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1、英语学习英语学习Disagreement_ tastes_ and asset pricesAbstract Standard asset pricing models assume that: (i) there is complete agreement among investors about probability distributions of future payoffs on assets;(ii) investors choose asset holdings based solely on anticipated payoffs; 2This paper provide
2、a simple framework for studying how disagreement and tastes for assets as consumption goods can affect asset prices.31. IntroductionStandard asset pricing models share two common assumptions: 1) complete agreement assumption: all investors know the true joint distribution of asset payoffs2) investor
3、s are concerned onlywith the payoffs from their portfolios; that is, investment assets are not also consumptiongoods41、For the first common assumption (complete agreement), there are two strands of research that relax it: 1)disagreement but the relevant weighted averages of investor assessments are
4、equal to the true expected values and the true covariance matrix of next periods payoffs, asset prices are set as if there is complete agreement. 2) investors get noisy signals about future asset payoffs, but they learn from prices. 5For the disagreement this papers goal: to provide a simple framewo
5、rk for thinking about how disagreement can affect asset prices.62、investors are concerned onlywith the payoffs from their portfolios; that is, investment assets are not also consumptiongoods。Apparent violations are plentiful：loyalty,Socially responsible investing This paper second goal is to charact
6、erize the potential price effects of asset tastes.7Our interest in these topics is in part due to evidence that the CAPM fails to explain average stock returns.three anomalies(about CAPM):value premium:momentum:size premium:This papers structure82DisagreementIn the section, we focus on a one-period
7、world where all assumptions of CAPM hold except complete agreement. suppose there are two types of investors: group A: the informed group D: the misinformed92.1The CAPM portfolio T: The informed investors in group A choose the true tangency portfolioportfolio D: The aggregate of the risky portfolios
8、 of the misinformedportfolio M: the value-weight market portfolio of risky assets10x: the proportion of the total market value of risky assets owned by informed investors.n: the number of risky assetsAnd and are the weights of asset j in portfolios M, T, and D, then the market-clearing condition is
9、or 11Let : the expected value of the return on T : standard deviation of the return on T :is the risk-free ratethen the Sharpe ratio: Group D investors are misinformed, so portfolio D is not typically the true tangency portfolio, and the Sharpe ratio is less than . 1213Since the market portfolio M i
10、s a positively weighted portfolio of T and D, M is between T and D on the hyperbola linking them, and SM is between SD and ST.Eq. (1) implies that T is M only if D is also M. In other words, the CAPM holds only if misinformed investors as a group hold the market portfolio.142.2 A more general perspe
11、ctive The market must clear, so the informed tend to offset the price effects of the misinformed. But when investors are risk averse, the offset is only partial and some of the price effects of erroneous beliefs typically remain.(how disagreement can affect prices)Stated this way, our argument is a
12、market equilibrium version of the limits of arbitrage15The equilibrium perspective also produces fresh insights. For example, Our analysis implies, however, that the price effects of erroneous beliefs do not disappear in time unless the beliefs of the misinformed about todays news converge to the be
13、liefs of the informed.162.3. Empirical implicationsIn principle, one can measure the extent to which prices are irrational: ST -SM, is an overall measure of the effect of misinformed beliefs on asset prices. An obvious problem is that we do not know the composition of portfolio T.(cant use MVE, With
14、out complete agreement, the assumptions of the CAPM do not suffice to identify T)17In short, complete agreement is a necessary ingredient of testable asset pricing models unless we are willing to specify the nature of the beliefs of the misinformed and exactly how they affect portfolio choices and p
15、rices18The two methods to measure the deviations from the CAPM pricing.(1) If disagreement is the only potential violation of CAPM assumptions, however, we can use the GRS test to infer whether disagreement indeed affects asset prices.(2) Jensens (1968) alpha is another measure of deviations from CA
16、PM pricing. where is the slope in the regression of on , and is the intercept.19Unless the misinformed happen to hold the true tangency portfolio T, so T, M, and D coincide, Jensens alpha for T is positive: To see this20from (4): we have 21 is the intercept ofSo Since (2) implies that because , 222.
17、4. Active management1 Active management when active managers have better information, they are among the informed who partially offset the actions of the misinformed and so make asset prices more rational. Except in the special case where misinformed investors hold the market portfolio, market effic
18、iency is reduced when informed investors switch to a passive market portfolio strategy.232 Jensens alpha Carhart (1997) is puzzled by his evidence that there are mutual fund managers who generate reliably negative estimates of Jensens alpha before fees and expenses. In our model, if the misinformed
19、do not in aggregate hold the market portfolio, their beliefs affect prices, and the result is negative alphas.(solve the puzzle)243 transaction costs Since costs impede both the misinformed, who distort prices, and the informed, who counter the distortions, their net effect on market efficiency is a
20、mbiguous.254 short selling short selling effect on market efficiency is ambiguous. Because, In our model, this is true when all short-selling is by informed investors. But it can be false when short-sale constraints limit the trades of misinformed investors.262.5. ExamplesExample 1 Daniel, Hirshleif
21、er, and Subrahmanyam (1998) : The misinformed buy too little of the assets with positive news and too much of the assets with negative news. Since all assets must be held, asset prices induce informed investors to hold the complement of the portfolio of the misinformed.27 This complement is the tang
22、ency portfolio T, but it is not the market portfolio M, so we do not get CAPM pricing.28Example 2Investors do not understand that profitability is mean-reverting. misinformed investors underweight informed investors overweight The portfolio of the informed is the true tangency portfolio, but it is n
23、ot the market portfolio, so we do not get CAPM pricing.293 whether lead to ICAPM the misinformed over-extrapolate the past fortunes of growth and value stocks, does asset pricing move away from the CAPM to a multifactor version ICAPM? Generally, the answer is no. 30In an ICAPM, the market portfolio
24、is multifactor efficient. Since the portfolio choices of the misinformed are based on incorrect beliefs, they are unlikely to produce price effects that put the market portfolio on the multifactor-efficient frontier implied by all currently knowable information.31There is a situation where overreact
25、ion and other behavioral biases can lead to an ICAPM, but one with irrational pricing. This happens when the biases produce expected return effects that are proportional to covariances of asset payoffs with state variables or common factors in returns.323. Tastes for assetsWe provide a simple analys
26、is of how tastes for assets as consumption goods can affect asset prices. We consider two cases:333.1. Tastes for assets do not depend on returns group A: evaluate assets based solely on dollar payoffs and thus the access to overall consumption they provide Group D : investors do have such tastes: t
27、hey get direct utility from their holdings of some assets, above and beyond the utility from general consumption that the payoffs on the assets provide.34Investors have tastes misinformedInvestors havent tastes informedSo we can express:Next is the same as disagreement.35There is one important respe
28、ct in which price effects induced by tastes can differ from those due to disagreement.Tastes are exogenous, and there is no economic logic that say stastes for assets as consumption goods eventually disappear. But economic logic does suggest that the price effects of disagreement are temporary.363.2
29、. Tastes for assets depend on their returnsIf investor utility depends directly on the amounts invested in specific assets, asset prices do not conform to the CAPM. And prices are unlikely to conform to Mertons (1973) ICAPM.ICAPM utility- tastes utility-37.As a logical possibility, however, ICAPM pr
30、icing can also arise because some state variables or common factors in returns affect investor utility solely as a matter of tastes.For example, Fama and French (1993) argue that the value premium is explained by a multifactor version of Mertons (1973) ICAPM that includes a value-growth return facto
31、r.(But this leaves an open issue.)384. CalibrationsDo misinformed investors have a big impact on asset prices, or are small price changes enough to induce informed investors to counter the demands of the misinformed? We use two sets of calibrations to explore this issue:391. The first examines in ge
32、neral terms how expected returns move away from the CAPM with variation in (i) the parameters of the joint distribution of the payoffs on the assets favored and disfavored by the misinformed. (ii) the amount of under- and overweighting of the two asset groups imposed on the informed402. The second s
33、et of calibrations we get more specific and use observed small and big stock returns, value and growth stock returns, and high and low momentum returns to explore how these three prominent CAPM anomalies distort the tangency portfolio of informed investors.414.1. Expected returns and misinformed bel
34、iefs: general factorsThe first set of calibrations studies the factors that determine whether the price effects of misinformed beliefs are large or small. Since the setup and calculations are tedious and the findings are not controversial, we leave the details to the Appendix42Some results1. The dis
35、tortions of the tangency portfolio held by the informed in turn depend on their share of invested wealth and the extent to which the aggregate portfolio of the misinformed deviates from the market portfolio.432. The calibrations also say that when the distortions of portfolio holdings are limited to
36、 risky assets, the price effects of erroneous beliefs are larger with lower correlations between the payoffs on risky assets over- and underweighted by misinformed investors.44We can give life to this correlation result in the context of the value and momentum anomalies of the CAPM.453. The final re
37、sult from the calibrations in the Appendix is that misinformed investors have less price impact when their bad information is limited to assets that are a small part of the market, so their tilt away from the market portfolio requires small adjustments by informed investors.464.2. Size, value, and m
38、omentum We now study more specifically what the observed returns associated with three prominent CAPM anomalies (size, value, and momentum) imply about the tangency portfolio of informed investors. We interpret the results as potential evidence on the wealth held by investors who are informed about
39、the behavioral biases that might give rise to the anomalies.471).Size premiumL: big stock portfolio-stocks accounting for 90% of aggregate market cap.(Low expected return)H:small stock portfolio-The stocks accounting for the remaining 10% of market cap48If we ignore measurement error and treat the s
40、ample means, standard deviations, and correlation as true parameters, we can infer how much informed investors must overweight small stocks and underweight big stocks to accommodate the demands of misinformed investors.(get )Process and result:49For we have Solving (8) for wH yields 50Table 151 meas
41、urement errorSince the estimates have measurement error, it interesting to ask how sensitive the tangency portfolios are to changes in the inputs. Since estimates of expected return are much less precise than estimates of portfolio betas, we focus on the impact of errors in estimates of E(RH) and E(
42、RL).525. ConclusionsOur calibrations to identify the general factors that determine the price effects of erroneous beliefs or tastes for assets as consumption goods say that distortions of expected returns can be large when misinformed investors or investors with asset tastes:53 (i) account for subs
43、tantial invested wealth;(ii) are misinformed about or have tastes for a wide range of assets; (iii) take positions much different from those of the market portfolio;(iv) underweight assets whose returns are not highly correlated with the returns on theassets they overweight.54Our analysis produces o
44、ther interesting insights. Some examples are: (P683)55Some insights about the anomalies(1) the value premium implies a somewhat more extreme tangency portfolio and more extreme distortions of expected returns than the size effect, and the tangency portfolio produced by momentum returns is by far the
45、 most extreme.56(2) The correlations between the High and Low portfolio returns of the three CAPM anomalies are similar, from 0.86 to 0.89, so the correlations are not a major source of the differences in price effects57two potentially complementary possibilities.(1) the relative wealth controlled b
46、y informed investors may be different for the three anomalies.58(2) The second possibility is that the differences in the price effects associated with the three CAPM anomalies are to some extent due to differences in the way they distort the portfolio positions of the misinformed.59Appendix. Calibr
47、ationsTo explore the price effects of misinformed investors, we compare two equilibria.(1) The first is a standard CAPM(2) In the second equilibrium, misinformed investors hold something other than the market portfolio, and asset prices must induce informed investors to hold its complement60Symbols:
48、 portfolio H: The risky assets underweighted by the misinformedportfolio L: The risky assets overweighted by the misinformedRF: the risk-free rateST : the Sharpe ratio for the tangencyPortfolio 61In the first equilibriumH and L satisfy the standard CAPM pricing relation, from the CAPM:62In the secon
49、d equilibrium :The misinformed then sell units of H :The misinformed then sell units of LletthenThe informed own units of H, units of L63 : the market-clearing prices per unit of H : the market-clearing prices per unit of L So and64Let PH and PL denote the dollar payoffs on portfolios H and L at the
50、 end of the period, with expected values E(PH) and E(PL), standard deviations and , and correlation . so and 65From E.q. A.3 and 66So Solving (A.4) for Similar we can get67From (A.5) (A.6)，we can get Fig. A168Two patterns are clear in Fig. A1. :(1) the price effects of erroneous beliefs are larger with lower correlation between the payoffs on H and L.(2) the relation between expected returns and the amount of over- and underweighting forced on informed investors69
