financial assets of the HNPO sector. Ret+N =a+bSentt+cWt/Dt+dSentt×Wt/Dt+t, (A.65) where Ret+N represents the excess return of the CRSP value-weighted index over the next N-month, Sentt represents the sentiment of investors variable, Wt/Dt represents the ratio of wealth to dividend in the model.
Ret+N =a+bSentt+cWt/Dt+dSentt×Wt/Dt+t, (A.70) where Ret+N represents the excess return over the next N-month, Sentt represents the investor sentiment variable, Wt/ Dt represents the wealth to dividend ratio in the model.
Alternative Regressions
Rte+N = a+bSentt+cWt/Pt+dSentt×Wt/Pt+t, (A.72) where Ret+N represents the excess return over the next N-month, Sentt represents the investor sentiment variable, Wt represents the total value of financial assets of the HNPO sector. Rte+N =a+bSentt+cWt/Pt+dSentt×Wt/Pt+Xt +t, (A.73) where Rte+N represents the excess return over the next N-months, Sentt represents the Gallup poll measure of investor sentiment, Wt represents the total value of financial assets of the HNPO sector. Rte+N = a+bSentt+cWt/Pt+dSentt×Wt/Pt+t, (A.74) where Ret+N represents the excess return over the next N-month, Sentt represents the investor sentiment variable, Wt represents the total value of financial assets of the HNPO sector.
Rte+12 =a+bSentt+cWt/Pt+dSentt ×Wt/Pt+t, (A.76) where Rte+12 represents the excess return over the next twelve months, Sentt represents investor sentiment, Wt represents total financial assets value of the HNPO sector.
APPENDIX TO CHAPTER TWO
Derivation of the Differential Equations
Numerical Procedure for Solving the Equilibrium
By the Chebyshev interpolation theorem, if N is sufficiently larger than nandm, and if the sum of weighted squares in (B.15) is sufficiently small, the approximate functions ˆh(z) and ˆl(z) are sufficiently close to the true solutions. We then apply the Levenberg-Marquardt algorithm and obtain a minimized sum of squared errors less than 10−11. Together, these findings indicate that the numerical solutions are an adequate approximation for the true hand j functions.
Additional Discussion about Return Expectations and Cash Flow Expec- tationstations
For an infinitely-lived agent, (B.18) further implies that the agent is aware of the fact that both her expectation about future price growth and her expectation about future returns are linked to her expectation about future dividend growth.
Figures and Tables
The dashed line represents the objective (rational) expectation of price growth, Et[(dPtD)/(PtDdt)], as a function of the sentiment variable St. The solid line represents the agent's subjective expectation of a price increase, Ete[dPtD/ (PtDdt)], as a function of the sentiment variable St. The dotted line represents the agent's expectation of a price increase, Eet[dPtD/(PtDdt)]= (1−θ)gD+θSt, as a function of the sentiment variableSt.
The solid line shows the agent's expectation of dividend growth, Eet[dDt/(Dtdt)], as a function of the sentiment variable St.
APPENDIX TO CHAPTER THREE
Figures and Tables
In the sample period, I plot four of the implied left-tail risks from investor expectations surveys (AA, II, and Gallup) and from return extrapolation. In the first three figures, I plot the implied left-tail risks from three investor expectations surveys. In the bottom left figure, I plot the implied left tail risks based on return extrapolation.
For example, Left Tail Probability based on AA represents the implied left tail probability based on the rescaled AA investor expectation series.
